ABSTRACT
Title of Thesis: IMPROVING NON-CONTACT TONOMETRY:
A DEEP NEURAL NETWORK BASED METHOD
FOR CORNEAL DEFORMATION MAPPING
Moshe Ackman, Lauren Cho, Kun Do, Aaron Green
Sam Klueter, Eliana Krakovsky, Jonathan Lin
Ross Locraft, James Muessig, Hongyi Wu
Glaucoma, a disease characterized by increased intraocular pressure (IOP), is
one of the leading causes of preventable blindness worldwide. Accurate measure-
ment of IOP is essential in monitoring glaucomatous progression in order to deliver
treatment and prevent long-term vision loss. Currently, non-contact tonometry,
known as an ?air-puff test?, is a common diagnostic method despite its inaccessibil-
ity, discomfort, high cost, and reliance on a trained professional. To improve upon
these shortcomings, we designed a cheaper tonometer integrating a novel depth-
mapping neural network with a custom air-puff generation system. We deformed
porcine corneas with a controlled-intensity air-puff while imaging the deformation
with a single stationary camera?a contrast to the standard Scheimpflug method.
From the footage, our neural network predicted a three-dimensional map of corneal
deformations. The network was able to predict a general negative trend between the
IOP and the corneal deformation extracted. We compared our results to accepted
literature deformation values and ground truth footage, allowing us to determine
that the deformation amplitudes were physically plausible. With a more robust
imaging setup, we present a promising alternative to traditional IOP measurement
methods. Future studies should make the simulated footage more representative
of clinical conditions to increase the generalizability of the neural network. Addi-
tionally, anatomical differences between porcine and human eyes as well as corneal
variability due to socio-demographic differences must be addressed for our results
to be applied to clinical settings.
IMPROVING NON-CONTACT TONOMETRY:
A DEEP NEURAL NETWORK BASED METHOD
FOR CORNEAL DEFORMATION MAPPING
TEAM CONTACT
Authors:
Moshe Ackman, Lauren Cho, Kun Do, Aaron Green
Sam Kleuter, Eliana Krakovsky, Jonathan Lin
Ross Locraft, James Muessig, Hongyi Wu
Mentor: Giuliano Scarcelli
Thesis submitted in partial fulfillment of the requirements of the
Gemstone Honors Program, University of Maryland, 2021
Discussion Committee:
Associate Professor Giuliano Scarcelli, Chair/Advisor
Assistant Professor Amal Isaiah
Professor Peter Kofinas
Professor Yang Tao
?c Copyright by
Team CONTACT
Moshe Ackman, Lauren Cho, Kun Do, Aaron Green
Sam Klueter, Eliana Krakovsky, Jonathan Lin
Ross Locraft, James Muessig, Hongyi Wu
2021
Acknowledgments
We would like to thank our mentor, Dr. Scarcelli, for his guidance in our
project; the graduate students in his lab, particularly Raymundo, for training us in
lab skills and protocol; our librarian, Ms. Rachel Gammons, for helping us pursue
and present research; and the Gemstone staff and faculty?Dr. Frank Coale, Dr.
David Lovell, Dr. Kristan Skendall, Dr. Leah Kreimer Tobin, Dr. Vickie Hill, and
Jessica Lee?for supporting our research endeavors.
ii
Table of Contents
Acknowledgements ii
Table of Contents iii
List of Figures v
List of Abbreviations vii
Chapter 1: Introduction 1
Chapter 2: Literature Review 5
2.1 Biomechanical Properties of the Cornea . . . . . . . . . . . . . . . . . 5
2.2 Contact Tonometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.1 Goldmann Applanation Tonometer . . . . . . . . . . . . . . . 10
2.2.2 Contact Lens Sensors . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.3 Non-Contact Tonometry . . . . . . . . . . . . . . . . . . . . . 17
2.2.4 Imaging Modalities in Ophthalmology . . . . . . . . . . . . . . 19
2.2.5 Computer Vision and Ophthalmology . . . . . . . . . . . . . . 24
2.2.6 Convolutional Neural Networks . . . . . . . . . . . . . . . . . 27
2.2.7 Clinical Considerations and Caveats . . . . . . . . . . . . . . . 35
Chapter 3: Methodology 37
3.1 Applanation System . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.1.1 Mechanical Design . . . . . . . . . . . . . . . . . . . . . . . . 39
3.1.2 Electrical Design . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.1.3 Eye Mounting . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.2 Imaging System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.2.1 Imaging Equipment . . . . . . . . . . . . . . . . . . . . . . . . 44
3.2.2 Pattern Projector . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.2.3 Choice of Projection Template . . . . . . . . . . . . . . . . . . 45
3.2.4 Calibration Procedure . . . . . . . . . . . . . . . . . . . . . . 46
3.3 Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.4 Data Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.4.1 Rendering Procedure . . . . . . . . . . . . . . . . . . . . . . . 48
3.4.2 Physical Accuracy of Rendering. . . . . . . . . . . . . . . . . . 50
3.5 Image Processing and Algorithms . . . . . . . . . . . . . . . . . . . . 51
3.5.1 Autoencoder Checkerboard Extraction (?CheckMark?) . . . . 52
iii
3.5.2 2D Surfaces With Convolutional Neural Network (?DeepSquish?) 55
3.5.3 Extracting Displacement from Ground Truth . . . . . . . . . . 60
Chapter 4: Results 65
4.1 Simulated Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.1.1 CheckMark . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.1.2 DeepSquish . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.2 Real Footage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.2.1 Ground Truth . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.2.2 Comparison with Network Prediction . . . . . . . . . . . . . . 72
Chapter 5: Discussion and Conclusion 76
5.1 Meaning and Significance of Results . . . . . . . . . . . . . . . . . . . 76
5.1.1 Simulated Results . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.1.2 Real Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.2 Comparison to Existing Works . . . . . . . . . . . . . . . . . . . . . . 79
5.3 Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.3.1 Puff Generation . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.3.2 Robust Modeling . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
Appendix A:Racial Equity Impact Analysis 90
A.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
A.1.1 Identifying Stakeholders . . . . . . . . . . . . . . . . . . . . . 91
A.1.2 Engaging Stakeholders . . . . . . . . . . . . . . . . . . . . . . 99
A.1.3 Examining the Causes . . . . . . . . . . . . . . . . . . . . . . 100
A.2 Our Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
A.2.1 Clarifying The Purpose . . . . . . . . . . . . . . . . . . . . . . 101
A.2.2 Considering Adverse Impacts . . . . . . . . . . . . . . . . . . 102
A.2.3 Advancing Equitable Impacts . . . . . . . . . . . . . . . . . . 103
A.2.4 Examining Alternatives or Improvements . . . . . . . . . . . 106
Appendix B:Relevant Code and Repositories 108
Appendix C:Modeling Process 109
C.1 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
C.2 Lighting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
C.3 Deformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
C.4 Simulated Movement and Parameters . . . . . . . . . . . . . . . . . . 110
Bibliography 111
iv
List of Figures
2.1 Operation of the Ocular Response Analyzer [1] . . . . . . . . . . . . . 6
2.2 A cross section of the human cornea with labeled layers and compo-
nents [2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 A patient getting their eye measured using the GAT [3]. . . . . . . . 10
2.4 Schematic of the corneal deformation by contact from the GAT with
influencing factors such as bending resistance of the cornea and sur-
face tension from liquid tear drops depicted [3]. . . . . . . . . . . . . 11
2.5 SENSIMED Triggerfish CLS in the eye, and components [4]. . . . . . 12
2.6 Schematic of a GWF bonded to a contact lens [5]. . . . . . . . . . . . 14
2.7 The tonometer in use [6]. . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.8 Schematics for the various methods for the applanation of the eye for
corneal IOP measurements are shown. The workings of a rebound
tonometer is shown in (A), of the GAT in (B), and the non-contact
air puff tonometer in (C). From [7]. . . . . . . . . . . . . . . . . . . . 17
2.9 The OCULUS Corvis STL is a non-contact air-puff tonometer with
a high-speed Scheimpflug camera [7]. . . . . . . . . . . . . . . . . . . 18
2.10 A patient being evaluated with the Placido topographer [8]. . . . . . 20
2.11 An example of a scene and its corresponding depth map. This depth
map was creating using an algorithm for monocular depth estimation,
AdaBins [9]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.12 An example of a multilayer perceptron with hidden layers. Note that
layers comprising multiple neurons allow for vector outputs [10]. . . . 29
2.13 Sample application of the Sobel convolution kernel on an image. Orig-
inal image is on left, convolved result is on right. . . . . . . . . . . . . 31
2.14 An example of a CNN used to classify images, VGG16. Note the
stacked convolution maps, ?pyramid? structure, and high number of
feature maps [11]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.15 High-level structure of an autoencoder used for denoising handwritten
digits [12]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.1 A photo (top) and schematic (bottom) of our experimental setup. . . 38
3.2 A schematic diagram of the electronic system. . . . . . . . . . . . . . 42
3.3 Deformation (left) with accompanying ground truth (right). . . . . . 44
3.4 Calibration plate pattern sample photograph, and suggested position
of calibration plate relative to Barron chamber(right). . . . . . . . . . 46
v
3.5 A simulated cornea with projected pattern (left) and corresponding
calibration plate (right). Simulated topography is complex to encour-
age model robustness. . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.6 Our process for IOP extraction from footage of an illuminated appla-
nation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.7 Real sample image of projected checkerboard on eye. . . . . . . . . . 52
3.8 Samples from the dataset used to train ?CheckMark?. Simulated
projection (left) and ground truth (right). . . . . . . . . . . . . . . . 52
3.9 The MA-Net architecture [13]. . . . . . . . . . . . . . . . . . . . . . . 53
3.10 Sample augmented images in the train set. . . . . . . . . . . . . . . . 59
3.11 A. The output of the ground truth Basler camera and B. the same
image with the Gaussian filter and binarization applied. . . . . . . . . 61
3.12 Visualization of our analysis process on sample frames.The orange
curve shows the edge at t! = 0, while the blue curve shows the edge
at a non-zero time. The Chamfer distance is taken between the orange
and blue contour at every frame. . . . . . . . . . . . . . . . . . . . . 62
3.13 Example plot of the magnitude of displacement for some time t > t0 . 63
3.14 Corneal Response for IOP 10 (cm) H2O. . . . . . . . . . . . . . . . . 64
4.1 Sample performance from CheckMark. Input image is on left, pre-
dicted ?clean? pattern is on right. . . . . . . . . . . . . . . . . . . . . 65
4.2 Training (red) and test performance (blue) for CheckMark. . . . . . . 66
4.3 Sample performance from DeepSquish. Predicted meshes are in front,
ground truth meshes are in back. . . . . . . . . . . . . . . . . . . . . 67
4.4 Training (blue) and test performance (orange) for DeepSquish (left).
Relevant performance metrics (right). . . . . . . . . . . . . . . . . . . 67
4.5 Localization heatmap generated using the Grad-CAM method for our
model. Note the focus on the pattern and distance from cornea edge. 68
4.6 An image from the ground truth view showing a ruler for calibration.
Each tick mark represents one millimeter, with each pixel being equal
to 16.56 micrometers. . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.7 Example plot of predicted deformation over time. . . . . . . . . . . . 69
4.8 The maximum deformation for each puff versus IOP for all trials
(top), and trials one through three (bottom) . . . . . . . . . . . . . . 71
4.9 An example of a deformation map generated from our real footage. . 72
4.10 Example plot of predicted deformation over time. . . . . . . . . . . . 72
4.11 Example plot of predicted deformation over time. . . . . . . . . . . . 73
4.12 Model correlation for each trial. . . . . . . . . . . . . . . . . . . . . . 73
4.13 Combined predicted datapoints from all trials. . . . . . . . . . . . . . 75
vi
List of Abbreviations
BCE Binary-Cross Entropy
CAE Convolutional Autoencoder
CCT Central Corneal Thickness
CLS Contact Lens Sensor
CNN Convolutional Neural Network
CST Corneal Visualization Scheimpflug Tonometry
GAT Goldmann Applanation Tonometer
GWF Graphene Woven Fabric
IOP Intraocular Pressure
OAG Open Angle Glaucoma
POAG Primary Open Angle Glaucoma
RNFL Retinal Nerve Fiber Layer
SD-OCT Spectral-Domain Optical Coherence Tomography
SES Socioeconomic Status
ST Scheimpflug Tonometry
vii
Chapter 1: Introduction
Glaucoma is a chronic disease characterized by increased pressure within the
eye and is the second leading cause of preventable blindness worldwide [14]. If di-
agnosed early, there exist treatments to slow the progression of glaucoma or lower
the risk of developing it entirely, such as medication or surgery [15]. These treat-
ments often involve consistent monitoring of intraocular pressure (IOP) as a way of
tracking progression of the disease. Tonometers, devices that measure IOP, are tra-
ditionally only used in specialized healthcare settings. As a result, and despite the
plethora of existing tonometer technologies, many people do not sufficiently monitor
their glaucomatous progression nor take medication at a recommended frequency
due to the prevalence of noncompliance among patients, especially of lower health
literacy and education levels. It has been shown that there exist differences in the
rate of glaucoma treatment compliance between socio-demographic groups in the
United States. One factor that causes this discrepancy is inaccessibility to measure-
ment devices [16] [17]. A health care provider requires special training to perform
the examination, meaning that optometrists are often geographically distant from
the communities that need the most help.
Many studies show that communities of color are disproportionately affected
1
by glaucoma in both prevalence and lack of treatment. One study by the Baltimore
Eye Research Group found that socioeconomic status (SES) was a significant factor
in determining an individual?s risk to developing glaucoma, and recent efforts dis-
tinguish prevalence of glaucoma between ethnic groups and communities with more
granularity [16, 17]. In addition, studies show that type of insurance impacts the
quality of glaucoma treatment, with Medicaid recipients 234% more likely not to
receive any glaucoma testing within the first 15 months after diagnosis [18]. Be-
cause Medicaid often provides healthcare for those who are unable to access private
insurance, disparities exist in treatment between communities of various SES. We
sought to address this issue by developing a streamlined measurement tool that can
be operated in small, general-practice clinics rather than requiring a system only
found in specialized care facilities, with the goal of increasing the frequency of IOP
examinations for the communities served by those clinics.
These differences in treatment are not exclusive to Medicaid or race, but
are pervasive throughout the population and intricately related to many socio-
demographic and institutional factors and barriers. Access to treatment and knowl-
edge as well as immigration status, incarceration status, or any language barriers
play a large impact on overall result of the disease, and it is crucial to understand
the place of research and experimentation in light of these real issues. This contex-
tualization is elaborated in our Racial Equity Impact Analysis in Appendix A, while
the majority of the rest of this paper focuses on the technical aspects and outcomes
of our experiment.
Current diagnostic tools can be broadly categorized into contact and non-
2
contact tonometry. Contact tonometry, such as Goldmann Applanation Tonometry
(GAT), requires the measurement device to make physical contact with the eye
because the IOP is calculated from direct pressure measurements in this approach.
Non-contact tonometry most commonly uses a puff of air to deform the cornea and
measures the IOP from the biomechanical response. One limitation of the current
standard tonometry techniques is that they only provide a measurement at a single
moment, although IOP is known to fluctuate throughout the day [19]. This IOP
fluctuation can be significant and is unique to each person, so many physicians
recommend measuring IOP at certain times of the day, or at the same time of day
for each measurement [20].
To ensure patients are regularly evaluated, so that any glaucomatic eye con-
ditions can be detected early, a new diagnostic method will be proposed that will
balance several considerations. First, the measurement must be precise and mean-
ingful. In other terms, the result must be accurate enough to determine whether an
individual is at elevated risk of developing glaucoma, with repeatability to add to
the confidence in the diagnosis. Next, the devices must be inexpensive enough to
be distributed in an accessible and equitable manner such that a broad population
would be able to utilize it regularly. Third, the devices must be streamlined enough
to be used with minimal training, making them more accessible to all populations.
Altogether, these three goals lead us to our guiding research question.
3
Research Question
How can we leverage modern machine learning techniques to streamline
and lower the cost of non-contact tonometry methods while
maintaining precision and accuracy?
To answer our question, we developed a two-part system. The first part is the
deformation and imaging of a cornea, and the second part is the analysis of those
images. For our experiments, we used porcine eyes collected biweekly from a local
butcher.
To deform the cornea, we deliver an air puff over a controlled time period
similar to that of existing non-contact tonometers. We then record the cornea with
a high frame rate camera while it is being deformed and collect a series of images.
The images are cleaned and processed by two neural networks that output a three-
dimensional corneal deformation map from the single view. By utilizing a neural
network in connection with a camera, we can overcome the need for multiple or
moving cameras in precise alignment, a limitation of current imaging techniques.
We will begin with a review of existing research on glaucoma monitoring and
corneal imaging techniques, followed by a description of our methodology and ex-
perimental protocol. We then will analyze our experimental results and discuss the
significance of our findings. Finally, we will examine the limitations of our study
and explore future directions and applications for this research.
4
Chapter 2: Literature Review
Since the invention of the ophthalmoscope in 1850 by von Helmholtz and the
invention of the Maklakoff applanation tonometer in the late nineteenth century, IOP
has been known to vary between people. However, the first significant advancement
towards glaucoma detection did not occur until 1950, with the creation of the GAT.
Since then, advances in engineering and medicine have greatly improved glaucoma
detection, which continues to spur on further research [21].
In the following sections, we describe notable advances and variations in tonom-
etry. We divide existing tonometers into two classes: contact and non-contact
tonometers. We discuss several variants of contact tonometers. Given the relative
novelty of non-contact tonometry, we review the methods used to retrieve corneal
movement without contacting the surface of the eye, which often rely on novel com-
puter vision algorithms and other image processing techniques. Finally, we discuss
clinical considerations and caveats in the measurement and monitoring of IOP.
2.1 Biomechanical Properties of the Cornea
Several biomechanical properties of the cornea have a significant effect on the
diagnosis of glaucoma. Studies have found that the three most important properties
5
are the intraocular pressure (IOP), corneal hysteresis, and central corneal thickness
(CCT). Corneal hysteresis is a measure of the viscoelastic damping effect of the
cornea [22]. A study by Medeiros et al. (2013) found that higher corneal hysteresis
and lower IOP resulted in a lower rate of visual field loss over time. Mangouritsas
et al. (2009) found that in patients with primary open-angle glaucoma, CCT had
more of an effect on corneal hysteresis than in non-glaucomatous patients [23].
Corneal hysteresis is measured by an Ocular Response Analyzer. The oper-
ation of this device can be seen in Figure 2.1. Similar to non-contact tonometers,
the Ocular Response Analyzer delivers a metered air puff to the eye over a period
of roughly 20 ms. During the puff, the air pressure is gradually increased until
the cornea is fully deformed, and then the air pressure is decreased. As the cornea
deforms, it passes through two applanation points: once as the cornea deforms to
concavity, and once more as it returns to its normal position. At these points, the
reflected light is maximized. The Ocular Response Analyzer measures the peaks of
the reflected light and records the air pressure at these points. The difference in
pressure represents the corneal hysteresis.
Figure 2.1: Operation of the Ocular Response Analyzer [1]
6
The gold standard for CCT measurement utilizes ultrasound pachymetry. It
is important to know a patient?s CCT when diagnosing glaucoma, as an abnormal
CCT may affect the accuracy of a tonometry reading [24]. A study by Sadoughi et al.
(2015) compared the precision of CCT measurements from ultrasound pachymetry
and the Orbscan II, which utilizes scanning-slit topography. The study found that
the two methods had good agreement for normal eyes (approximately 501-570 mi-
crons thick), but the Orbscan II tended to overestimate the CCT more than ultra-
sound pachymetry, and the discrepancy was even greater in thinner corneas. Fur-
thermore, several studies have reported that a thinner CCT leads to underestimation
of IOP measurement and has been identified as a good predictor of glaucomatous
progression. It is unclear, however, if the increased risk of glaucoma is primarily due
to greater IOP measurement error or if it is due to biomechanical differences [25].
When attempting to characterize these biomechanical properties, there are
several confounding physiological factors that affect how they are assessed in both
clinical and laboratory settings [26]. The stroma, which comprises over 90% of the
cornea?s thickness, is made up of a complex intertwining network of collagen fiber
that provides structural support by inserting into an anterior membrane called the
Bowman?s layer [27]. These collagen structures vary substantially throughout the
cornea. For example, the collagen across the central cornea in the mid to posterior
stroma run in two orthogonal directions along the nasal-temporal and superior-
inferior and provide high tensile strength to resist large ocular deformation and
forces imposed during blinking [28]. The collagen in the peripheral cornea forms a
circumferential arrangement and demonstrates higher circumferential strength, pro-
7
viding stability to the curvature of the central cornea and absorbing small changes
in IOP [29]. Collagen crimp, a term used to describe the waviness of collagen fibers
under tension, is also thought to contribute significantly to absorbing fluctuations
in IOP [30]. While regional variability in collagen crimp has not been explored in
detail, initial studies found that the limbus and peripheral cornea show higher wavi-
ness, tortuosity, and amplitude than the central cornea [31]. Like other biological
tissue, the cornea is viscoelastic and hence exhibits hysteresis and creep during de-
formation [32]. In addition to its complex collagen orientation and structure, the
cornea responds differently to different modes of corneal strain, demonstrating non-
linear, hyperelastic stiffness behavior over a range of IOP [33]. Studies also suggest
that age affects corneal stiffness, approximately doubling it from age 20 to 100 [34].
Figure 2.2: A cross section of the human cornea with labeled layers and components
[2]
Studies have shown that the corneal endothelium is responsible for regulating
corneal hydration to maintain high corneal transparency in fluctuating physiological
environments [35]. There is significant variability in the hydration of the cornea
8
both in vivo and in experiments performed with corneas ex vivo. Corneas that are
analyzed ex vivo are unable to maintain physiological hydration levels, leading to
loss of function in the endothelial pump and subsequent swelling [36]. Corneas in
vivo also have variable hydration levels, with water content varying by 7.2% on
average in healthy subjects throughout the day [37]. Factors including humidity,
contact lens usage, and age all influence corneal hydration [38?40].
While important for properly diagnosing ocular diseases and facilitating effec-
tive, patient-specific treatment, quantification of corneal biomechanical properties
poses a complicated challenge. Thus it is important to reconcile the laboratory tech-
niques used ex vivo, the factors evidenced above that influence corneal variability,
and the genetic and ethnic variability between patients when developing a reliable
clinical method.
9
2.2 Contact Tonometry
2.2.1 Goldmann Applanation Tonometer
Figure 2.3: A patient getting their eye measured using the GAT [3].
The GAT quickly gained wide acceptance and became the ?Gold Standard?
for IOP measurements [21]. Typically, applanation tonometry requires both a small
instrument and an ophthalmologist to support the eyelids of the patient [3]. In
Figure 2.3, a patient?s IOP is measured using the GAT.
The GAT measures the force required to applanate a given surface area of
the cornea. When the bending resistance becomes equal to the surface tension,
the applanation pressure is recorded and considered equal to the IOP based on the
Imbert-Fick Law, expressed as
W
P = (2.1)
A
and shown visually in Figure 2.4.
10
Figure 2.4: Schematic of the corneal deformation by contact from the GAT with
influencing factors such as bending resistance of the cornea and surface tension from
liquid tear drops depicted [3].
When a sufficient pressure is applied, the cornea will applanate, meaning the
concavity of the cornea will flatten. It is only under this assumption that the Imbert-
Fick law can be applied and (2.1) is used; otherwise, the effect of corneal thickness
is no longer negligible so (2.1) is invalid. The pressure required to applanate the
cornea is measured to determine the IOP [41].
Although robust, there is a risk of contamination from contact with the prism
tip [42]. GAT has also been generally shown to significantly underestimate intra-
cameral IOP, otherwise known as the IOP within the anterior chamber of the eye
since there is a complex biomechanical response when the corneal surface is ap-
planated [43].
Other drawbacks to GAT include the reliance on professionally trained opera-
tors. This means that IOP is almost never measured at night, when many researchers
claim the IOP can be at its maximum. Additionally, only 2D cross-sectional im-
ages of the fluctuating IOP can be obtained. GAT is also complicated because it
requires the administration of a topical anesthetic agent and sodium fluorescein on
the corneal surface to prevent movement of the eye during measurement. Even if
11
the method was used at night, sleep would be interrupted as GAT requires a specific
head posture to determine the IOP of an individual [44].
Therefore, although GAT still remains the ?gold standard? and foundation of
tonometry, further directions of tonometry will need to be explored to mitigate the
shortcomings of GAT such as lack of comfort, lack of portability, required exper-
tise reliance, invasiveness, and measurement of a single-isolated value rather than
continuous IOP monitoring.
2.2.2 Contact Lens Sensors
Figure 2.5: SENSIMED Triggerfish CLS in the eye, and components [4].
Not all newer methods for measuring IOP utilize non-contact tonometry. Con-
tact lens sensors (CLS) represent a promising, less invasive technology to measure
IOP, and often use piezoelectric, transparent, flexible sensor materials.
CLS methods were first approved in 2009 when the European Regulatory Au-
thorities approved Triggerfish from SENSIMED, which was later approved by the
United States Food and Drug Administration in 2016. Triggerfish is a disposable
silicone contact lens with an embedded electromechanical sensor that can detect
changes in the curvature of the cornea due to IOP variations, and is shown in Fig-
ure 2.5 [44].
12
The main problem that the Triggerfish CLS sought to address is the lack of
continuous monitoring of IOP, as IOP can fluctuate widely over a day due to dif-
ferences and variations in circadian rhythms, physiological postural changes, and
blood pressure variations. Hence, the Triggerfish CLS has a 24-hour sensing mech-
anism to detect the fluctuations in IOP throughout the course of the day. CLS are
promising because they can detect specific changes in the IOP through the course of
time worn, when used in conjunction with software algorithms such as the B-spline
smoothing transform or the Triggerfish software with an incorporated cosinor-based
function. However, obtaining relevant biomechanical parameters is difficult, and is
the main limitation for the practicability of this smoothing transform method [44].
In continuation, although Triggerfish CLS is a promising technique, it has
several limitations. It is worn on the eye, so users may experience conjunctival
hyperemia, which is an inflammation of the eye due to excess blood buildup in
vessels, that causes vision obstruction, ocular pain, transient myopia and/or blurred
vision. The major problem with CLS is that it not only causes these discomforts
from long-term use, but can also alter IOP measurements. A study by Miki et
al. in 2020 found that after 24 hours of wearing the CLS, participants? central
cornea became steeper whilst the mid-peripheral cornea became flatter. The myopic
spherical equivalent also increased by approximately 1 diopter [45]. Tojo et al.
in 2019 discovered the corneal thickness increased and the corneal curvature was
altered, which can impact IOP measurements, meaning that this method is limited
in terms of accuracy [46]. Therefore, the Triggerfish CLS needs to be improved for
larger practicability.
13
Figure 2.6: Schematic of a GWF bonded to a contact lens [5].
More recently, the integration of a graphene-woven fabric (GWF) into a con-
tact lens has crated a high resolution, non-invasive tonometer that provides contin-
uous monitoring [5]. GWFs are used in many other nano-optics and nano-electronic
applications such as catalyst carriers, heat insulation materials, and radiation-
resistant coatings. GWFs are electrically conductive, transparent, easy to handle,
and have low fabrication costs, which are all valuable properties for this class of
flexible photo-voltaic and composite materials [47].
The GWF is a graphene mesh tightly mounted on the cornea by homogeneous
hydrophilicity that is very sensitive to changes in strain. When the IOP increases,
the GWF stretches and creates micro-tears, increasing the electrical resistance of
the material, or decreasing the current at a constant applied voltage by Ohm?s law.
The opposite also holds true, when the IOP decreases, the current will increase.
The fluctuation in electrical current can be monitored by the device, and measure
the effective change in IOP. The working principle of the GWF IOP measurement
can be seen in Figure 2.6 [5].
This device has a device resistance change resolution of 6.8% per in the vari-
14
ation range of 0-10 . Previous contact lens tonometers have suffered from high
production costs, but this sensor requires fewer components and is much cheaper.
Finally, the GWF is roughly 80% transparent, so blocking light is of little concern [5].
Thus, the GWF CLS shows great promise in disadvantaged communities or coun-
tries, owing to its potential as a low-power, low-cost, high-resolution, disposable
option.
However, the greatest limitation of this method is that it has to be calibrated
before every use, and requires the aid of GAT for a baseline. This dependence
on GAT means that GWFs are promising as a secondary method to detect IOP
but cannot be reliable and stable as a standalone method. Also, factors such as
corneal thickness and Young?s modulus can vary between individuals, explaining
why this method is better suited to determine IOP fluctuations per individual in a
given environmental condition such as constant temperature. However, when the
GWF is applied to different individuals, because the contact lenses and the piece of
equipment varies, the requirement of the calibration makes the GWF not as robust
as other methods, such as the ?gold standard?, GAT [5].
In conclusion, CLS methods are very promising as breakthroughs in electronics
and micro-fabrication technology occur. The biggest benefit to CLS methods in
comparison to other methods is the ability to continuously monitor IOP without
disturbance to everyday activities, including sleep [44]. Further refinements and
innovations are necessary, but it is an emerging technique and could be used in
conjunction with other tonometers, such as the system we later propose in this
paper.
15
2.2.2.1 Rebound Tonometry
Figure 2.7: The tonometer in use [6].
Rebound tonometry is a new type of contact tonometer that drops a mag-
netized, disposable probe towards the cornea and uses a solenoid to measure the
deceleration of the probe. The device then employs the principle that higher IOP
causes a quicker deceleration to calculate the IOP [48]. An example of this rebound
tonometer is the iCare rebound tonometer, seen in Figure 2.7.
These tonometers are portable, easy to use, and are not discomforting for the
patient, yet suffer from a high product cost. However, the iCARE rebound tonome-
ter is very susceptible to changes in corneal hysteresis and corneal resistance factor.
It also overestimated higher IOP and underestimated lower IOP when compared
to GAT [49]. Rebound tonometry has also been shown to produce different re-
sults when the patient is sitting versus supine, and shows greater variation between
different ages [50].
16
2.2.3 Non-Contact Tonometry
Figure 2.8: Schematics for the various methods for the applanation of the eye for
corneal IOP measurements are shown. The workings of a rebound tonometer is
shown in (A), of the GAT in (B), and the non-contact air puff tonometer in (C).
From [7].
Contact-based methods of tonometry generally require sterile tips and anes-
thetic. As a less intrusive alternative to the GAT, non-contact methods have
emerged as the clinical standard for tonometry. The most popular method of non-
contact tonometry is the air-puff tonometer which uses bursts of air to apply pres-
sure to the cornea. The diagram depicting the experimental principle of air puff
tonometry is shown in Figure 2.8C.
When a sufficient pressure is applied, the cornea will applanate, meaning the
concavity of the cornea will flatten [51]. The pressure required to applanate the
cornea is measured to determine the IOP. Similar to GAT, the air-puff tonometer
is susceptible to corneal variability. Additionally, the time scale of the air-puff
tonometer is very short, which results in an increased susceptibility of measurements
to momentary pressure variations [52]. One solution to this problem is to use an
air puff of longer duration. Increasing the duration of the air puff is the method
adopted by the commonly used Corvis Tonometer, which has been shown to agree
17
well with GAT [53]. However, this method is somewhat aggressive and often induces
blinking upon measurement. This blinking may itself affect the IOP and may be a
significant source of error for air puff tonometry [54], which we discuss in Section
2.2.7.1.
2.2.3.1 Corvis and Air-Puff Tonometry
Figure 2.9: The OCULUS Corvis STL is a non-contact air-puff tonometer with a
high-speed Scheimpflug camera [7].
One popular example of a non-contact tonometer is the Corneal Visualization
Scheimpflug Technology (Corvis or CST) tonometer which applanates the cornea
with an air-impulse [53, 55]. The Corvis then measures the deformation of the eye
with an ultra-high speed Scheimpflug camera, capable of recording 4330 fps within
a 100 ms time duration [53]. The Corvis instrument is shown in Figure 2.9.
The CST camera is able to detect excellent resolution on the order of 640 ?
480 pixels, and replay eye movement in ultra-slow motion [53]. The device can
measure pressures between 1 and 60 mmHg, making it an excellent candidate as an
instrument to measure IOP, which typically ranges between 12 and 22 mmHg [56]
in a normal eye and causes rapid vision loss above 40-50 mmHg [57].
18
Although the theory behind the CST is not as easily understood in relation
to other commonly used tonometry techniques like GAT and rebound tonometry,
it can also measure biomechanical properties in the eye such as corneal thickness.
Additionally, the CST had the best intraobserver and interobserver variability in
measurements of IOP, and was not as affected by the biomechanical properties in
terms of measurement variability [53].
The deformation time from the applanation of the cornea largely influences
the precision and decreased variability of the IOP measurements. For instance,
many non-contact tonometers measure the IOP in less than 5 ms, and the CST
puff measurements are separated by an average of 15 ms. The study by Hong et
al. found that applanation time plays a significant factor in the variability of the
calculated ?read? IOP values yet the difference between the differences in IOP and
the time it took to applanate the cornea was statistically marginal (p = 0.067) [53].
However, more research is needed to determine the effect of the applanation time
on the accuracy of the instrument IOP readings.
2.2.4 Imaging Modalities in Ophthalmology
Increased IOP limits blood flow, causing degeneration in retinal ganglion cells.
The death of these cells causes enlargement of the optical disk, or optical nerve
head [58] and a thinning of both the retinal nerve fiber layer (RNFL) and macula.
Since glaucoma is a progressive disease, it is vital to obtain qualitative information
about these structural changes to best intervene in glaucoma progression. Addition-
19
ally, these structural pathologies are evident well before vision loss [59, 60]. Three
well-developed in vivo imaging techniques to achieve this are Scheimpflug imaging,
confocal scanning laser ophthalmoscopy, scanning laser polarimetry, and Spectral-
Domain optical coherence tomography (SD-OCT). These methods significantly vary
on how they obtain data for monitoring purposes, but all have shown promising re-
sults for monitoring structural changes due to glaucoma. This section describes each
method, names the devices that use it, and discusses its advantages and disadvan-
tages.
2.2.4.1 Corneal Topographers
Figure 2.10: A patient being evaluated with the Placido topographer [8].
Most corneal topographers are based on the Placido topographer, which was
introduced in 1880 by Antonio Placido and further developed by Allvar Gullstrand
in 1896, who developed a numerical algorithm to accompany the method [61]. A
set of high-contrast concentric rings are placed in front of the cornea (Figure 2.10),
creating contour-like reflections whose displacement may be analyzed to calculate
corneal wavefront parameters like astigmatism, trefoil, and coma [62]. More re-
cent variations on the method sometimes employ other patterns and methods of
20
projection. The Orbscan topographer, for example, uses a ?scanning slit? pattern
projected from multiple angles, which creates 240 reference points on each slit for
analysis [63]. In general, reflection-based methods have been found to have excellent
accuracy and repeatability [64?66].
Originally, the contours produced by such topographers were evaluated only
qualitatively, in comparison to standardized images of ?normal? corneas [67]. How-
ever, as computing power increased and the implementation of increasingly complex
image processing algorithms became feasible, it became possible to produce quanti-
tative intensity maps of corneal power using algorithms that detected and processed
variations in some or all of the reflected rings (see Section 2.2.7.1 for a discussion of
these algorithms).
More recently, corneal topographers have begun using the Scheimpflug imaging
technique to capture corneal thickness and other corneal properties that are only
accessible from a side perspective. The most well-known of these topographers is
the OCULUS Pentacam [68] and the Ziemer Galilei [69]. In the following section,
we describe the principles behind Scheimpflug imaging.
2.2.4.2 Scheimpflug Imaging
Scheimpflug imaging relies on the Scheimpflug principle. A photograph of an
object plane that is not parallel to the image plane can be maximally focused given
?certain angular relations among the object, the lens, and the image plane? [69]. By
being able to vary the plane of focus by varying the camera angle, the composition
21
of many images is able to produce a reliable image from the anterior cornea to the
posterior lens surface.
Modern Scheimpflug corneal imaging systems use rotating cameras to image
cross sections of the cornea that are illuminated by slit beams at different angles.
These images are then interpreted by an algorithm that reconstructs a 3-D to-
mographic map of the cornea?s anterior segment and also calculates other physical
information such as the topographic corneal thickness and the corneal curvature [70].
The Pentacam (Oculus Optikgeraete GmbH, Wetzlar, Germany) uses a single
rotating Scheimpflug camera illuminated by a 470 nm blue LED to capture images
of the anterior segment, while a second stationary camera is used to detect and
measure the pupil, which helps with aligning the images and compensates for ocular
movement. In this device, Scheimpflug imaging takes approximately 2 seconds to
image 25 to 50 different cross sections between 0 and 180 degrees in a single scan,
accumulating approximately 25,000 data points to be used for reconstruction of the
anterior segment using its proprietary software [71].
The newer Galilei (Ziemer Ophthalmic Systems AG, Port, Switzerland) dual
Scheimpflug analyzer combines corneal tomography from Scheimpflug imaging and
Placido disc topography to also obtain a comprehensive curvature profile of the
central cornea [72].
22
2.2.4.3 Optical Coherence Tomography
Optical coherence tomography (OCT) is a non-contact, non-invasive method
that uses low coherence interferometry to obtain high-resolution tomographic images
of biological tissues [73]. Since (RNFL) health is a strong indicator of glaucomatous
damage [74], OCT is frequently used to obtain measurable information about retinal
layer thickness. The earliest variant, known as Time Domain-OCT, relied on the
delay time from back-scattered light to construct a 2D image of the optic nerve.
Time Domain-OCT provided an axial resolution of 10 ?m and takes about two
seconds to provide a 2D image of the optic nerve [75]. Recent advancements have led
to SD-OCT, allowing for 3D imaging of the optic nerve [76] with an axial resolution
of 5 ?m. Currently, the standard device in clinical settings is Spatial Domain-
OCT). There remains a significant difference in measurements taken by different
SD-OCT devices. For example, one commonly used brand, the RTVue, gives a
much higher peripapillary RNFL thickness than other brands [77]. Since comparing
results over time is essential to make a proper treatment plan, switching imaging
devices or going to another practice can lead to misdiagnosis. Additionally, cataracts
and vitreous debris can lead to a false reading of an increase in RNFL thickness.
Meanwhile, myelinated RNFL, epiretinal membrane, swelling of optical nerve head,
and peripapillary retina can lead to false increase readings of the retinal nerve fiber
thickness [78].
In summary, OCT is a valuable method for monitoring existing ocular damage
and providing information to clinicians to help prevent further damage. Different
23
pathologies can reduce the accuracy of OCT measurements. Additionally, different
SD-OCT brands do not have a consistent baseline. With this in mind, OCT mea-
surements are most valuable when used alongside other diagnostic methods such as
visual field tests and other evaluation methods.
2.2.5 Computer Vision and Ophthalmology
2.2.5.1 Depth Estimation
Figure 2.11: An example of a scene and its corresponding depth map. This depth
map was creating using an algorithm for monocular depth estimation, AdaBins [9].
The practice of estimating corneal topography from camera images may be
reduced to the classic computer vision problem of depth estimation. Solutions to
the problem attempt to label each pixel of an input image with a value representing
its distance from the camera; a completely labeled image is known as a depth map.
To date, devices like Corvis or the Pentacam rely on moving camera technology and
the composition of many separate images to solve this problem. Indeed, traditional
solutions in computer vision have focused on the use of computer stereo vision to
most accurately regress 3D geometry from images. Broadly, these approaches rely
on feature extraction and matching using engineered features like SIFT or SURF
24
[79, 80], before applying calculations based on feature movement and parallax to
calculate object depth [81,82]. The defining feature of these approaches is that they
require multiple images or motion of the camera. Consequently, existing methods
for depth estimation in ophthalmology require additional equipment to move the
camera and acquire the necessary data.
However, more recent advances in computer vision have focused on a differ-
ent solution to the problem, monocular depth estimation. As its name suggests,
monocular depth estimation seeks to solve the depth regression problem using only
a single input image. Although a monocular perspective introduces unavoidable
scale ambiguities to the solution space, with low-resolution supplementary infor-
mation and correct assumptions about geometry, it is possible to accurately solve
the depth estimation problem [83?85]. This would eliminate the need for moving
parts and multiple images currently demanded by computer stereo vision and other
multi-image algorithms.
Monocular depth estimation has attracted particular attention since the ad-
vent of convolutional neural networks (CNNs). There have been a myriad of network
architectures created to solve the problem, with increasingly promising performance
and generalization capabilities [86?89]. Most approaches are based on the convolu-
tional autoencoder (CAE) architecture, in which a CNN learns to extract specific fea-
tures from input images. CAEs have also shown promise in image denoising [90?93],
medical image segmentation [94?96], and feature extraction [97?99]. We describe
the principles of neural networks and their current applications in ophthalmology in
Section 2.2.6.
25
2.2.5.2 Structured Light and Ophthalmology
These algorithms are designed to work on a wide variety of scenes and per-
spectives. However, they become most effective when given access to supplemen-
tary information. An especially notable example is the structured light approach
to depth estimation, which allows for precise reconstruction of an object?s topogra-
phy [100?102]. This approach projects a fixed, regular pattern onto an object. The
distortions caused by the object?s geometry are then used to compute highly precise
representations of its surface. Aside from engineered algorithms, highly accurate
reconstructions have also been produced by CAEs, with the added benefit that pre-
processing and denoising steps taken by other algorithms are learned implicitly by
the network. In addition, because CAEs mainly rely on the convolution operation,
they are easily parallelizable, allowing for greater optimization and faster execution
times compared to engineered algorithms [103].
Structured light-like algorithms that appear in ophthalmology are typically
known as videokeratography. The Placido and Pentacam topographers may be
considered examples of monocular structured light reconstruction, though neither
method takes advantage of deep learning. A number of solutions have been de-
veloped to automate and enable quantitative analysis of the images generated by
Placido-style topographers. Two prominent examples of current computer vision
techniques in the field are the SimK and CorT algorithms. However, the SimK al-
gorithm does not make use of the information from all Placido rings. Instead, it uses
only one ring within the series to generate its estimate. The newer CorT algorithm
26
takes advantage of the distortion of all visible Placido rings and has been shown to
achieve greater accuracy as a result [104,105].
2.2.6 Convolutional Neural Networks
In this section, we describe the basic mathematical structure of neural net-
works, beginning with the multilayer perceptron before moving to CNNs. We also
describe the process by which these networks are trained, under the paradigm of
supervised learning. We conclude by summarizing current applications of CNNs in
ophthalmology.
2.2.6.1 Design and Architecture
Neural networks have undergone extensive modifications. Although their full
history is beyond the scope of this review, we begin by describing the quintessential
neural network, the multilayer perceptron (MLP), which motivates many of the
concepts underlying modern neural networks.
Artificial neural networks use mathematical abstractions of biological neurons.
An MLP is an extension of the perceptron, introduced by Rosenblatt in 1958 [106].
Given a set of inputs x = x1, . . . , xn, the perceptron outputs either 0 or 1. The
output is determined using a ?threshold? function on a linear combination of the
elements in x. Mathematically, the output y of a single neuron within the perceptron
may be represented as
27
(? )n
y = (w ? x + b) = (w1x1 + . . .+ wnxn + b) = wixi + b (2.2)
i=1
where b is some bias term learned by the perceptron and w is a set of learned
weights.
The perceptron is an example of a linear classifier, which creates a hyperplane
to classify its inputs. However, this creates an issue as few training sets are linearly
separable. For instance, the binary XOR function is not linearly separable and
therefore cannot be learned by a single perceptron, as famously shown by Minsky
and Papert in their 1990 book Perceptrons. Although it is possible to learn such a
function by stacking ?layers? of perceptrons in series, such a system is difficult to
train using Rosenblatt?s learning rule, and relatively inefficient [107].
Modern perceptron neurons circumvent this issue by applying a nonpolynomial
differentiable activation function ? to the output of each of their neurons. In fact,
the modern perceptron neuron is nearly identical to that described by Rosenblatt
in Equation (2.2), except that the function is replaced by ?:
(? )n
y = ?(w ? x + b) = ?(w1x1 + . . .+ wnxn + b) = ? wixi + b (2.3)
i=1
The resulting neurons can learn non-linearly separable data on their own,
may be stacked, and may learn using the much more powerful backpropagation
algorithm because their output is fully differentiable, which is discussed in Section
28
2.2.6.2. When stacked in layers, we obtain the modern multilayer perceptron, which
may approximate any continuous function to an arbitrary degree of accuracy given
enough nodes using a nonpolynomial activation function [108].
See Figure 2.12 for a graphical representation of a MLP, where each circular
node represents a single perceptron as described in Equation (2.3). MLPs have been
used for a broad variety of tasks in classification and regression [109,110].
Figure 2.12: An example of a multilayer perceptron with hidden layers. Note that
layers comprising multiple neurons allow for vector outputs [10].
Most neural network architectures employ the sigmoid, hyperbolic tangent
(tanh), softplus or rectified linear unit (ReLU) functions as activation functions.
The first three functions are more common in sequence-based or vector-based input
networks. The ReLU function has found usage in modern deep learning networks,
which can have up to thousands of layers and encounter issues when trying to
backpropagate through the other functions [111].
From Perceptrons to Convolutions
Although MLPs can approximate any continuous function, as discussed above,
in practice this often requires an impractical number of nodes and can be very dif-
ficult to train. In addition, the ?fully-connected? architecture of an MLP does not
lend itself naturally to images, as they often contain locally-dense features which
may appear at any point within the image at different angles and scales [112, 113].
29
In 1989, Yann Lecun et al. introduced CNNs to process image data using less pa-
rameters and greater emphasis on spatially invariant local patterns, showing their
effectiveness in recognizing handwritten digits [114]. The advent of graphical pro-
cessing units (GPUs) and the discovery that deep CNNs with many layers had great
representative power introduced the deep CNN, which has become commonplace in
image processing tasks [115] and achieved superhuman performance on computer
vision tasks [116].
CNNs are based on the convolution operation. This operation ?slides? a small
convolution kernel over the input image, using it to take a weighted sum of each
pixel?s neighbors. Let a given image of height H pixels and width W pixels be
represented as a 2D matrix I with H ?W elements, and a given convolution kernel
be represented as a 2D matrix K with R rows and C columns (assume R and C are
odd). Then mathematically, the convolution operation may be represented as
?
I ?x,y = Ki,jIx+i?R?1 ,y+j?C?1 (2.4)
2 2
i,j
where (x, y) index I, (i, j) zero-index K, and I ? is the resulting convolved image.
One caveat is that there are not enough ?neighbors? at the edge of I to use in
the convolution operation. This is often addressed either by padding the image
with zeros or some other constant values, image reflection, ?wrapping?, or cropping
pixels that do not have enough neighbors. However, we omit the specifics of these
workarounds in our formulation.
30
Figure 2.13: Sample application of the Sobel convolution kernel on an image. Orig-
inal image is on left, convolved result is on right.
As an example, Figure 2.13 shows the results of the Sobel convolution kernel,
an engineered kernel created by Irwin Sobel to detect high-frequency features (like
edges) in an image. The Sobel kernels have the entries
?? ???1 0 ?1? ???? ?
? ?
1 2 1 ?
Gx = ?? ?
? ?
?2 0 ?2??
?
G = ?y ?? ?? 0 0 0 ???? (2.5)
1 0 ?1 ?1 ?2 ?1
which are analogous to the discrete derivatives of the image intensity [117].
CNNs, however, begin with randomly initialized convolution kernels and learn
to update their entries to extract the most salient features in an image?in effect,
they are automated feature extractors. By applying convolutions in series, a CNN
can learn to recognize higher and higher-level features [115]. Figure n shows an
example CNN architecture.
31
Figure 2.14: An example of a CNN used to classify images, VGG16. Note the stacked
convolution maps, ?pyramid? structure, and high number of feature maps [11].
Figure 2.15: High-level structure of an autoencoder used for denoising handwritten
digits [12].
Convolutional Autoencoders
CAEs are a special subset of CNNs. However, every autoencoder performs
dimensionality reduction on input data, before learning to reconstruct it in some
way. In the case of images, this often refers to the operation of subsampling, in
which an image is reduced in size by a constant factor. The autoencoder is then
forced to reconstruct the original input image as completely as possible using only
its compressed representation. This makes autoencoders extremely useful for feature
extraction, as the network must learn to preserve the most relevant features of the
image [118].
Autoencoders can also be used for other purposes. Figure 2.15 shows an
32
example of an autoencoder used for denoising. Once a compressed representation
has been learned by the encoder, it is also possible to train a decoder to reconstruct
this representation in such a way that features in the input image are omitted or
modified. This allows autoencoders to output denoised versions of input images,
segmentation masks, and depth maps as discussed in Section 2.2.5.1.
2.2.6.2 Supervised Learning and Optimization
In this section, we briefly describe the core principles of supervised learning and
backpropagation, which we use to train our network. Although we have described
the mechanism by which neural networks output their predictions, we have not
described how they learn to adjust their weights. In supervised learning, examples
are annotated with ground truth labels to help guide predictions. Outputs from the
network are then compared with these labels to determine how the weights of the
network should be adjusted.
Loss Functions
Loss functions are the method by which labels are compared to network out-
puts. Let a network be f , such that for some x in the training set we have f(x) = y?,
and our ground truth label be y. Then our loss function L(y, y?) outputs some value,
the magnitude of which represents the loss of the network output. To enable back-
propagation, L must be differentiable. The mean squared error and cross-entropy
functions are the two most common loss functions used in supervised learning [119].
Backpropagation
33
Once the loss function has output a loss value, the network?s parameters are
adjusted to reduce it. Backpropagation is the most popular method to compute the
necessary adjustments [120].
We may view a feedforward neural network as the composition of a series
of differentiable processes. Because the loss function is itself differentiable, we can
calculate the partial derivative of any weight in a network with respect to its output.
In other words, given some y, y? as described in the previous section, let the output
of the loss function be C = L(y, y?). Then our goal is to find ?C for every weight
?W
W in the network.
To calculate this quantity, we employ backpropagation. This algorithm cal-
culates the derivatives of each layer, iterating backwards from the output. Intu-
itively, it takes advantage of the fact that because a feedforward neural network is
a composition of functions, one may iteratively apply the chain rule to continuously
differentiate its output.
Once this gradient has been computed, different gradient descent algorithms
and optimizers are used to decide the exact calculation used to adjust each weight.
Examples of these algorithms include stochastic gradient descent, Adagrad, Adadelta,
or Adam [121].
2.2.6.3 Applications in Ophthalmology
Prior applications of CAEs and neural networks in ophthalmology seem to
focus on classifying corneal diseases like keratoconus based on existing corneal to-
34
pography data [122, 123], or detecting the presence of disease from images of the
retinal fundus [96].
Lavric and Valentin classified corneal topography maps in 2019, searching
for keratoconus, and achieved a test accuracy of 99.33%. Similarly, Ze?boulon et
al. classified corneal topography measurements with keratoconus and histories of
refractive surgery, achieved a similar accuracy of 99.3% (n = 300), and concluded
that ?using combined corneal topography raw data with a CNN is an effective
way to classify examinations and probably the most thorough way to automatically
analyze corneal topography? [122, 123]. These results for keratoconus demonstrate
promise in extending CAE and similar techniques to other ophthalmic diseases such
as glaucoma.
2.2.7 Clinical Considerations and Caveats
2.2.7.1 Effect of Blinking on IOP
The increase in IOP due to blinking, both voluntarily and involuntarily, has
been observed in humans. Pressure measurements taken immediately after blinking
show an increase of 10 mmHg for normal, unforced blinking, while pressures can
be much higher (on the order of 90 mmHg) for ?squeezing,? or forceful, conscious
closing of the eyelids [124].
These increases represent momentary spikes in the IOP lasting around 60 sec-
onds [125]. Therefore, the effect of blinking-induced pressure increases is substantial
for fast measurements lasting less than a minute, such as those involved in standard
35
air-puff tonometry. In the case of air-puff tonometry, the effect is especially signifi-
cant since the air burst tends to cause forceful blinking. Therefore, when measuring
IOP by air-puff tonometry, the measurement is increased by subsequent failed at-
tempts marred by blinking.
In order to reduce error caused by blinking, two possible avenues may be
pursued. One is continuous monitoring of IOP. If the IOP is continuously monitored,
blinking can be observed as a pulse in pressure. The baseline pressure before and
after blinking may still be observed [125,126].
Another solution is to decrease the occurrence of blinking during measurement.
Since blinking occurs as a response to anticipated trauma from a forceful, large air
puff, blinking can be largely prevented by decreasing the size and forcefulness of the
air puff.
Because blinking can produce a large pressure increase without the application
of force by an outside device, this was considered as a potential research avenue. The
movement of the cornea could be measured by a camera after a patient blinks. Ul-
timately, this direction was not pursued in this project because of the complications
caused by potential anatomical and behavioral differences. The pressure increase
due to blinking depends both on the forcefulness of the blink and the physical prop-
erties of the eye and eyelid. Therefore, standardization of the pressure applied by
blinking across different patients is difficult.
36
Chapter 3: Methodology
In this section, we describe our experimental setup and the architecture and
training process for our proposed algorithm. Our setup comprised of an applanation
system and an imaging system, which delivered air puffs and imaged the resulting
deformation respectively (Figure 3.1). We name the components used in the setup,
describe our design process, and elaborate upon our proposed calibration method
for our tonometer.
37
Figure 3.1: A photo (top) and schematic (bottom) of our experimental setup.
3.1 Applanation System
The applanation system consisted of a mechanical system which allowed for
air flow from a pressurized air source through a nozzle, generating puffs whose
intensities and time intervals are controlled by an electronic microcontroller. These
puffs then applanated a mounted porcine cornea.
38
3.1.1 Mechanical Design
To deliver an air puff with consistent pressure, we used a compressed air tank
as a gas source with a single stage regulator to control the output pressure. The
air flowed through a length of polyurethane tubing. Between puffs, a three-way,
two-position solenoid valve exhausts the gas away from the eye. An analog pressure
gauge was situated between the nozzle and the solenoid valve to provide a quanti-
tative readout during this time. The tubing terminated at a 2 mm plastic nozzle to
concentrate the puff onto a small area of the cornea.
Iteration 0: Mechanical Pumps for Puff Generation
Initially, we investigated the use of mechanical pumps to generate an air puff.
The first pump was the Diaphragm Electric Operated Positive Displacement Pump
from RS Pro, acquired from Allied Electronics Automation. This pump has a flow
rate of 150 mL/min at 1 bar, with an operating voltage range of 1.5 to 4.5 V. The
next pump we used was the Vacuum Pump from SparkFun. It has a flow rate
between 9 and 15 L/min at 12 V.
Neither of these pumps were able to provide adequate pressure to deform the
corneas tested in our setup. As a result, this design was not pursued further.
Iteration 1: Compressed Air Source
Rather than purchase a large pump to generate puffs, we decided to try using a
compressed air source. We acquired a tank of industrial-grade compressed nitrogen
gas from Airgas. This tank had a two-stage pressure regulator which controlled the
gas pressure released. This method generated enough pressure to deform a cornea.
39
Iteration 2: Two-Valve System
Our first system used two NITRA two-way, two-position solenoid valves. The
solenoid valves actuate at 15 A, so an external power supply was required. The
valves consisted of a magnet attached to a diaphragm inside a solenoid. Below the
diaphragm was a channel to allow air flow. In a normally-open valve, the resting
position of the magnet is up, allowing air flow through the valve. When the solenoid
actuates, the magnet is forced down such that the diaphragm blocks the passage of
air through the valve. In a normally-closed valve, the magnet is in the low position
when no current is applied, blocking air flow through the valve. The solenoid valves
we acquired had a 12-14 ms complete cycle response time, which denotes the time
duration required to go from the rest state to the active state, then back to the
rest state. This cycle time enabled us to create puffs with a similar duration to the
industry standard Corvis, which has a puff duration of roughly 15 ms.
Two valves were connected to the air source in series with flexible tubing. In
this configuration, the input valve, or the valve closer to the air source, was opened,
allowing the space between the two valves to pressurize. When the appropriate
pressure was reached, the input valve closed and the output valve opened. This
opening caused air to flow through the nozzle, puffing the cornea.
Iteration 3: One-Valve System
When the two-valve system was tested, the pressure between the two valves
could not be precisely measured and controlled. As a result, this chamber often
over-pressurized and the fittings disconnected. To mitigate this, we changed our
system to only use one NITRA three-way, two-position valve.
40
The three-way valve has one input and two outputs. In the ground state, the
valve connects the input to an exhaust output, which vents the pressurized gas to
the atmosphere. When power is supplied to the valve, it changes the output such
that the compressed air is sent through the tubing length and out the nozzle. This
valve allowed us to control the intensity of the puff by adjusting the pressure of the
air source, and control the puff duration by changing the amount of time that the
relay is energized.
Final Design: Fume Hood Air Source
By our third iteration significantly more gas was used, causing the nitrogen
tank to deplete quickly. To avoid any delays related to replacing the tank, we
changed our air source to a pressurized fume hood air line.
3.1.2 Electrical Design
A normally-open electromagnetic relay was used to operate the solenoid valves.
The relay was connected to a DC power supply with variable voltage and current
modes, and to one of the digital pins on an Arduino Uno microcontroller. The
relay output was connected to the solenoid valve. A schematic diagram of the
configuration can be seen in Figure 3.2.
41
Figure 3.2: A schematic diagram of the electronic system.
A program running on the microcontroller set the voltage on the digital pin
connected to the relay. A square pulse was applied to the pin, causing the relay
to close. The duration and frequency of pulses could be changed by the software.
When a pulse was sent to the digital pin, the circuit between the power supply and
the solenoid valve closed, causing the valve to open and air to flow. Through this
system, pulse lengths could be controlled with a resolution of one ms, however the
lower limit of actuation time was constrained by the power supply. At the valve?s
recommended operating voltage of 15 V, the minimum cycle time was found to be
roughly 35 ms, and somewhat dependent on the pressurized air within the valve.
Increasing the voltage to the maximum output of the power supply, 18.5 V, reduced
this time to roughly 25 ms.
Through a combination of manual pressure adjustment using the regulator,
42
pulse duration adjustment using the software controls, and nozzle size selection, the
properties of the air puff could be varied widely to replicate the puff found in the
Corvis, other commercially available tonometers, as well as any other variations we
were interested in testing.
3.1.3 Eye Mounting
Porcine eyes were used to test our system. The eyes were stored in a refriger-
ated container until they were ready to be used. After the cornea was removed from
the eye tissue with a razor, the lens was removed, and the remainder was cleaned
using Dulbecco?s phosphate-buffered saline solution. The cornea was then mounted
onto a Barron Anterior Chamber, which allowed the IOP to be artificially set. A
water column was used to manually vary the intraocular pressure over a range of
IOP values on a given sample.
3.2 Imaging System
Our imaging system was comprised of two cameras and a projector. The
projector was used to apply the necessary structured light pattern, while the cameras
were used to create input footage and ground truth respectively.
43
3.2.1 Imaging Equipment
Figure 3.3: Deformation (left) with accompanying ground truth (right).
We imaged the cornea simultaneously from two different angles to produce
input footage and a corresponding ground truth. The input footage was taken
at 500 fps using a Basler acA640-750 ?m camera, while the ground truth angle
was taken at 160 fps using a Basler acA2000-165 ?m camera. Without equipment
restrictions, the same type of camera should be used for both angles; however,
instead we synchronized the ground truth with the input footage by slowing it down
by a factor of 0.32. The input footage was taken at a 45? angle to the cornea, while
the ground truth was taken at a 90? angle to the cornea, directly from the side.
To obtain 160 fps performance from the high-resolution ground truth camera, we
used the Basler Pylon software to crop the camera?s output resolution to 296?1088
pixels. See Figure 3.1 for a schematic of our experimental setup. Figure 3.3 depicts
an example of a deformation and its corresponding ground truth.
44
3.2.2 Pattern Projector
We used an Opto Engineering 3D LTPRSMHP3W-G pattern projector that
was designed for use in structured light applications, and use the PTGR050450P
grid pattern as a projection template. The pattern grid has 22 rows and columns,
with a line spacing of 0.45 mm and line thickness of 0.05 mm. The projector is
pointed at a 45? angle to the cornea.
3.2.3 Choice of Projection Template
We chose to project a regular grid onto the eye, in contrast to the Placido
topographer?s concentric rings and the Orbscan?s scanning slit pattern. We believe
that a regular grid has advantages over both varieties.
The concentric circles used by the Placido topographer implicitly define distor-
tion radially, with respect to a definite center; however, it is not always clear where
this ?center? may be, and centering the pattern requires care and time. Addition-
ally, it is often necessary to use multiple rings to understand the full extent of a
deformation [104,105], requiring that more of the pattern be analyzed. In contrast,
we expect that a grid will have a higher density of information at every intersection.
Rather than concentric circles, the Orbscan topographer employs 40 scanning
slits projected from two angles, creating 240 intersection points on each slit [68].
However, creating more points of reference using a grid is not difficult; for instance,
our grid has 16 ? 16 lines with 256 points of intersection. Denser grids could be
employed to create more information as necessary.
45
Existing methods may use these radial or low-resolution patterns in the interest
of algorithmic tractability. These methods use explicit selection of features, either
by ring or by intersection, which places an upper bound on the number of features
that may be processed in a reasonable time. Algorithms must compute astigmatism
scores or compare the movement of feature points between fixed camera perspectives
[104, 105]. By contrast, the high information density within a regular grid used in
combination with a CNN, does not rely on manually-extracted features and may
instead rely on more general patterns of grid deformation. Additionally, because
the features extracted by a CNN are largely spatially invariant, these networks are
more robust to a variable number of intersection points and allow for scaling of grid
density.
3.2.4 Calibration Procedure
Figure 3.4: Calibration plate pattern sample photograph, and suggested position of
calibration plate relative to Barron chamber(right).
To resolve the ambiguity caused by variations in focal length and the positions
of the projector and cornea, we imaged a calibration shot to establish scene priors
regarding depth of field, camera viewpoint, and projection angle. An example cali-
46
bration plate is shown in Figure 3.4, along with its position relative to the Barron
chamber. To create this image, we substituted the Barron mount for a featureless
flat metal plate while keeping the projector and camera intact. We attempted to
position the plate exactly at the base of the cornea on our mount. Our algorithm
then used this calibration plate as an additional input when considering corneal
deformation footage taken with the same scene priors, which is discussed in more
detail in Section 3.5.2.
3.3 Data Collection
Many tests were involved in tuning the parameters of the experimental setup.
This includes changing the frame rate and exposure settings of the cameras, adjust-
ing the focus of the cameras and projector, varying the puff intensity and duration,
and varying the IOP of the cornea. Once the optimal parameters were achieved,
data were collected for use in the final analysis.
During data collection, the knob on the fume hood air source was opened an
appropriate amount and then kept in position for the duration of the test. This
ensures that the intensity of the puff is as consistent as possible throughout the
different measurements. The IOP is then set to 10 mmHg according to the water
column manometer. The microcontroller began puffing the cornea for 5 seconds at
500 ms increments. Once the cameras record these puffs, the IOP was raised by 2
mmHg, and the process was repeated. Once data were collected at 28 mmHg, or
the limit of the manometer column, the pressure was decreased to 10 mmHg, and
47
the process was repeated. In total, we completed three of these cycles.
3.4 Data Simulation
With the resources and time available to us, only simulated data would provide
ground truth data with enough quantity and resolution to train our network for this
task. We rendered 20,000 frames of simulated deformation and then augmented
this simulated data using a variety of transformations (as described in the next
subsection) to increase its size to 80,000 samples. We used the free and open-source
3D computer graphics software Blender, version 2.91.2. Figure 3.5 shows an example
of a simulated cornea, along with its corresponding calibration plate.
3.4.1 Rendering Procedure
The render starts with spherical mesh sectioned to approximate the corneal
surface. A Displace modifier is added to the mesh, in which the texture is a 2D
gradient that falls of spherically from the origin. When applied to the mesh, this
results in a ?puffed? surface, and the strength of the modifier can be varied to
achieve appearances between resting and ?puffed?.
In the first two iterations of our simulated datasets, we modeled the cornea
using an infinitely thin mesh with a Glass BDSF (bidirectional scattering distribu-
tion function) node. Our third iteration focuses on greater physical accuracy, and
includes thickness and scattering effects within the corneal surface.
Iteration 0: Simulated Iris and Grid Projection
48
This iteration was focused on simulating the effect of projecting a pattern on
an iris. We modeled the iris using a circular disk, textured using a sample image of
a real iris. We then projected a checkerboard onto the cornea using a Blend shader
with a coefficient determined using the Fresnel node, resulting in a ?mixed? image,
which is shown in Figure.
Iteration 1: Basic Grid Distortion
Figure 3.5: A simulated cornea with projected pattern (left) and corresponding
calibration plate (right). Simulated topography is complex to encourage model
robustness.
In our first iteration of simulation, we focused on reproducing the pattern dis-
tortion. Consequently, we ignored physical scattering effects and thickness, instead
modeling the cornea as an ideal refractive element with an IOR of 1.45 using the
Glass BSDF node. The results are shown in Figure 3.5. Note that no scattering or
defocus is present in the resulting patterns.
Iteration 2: Simulated Iris and Grid Projection
In the second iteration of our data generation, we attempted to improve the
similarity between our rendered images and the captured images. This was accom-
plished in two main ways: adding thickness and volumetric scattering to the cornea,
and improving the lighting in the scene.
The mesh is given both a surface and volumetric shader, which controls how
49
light is reflected off of the mesh. The surface shader uses the Principled BSDF
node with maximum metallic and specular character. The roughness is decreased
to a low value, and the alpha of the surface is decreased slightly to allow some light
to pass through. The volumetric shader consists of both volumetric scattering and
volumetric absorption nodes. The densities of the absorption and scattering nodes is
adjusted to match the experimental conditions. The combination of these properties
creates a material that both reflects light off of the surface and within the volume
of the cornea.
The lighting of the scene consists of several spot lamps with a grid pattern
applied to them. The size of each lamp is adjusted to control the sharpness of the
pattern on the cornea, and the brightness is adjusted to simulate a gradual blurring
of the pattern. Additionally, the lamps are divided into groups that reflect only off
of the surface of the cornea, and a group that reflects only off of the volume of the
cornea. In this way, the relative intensity of the specular reflection can be adjusted
to match the collected footage.
3.4.2 Physical Accuracy of Rendering.
When rendering simulated data, our goal was to reproduce experimentally-
gathered images as accurately as possible. That being said, some details of the
scene, such as the mount and the ambient environment, are difficult to accurately
reproduce. As such, we focused on reproducing the deformation of the grid pro-
jected onto the cornea, while the environment only bears a loose resemblance. This
50
reproduction allowed us to augment the data during training which, in turn, helped
the network identify that background details can be discarded.
Blender provides several rendering engines. In the interest of achieving a
realistic render, we chose the path tracing-based Cycles rendering engine, which
aims to reproduce optical phenomena as faithfully as possible by simulating the
bounces of individual rays of light emanating from light sources. In this way, the
rendering engine could most accurately capture complex reflection and refraction
even on surfaces with complex topography.
A detailed description of the modeling process is included in Appendix C.
3.5 Image Processing and Algorithms
Figure 3.6: Our process for IOP extraction from footage of an illuminated applana-
tion.
Our algorithm attempted to predict corneal topography from a monocular
video. To make it more generalizable, we separated the operation of the algorithm
into two parts: one which extracted the projected pattern from an image of the eye
(CheckMark), and one which predicted the topography corresponding to a ?pure?
51
pattern (DeepSquish).
CheckMark is a CAE, while DeepSquish is a deep CNN following the ResNet
skip connection architecture [127] that ultimately outputs points on a 2D surface.
In the following subsections we detail the architecture, training, and performance
of these networks. We also demonstrate that our network displays promising per-
formance on real footage using only simulated data as training input. We describe
our process for verifying our network?s predictions using our ground truth footage.
3.5.1 Autoencoder Checkerboard Extraction (?CheckMark?)
Figure 3.7: Real sample image of projected checkerboard on eye.
Figure 3.8: Samples from the dataset used to train ?CheckMark?. Simulated pro-
jection (left) and ground truth (right).
52
Introduction
Any algorithm attempting to make use of reflected light from the cornea will
face significant difficulty from the patterns of the eye itself, particularly from the
iris (Figure 3.7). To circumvent this difficulty for following stages of the algorithm,
we extracted a clean pattern from the image using a CAE.
Figure 3.9: The MA-Net architecture [13].
Architecture
We performed transfer learning using the MA-Net architecture, first suggested
as a method for segmenting liver and tumor images [13]. The architecture is designed
to extract features at multiple scales, and learn relationships among pixels using a
spatial attention module. We show a broad overview of the MA-Net architecture
in Figure 3.9, although we do not show the custom modules for spatial attention
and multi-scale feature fusion. Note the Position-Wise Attention Block (PAB) and
custom ResBlocks, which differentiate this architecture from a U-Net autoencoder
[128].
Loss Function
53
We used sum of the binary-cross entropy (BCE) and Jaccard distance loss
functions as our loss function to minimize. These loss functions were well-suited for
this task because the problem of extracting a clean checkerboard from an image was
essentially binary segmentation.
The Jaccard distance term was especially important for our task, as our ground
truth labels were imbalanced (i.e. there was a high ratio of ?foreground? or checker-
board pixels to ?background? pixels). The Jaccard distance term is known for
its ability to adequately represent loss in such imbalanced situations and preserve
pixel-wise detail, where other loss functions may inaccurately average away these
nuances [129]. We could also have used the Dice score, which is closely related to
the Jaccard distance, but found better performance when training with Jaccard.
Given a ground truth image y and network prediction y?, our loss function L
was formulated as
? ( )|y ? y?|
L(y, y?) = bce(y, y?)+(1?J(y, y?)) = (yi log y?i + (1? yi) log yi)+ 1? |y ? y?|
i?|y|
(3.1)
where i indexes the image pixels, and the intersection and union operations
are done element-wise over y and y?.
Training
Our dataset was 250 256? 256 simulated renders of checkerboard patterns of
varying density (i.e. number of squares) and angle projected on eyes with varying
pupil size and iris color. Figure 3.8 shows an example of an input and corresponding
54
ground truth label from this dataset. We normalized images by dividing them by 255
(0-1 scaling). In addition, we augmented the images by applying random rotations,
Gaussian noise, and adjusting the brightness and contrast of the images to help
prevent the model from memorizing the train set.
We implemented CheckMark using PyTorch 1.8.0 and the segmentation-models
library, and train our model on an NVIDIA GeForce RTX 2070 SUPER. The ob-
jective function was optimized using the Adam optimizer with a weight decay of
1 ? 10?5. We used a learning rate of 1 ? 10?3 for the first 10 epochs, and used
a learning rate of 1 ? 10?4 for remaining epochs. Weights were initialized using
weights from a ResNet-34 architecture trained on the Imagenet dataset. Finally, we
trained our model using a batch size of 6 for 50 epochs.
3.5.2 2D Surfaces With Convolutional Neural Network (?DeepSquish?)
Introduction
Once a grid had been extracted from our image, we used a second network to
process this grid and output a corresponding topography. To output this topogra-
phy, we present ?DeepSquish?, a residual CNN, and output the corneal topography
as a 2D surface. We also present a loss function that preserved surface normals and
detail without explicit calculation of normal vectors or surface derivatives.
Related works in the literature generally regress either depth maps, meshes,
or point clouds. Because we are regressing a continuous, thin 2D surface, we elect
to predict depth maps. However, our method differs from most approaches to depth
55
map prediction in our choice of viewpoint. Most, if not all, approaches output depth
maps from the viewpoint of the camera. This viewpoint is a natural choice given the
wide variety of scene geometries; solutions are aimed at generalizing across many
possible shapes and sizes.
However, our network outputs a depth map that is treated as a top-down view
of the imaged cornea, represented as 2D surface intensity values on a fixed grid.
We took this approach because corneas are mostly constant in radius; moreover,
the size of the area we are predicting is bounded by the size of the pattern being
projected on it. By having our network output a top-down depth map rather than a
camera-perspective map, the network represented every part of the corneal surface
with equal resolution, as well as parts of the cornea that may be occluded from the
camera viewpoint.
Architecture
As with CheckMark, we employed a model architecture that was very similar
to the ResNet in its use of residual blocks and skip connections. The network was
not quite an autoencoder, as it only had a downsampling path and dis not upsample
the input again.
To make the network fully convolutional and support variable-size inputs, we
avoided using any fully-connected layers and instead used the fractional max pooling
layer introduced by Graham (2014) [130] to downsample the final feature maps to
the desired resolution. In our case, we downsampled the final feature maps to a
17? 17 pixel map to achieve reasonable convergence times. However, if given more
data, there is no reason that the output depth map could not be a different size.
56
We also employed the Convolutional Block Attention Module (CBAM) to allow
the model to employ both spatial and channel-wise information at each feature
layer. This module gave the network a larger effective receptive field, an important
capability for this class of problem [131]. We employed a CBAM module in each
residual block.
57
Loss Function
We minimized the sum of the mean-squared error (MSE) term and a custom
loss function that was designed to encourage the preservation of fine surface detail.
This custom loss function was designed to specify the similarity of a point?s
elevation to its surroundings, a metric we call the ?peak? loss. Specifically, let y
and y? represent the ground truth and predicted depth maps, respectively. Let each
depth map be an N ? N depth map of values on a evenly spaced grid from ?1 to
1. Then the equation for our custom loss function Lpeak is
? ?
Lpeak(y, y?) = yi ? yj (3.2)
i?|y| j?|y|=6 i
and the equation for our complete loss function L is
L(y, y?) = ||y ? y?||2 + Lpeak(y, y?) (3.3)
where subtraction is done element-wise over y and y?.
Compared to other surface normal-focused losses that explicitly calculate sur-
face normals and are based on the cosine distance or dot product, we found that
Lpeak is effective and more efficient.
Training
In this subsection, we describe our training process, including model hyperpa-
rameters, training hardware, and data augmentation.
58
Figure 3.10: Sample augmented images in the train set.
Data Augmentation
Aside from simulating different projection and camera angles, we also aug-
mented the data to make the model robust to changes in lighting, rotation, texture,
and scale. To achieve this, we applied the following transformations to the images
with random probability and parameters:
? Affine transformations (scaling, rotation, shifting)
? Brightness, saturation, contrast
? Gaussian noise (variance up to 0.05)
? Gamma correction
? Coarse dropout (cutting random-sized holes out of the image)
We applied coarse dropout during data augmentation to help make the model
more robust to loss of information in some sections of the pattern, e.g. because of
59
intense specular highlights or irregular surface normals. See Figure 3.10 for example
image augmentation, and Appendix B for a link to our repository and our exact
augmentation pipeline.
Hyperparameters and Execution
We implemented DeepSquish using PyTorch 1.8.0 and trained it on an NVIDIA
GeForce RTX 2070 SUPER. The objective function was optimized using the Adam
optimizer with a weight decay of 1 ? 10?5. We use a learning rate of 1 ? 10?3
for the first 10 epochs, and use a learning rate of 1 ? 10?4 for remaining epochs.
Convolution layers were initialized using Kaiming random initialization. Finally, we
trained our model using a batch size of 3 for 20 epochs.
3.5.3 Extracting Displacement from Ground Truth
In addition to the footage used by the neural network, we also processed the
ground truth footage in order to extract the deformation of the cornea.
The ground truth data was collected as a series of bitmap images which are
grouped into folders for each trial, with the IOP and time of measurement recorded.
Mathematica was used to analyze these images. First, the images were imported to
a multidimensional list organized by the group of puffs and the time step within each
group. In order to smooth the image, a Gaussian Filter was applied to the images
with a kernel radius of 3 pixels. The image was then binarized with a threshold of
.1. This modified the brightness of each pixel such that any pixel with a brightness
above the threshold is assigned a value of 1, and all other pixels are assigned a value
60
of 0. A selected example can be seen in 3.11 The images were then converted to
image data, which turned each image object into a two dimensional list of 1s and
0s.
Figure 3.11: A. The output of the ground truth Basler camera and B. the same
image with the Gaussian filter and binarization applied.
The front edge of the cornea was then extracted from each image. Each image
in the image data list was sorted through row by row. In each row, the x-coordinate
of the rightmost bright pixel was stored in a new list. The result of this operation
was a new set of lists that contains a list of values corresponding to the position of
the front edge of the cornea for each set of puffs. This list was then exported to a
set of CSV files, split by each trial, for further analysis and visualization.
61
Figure 3.12: Visualization of our analysis process on sample frames.The orange
curve shows the edge at t! = 0, while the blue curve shows the edge at a non-zero
time. The Chamfer distance is taken between the orange and blue contour at every
frame.
Another Mathematica notebook was used to calculate the relative deformation
from these lists of absolute position. The CSVs were imported, each processed row
by row. The Chamfer distance was then calculated between the undeformed curve
at the first time step of the trial, t0, and the deformed curve, t > t0 (Figure 3.14).
Rather than search the entire curve, only points with x-values within 30 pixels were
considered. The two-dimensional distance was then computed between the point
of interest and each of the closest points on the curve at t=0, and the minimum
value was stored in a new list. When this was done for every point in every curve,
it showed the relative displacement between all curves at t > 0 and the initial curve
at t0. This showed only noise when there was no deformation of the cornea and a
clear, roughly parabolic, deformation during the puff. This list was also exported
to CSVs for further analysis and visualization.
62
Figure 3.13: Example plot of the magnitude of displacement for some time t > t0
Finally, another Mathematica notebook was used to extract the maximum
deformation at each timestep. From the footage and from this analysis, we observed
that the cornea deforms in a complex manner: the center of the cornea is formed
downward, while the base of the cornea is pushed out. Upon the rebound, this is
inverted, and once the puff has stopped entirely the whole surface oscillates about its
rest position. While this information was valuable, in order to calibrate our system
we are only interested in the deformation of the spot on the cornea where the puff
strikes it. As such, we pruned the data by removing points on either side of the
cornea. This resulted in a list for each series of puffs that shows, at each timestep,
the maximum deformation from rest of the center of the cornea.
63
Figure 3.14: Corneal Response for IOP 10 (cm) H2O.
From these lists, the maximum displacement for each puff was extracted by
first setting a threshold on the minimum peak value and then finding the maximum
through a comparison with neighboring values. The maximum deformation for each
trial was then averaged. The displacement was plotted versus IOP for each puff.
64
Chapter 4: Results
We evaluated the performance of our algorithm on simulated data before test-
ing its ability to generalize to real footage. In our experiments, we measured the
network?s ability to accurately reproduce surface topography and capture the am-
plitude and period of deformations.
4.1 Simulated Data
4.1.1 CheckMark
Figure 4.1: Sample performance from CheckMark. Input image is on left, predicted
?clean? pattern is on right.
CheckMark achieved excellent performance on the test set, successfully dis-
playing the ability to extract a complete checkerboard pattern with sharp edges
from images containing simulated irises (Figure 4.1). The network converges to a
65
train error of 0.25 and a validation error of 0.1946 in 50 epochs (Figure 4.4).
Figure 4.2: Training (red) and test performance (blue) for CheckMark.
RMSE Jaccard
0.1946 .031
4.1.2 DeepSquish
Performance
DeepSquish also achieved excellent performance on the simulated dataset,
achieving a test error of 0.031 in 20 epochs of training. As seen in Figure 4.3,
the network is able to reproduce even complex surface topography with very little
qualitative difference.
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Figure 4.3: Sample performance from DeepSquish. Predicted meshes are in front,
ground truth meshes are in back.
Figure 4.4: Training (blue) and test performance (orange) for DeepSquish (left).
Relevant performance metrics (right).
MSE Lpeak
0.00523 0.09939
Model Interpretability
It is important to understand what features our network uses to make its
predictions. To this end, we analyzed our network using the Grad-CAM method
[132], which is often used to create ?visual explanations? of a network?s prediction
process. To achieve this, Grad-CAM uses backpropagation to compute a weighted
sum of the activations for some feature layer. Feature map pixels with high positive
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Figure 4.5: Localization heatmap generated using the Grad-CAM method for our
model. Note the focus on the pattern and distance from cornea edge.
gradients are considered ?important? to the network, allowing for the creation of
an localization heatmap. In our case, we would expect to see a localization map
that is strongly focused on the projected pattern, which would greatly decrease the
probability that the model is operating on memorization or bias. We ran Grad-CAM
on an intermediate feature layer in our model (layer 11, BatchNorm2d), following the
intuition that deeper layers provide higher-level visualizations, and show a sample
heatmap in Figure 4.5.
Our results show heavy focus on the grid lines, as well as the region between
the edge of the pattern and cornea, as indicated by the concentration of red near
the grid lines. This strongly suggests that the model is indeed learning the location
and shape of deformations based on pattern shapes and locations.
4.2 Real Footage
In this section, we discuss the extracted deformation data from our ground
truth footage, and compare it to the output of the network. We analyze how the de-
formation of the cornea correlates to increases in IOP, and compare trends observed
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in the ground truth to trends predicted by our algorithm.
4.2.1 Ground Truth
Figure 4.6: An image from the ground truth view showing a ruler for calibration.
Each tick mark represents one millimeter, with each pixel being equal to 16.56
micrometers.
Figure 4.7: Example plot of predicted deformation over time.
The ground truth footage consisted of 196 puffs over a range of IOP values
between 10 and 28 mmHg. The extracted deformation for each puff, calculated in
pixels, was converted to a distance in millimeters using an image captured with a
ruler, shown in Figure 4.6, for scale. The measured deformation versus IOP for each
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puff is shown in Figure 4.8. A linear regression of the data yielded a line of best fit
with the equation 0.820856? 0.0184785x and an R2 value of 0.913358. This reveals
a clear negative correlation between the deformation and IOP; however, inspection
of the data also reveals that there is a group of outliers below each group of data
points.
For many of the groups of puffs, the first puff resulted in a significantly different
amount of deformation. As is the case with many test of the mechanical properties
of organic tissue, it seemed that a pre-stressing step is required to probe the true
properties mechanical properties of the biological specimen. Once these pre-stressing
data points were removed from the set, as shown in Figure 4.8, the line of best fit
changed only slightly to 0.840319 ? 0.0189514x, while the R2 value increases to
0.968.
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Figure 4.8: The maximum deformation for each puff versus IOP for all trials (top),
and trials one through three (bottom)
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4.2.2 Comparison with Network Prediction
Figure 4.9: An example of a deformation map generated from our real footage.
Iteration 1: Basic Grid Distortion
Figure 4.10: Example plot of predicted deformation over time.
In this test, we used a network that was trained on the first simulated dataset as
described in Section 3.4.1, which did not include optical imperfections or scattering
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effects from the cornea. The resulting trend is shown in Figure 4.10. We observed a
weak negative linear correlation between IOP and deformation amplitude. A linear
regression produced a line of best fit with an equation y = ?0.023x+ 1.402 and an
R2 of 0.555.
This shows that although the data simulated in this iteration bears some
resemblance to our real footage, it is still quite dissimilar to the real footage we
gathered. In the next section, we describe the substantial improvement obtained by
training the same network on the dataset created in Iteration 2.
Iteration 2
Figure 4.11: Example plot of predicted deformation over time.
Figure 4.12: Model correlation for each trial.
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We applied a similar process to the network output, storing the output mesh
for the first frame of the footage and then calculating the Chamfer distance between
it and predictions made for following frames. We did this for the two-dimensional
surface output by the network, in contrast to the one-dimensional contour extracted
from the ground truth. An example of the resulting deformation plot is shown in
Figure 4.11.
It is important to note that the ground truth does not show the concavity of the
deformation, making it difficult to confirm our results for the predicted amplitude.
In addition, we could not quantitatively locate the puff in the axis moving away from
the camera. Therefore, we compared the trend of predicted maximum deformation
versus increases in IOP to that found in the ground truth, and compared the profile
of the predicted deformations to the ground truth footage.
To extract the trend for maximum deformation versus IOP, we extracted the
peak deformation amplitudes in each time series. We then plotted the resulting
points against IOP, and investigated the correlation obtained. In Figure 4.13, we
show that we find strong negative linear correlations in each trial, with R2s between
0.939 and 0.988.
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Figure 4.13: Combined predicted datapoints from all trials.
When combined, the datapoints from the resulting trials have an R2 of 0.818.
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Chapter 5: Discussion and Conclusion
5.1 Meaning and Significance of Results
The foundation of our imaging and analysis system is our DeepSquish neural
network, so we begin this section by discussing the results of our neural network
training using simulated data and then discuss the meaning and significance of our
results of using our network on footage from real corneal deformations.
5.1.1 Simulated Results
Our neural network receives an input image of a cornea, extracts a cleaned
version of the projected checkerboard mapping (CheckMark), maps a predicted three
dimensional topography of that pattern (DeepSquish), and outputs that mapping.
Our first tests for the network involved only the extraction of clean checker-
board patterns from realistic images. In order to train and test this portion of the
network, we created simulated images given limited experimentation time and ac-
cess. We simulated differences in illumination, focus, and angle. We found that our
CAE is capable of extracting patterns from mixed images, achieving a Jaccard loss
index of 0.03. This result means that, when given an imperfect simulated image,
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our first network is able to output a clean mapping to be interpreted. It also is
significant enough that we are able to test this network on real images, the results
of which are discussed in the next section.
The tests for the next part of the network were aimed at finding the effective-
ness of our neural network for transforming a clean checkerboard pattern to a three
dimensional topographical mapping. Our tests for this network showed that the
network learned simulated footage very well, reproducing complex surface detail,
giving us the confidence to test our network on real-world footage and see if it was
possible to generalize using only simulation.
5.1.2 Real Results
Due to the COVID-19 pandemic, we were unable to perform a large quantity
of tests of real footage, but we were still able to establish a proof of concept using
a network trained only on simulated footage.
The main test involving our network and real imaging system was a series of
videos taken at several different IOPs. While holding the puff intensity constant,
we show that our neural network is able to predict a clear correlation between
deformation and increase in IOP. The network predicts a deformation of 1.3 mm
at an IOP of 10 mmHg, decreasing to 0.78 mm at 28 mmHg. This presents an
expected amount of deformation; other studies have reported a deformation of 1.3
mm at an IOP of 14 mmHg [133]. This test means that our network can both
clearly distinguish between different IOPs when puffed at the same air pressure,
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and provide a physically appropriate prediction of the deformation. This is the
basis for tonometry, and it shows that our system has potential as a method of
determining IOP.
When using the first batch of simulated data, we conclude that the poor R2
value within the results is largely due to the fact that the distribution within the
simulated footage is simply too different from the real footage. Our Grad-CAM
analysis and performance on simulated data suggests that the network is able to
successfully learn the relationship between deformation and pattern distortion, but
real-world data will be needed to make our model robust to the different varieties
of optical distortion. Although we were able to simulate the basic phenomenon of
pattern deformation, we were unable to capture more complex optical effects like
projector depth of field and specular highlight. A potential remedy for this issue is
to obtain more precise ground truth data for real footage, allowing us to train our
network on real data and avoid using simulated data entirely.
The improvement when using a version of our network trained on the second
batch of our simulated data is further support for this hypothesis. We observe a
rise in R2 from 0.555 to 0.812 among all combined trials, with a per-trial R2 of
0.939 to 0.988. This substantial improvement suggests that it is important, but
still computationally tractable, to create a version of our neural network that can
generalize to the real world using improved simulation capabilities.
At the same time as we recorded images of the projected pattern, we also
measured the profile of the cornea from a 90? angle, which captures the profile
view of the cornea during deformation. We compared our predicted deformations to
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the measured ground truth and found that, while the deformations show a similar
slope, the magnitude of deformation predicted by the neural network is about twice
as high as the ground truth measurement. This is explained by the fact that once the
cornea is deformed past applanation, the concavity cannot be seen from the profile
view. At this point, the ground truth deformation will slowly increase while the
deformation at the apex will continue. This also means that the difference between
the two measurements should be greater for larger deformations and decrease as the
deformation shrinks towards applanation. This can also be seen in the data, further
supporting the efficacy of the system.
Although the ground truth shows a strong correlation between IOP and defor-
mation magnitude, there is still a large variance within the data at each IOP. Aside
from the initial pre-stressing puffs showing consistently less deformation, the rest of
the variance appears to be random, indicating that it is caused by variability within
the instrumentation, such as variation in the flow rate of air or small differences in
the cycle time of the valve, and not drying of the cornea or another degradation
mechanism within the tissue.
5.2 Comparison to Existing Works
The use of structured light to recover corneal topography is not new. How-
ever, we believe our method is unique algorithmically. Neural networks have not
yet been used to analyze anterior corneal reflections to recover topography. Instead,
as mentioned, applications of deep learning in ophthalmology have focused on the
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classifying of corneal topography data rather than predicting it [134]. Existing algo-
rithms for the recovery of corneal topography rely on hand-engineered features, can
be computationally intensive, and are sometimes forced to ignore some information
for the sake of computational tractability, as in the case of the SimK algorithm. In
contrast, we suggest that experiments on simulated and real data show that neural
networks learn to take advantage of minute pattern deformations across the corneal
surface, and are much easier to parallelize.
In addition, our tonometer is different from existing non-contact tonometers
in several respects. Aside from the algorithmic difference, which we have discussed,
there are also differences in equipment requirements. Other non-contact tonometers
have taken advantage of the Scheimpflug imaging technique and thin-slit illumina-
tion to get high-resolution information about a cross-section of the cornea. However,
this method necessitates the use of a rotating camera, and can only recover a thin
slice of the corneal surface, which requires the ophthalmologist to carefully center
the resulting puff in order to achieve near-radial symmetry. By contrast, our method
has the potential to recover the entire corneal surface in 3D, possibly removing the
need for careful centering and allowing for more comprehensive analysis of corneal
deformation. Consequently, we believe that our presented method may be incorpo-
rated in a device with fewer moving parts, fewer operational restrictions, and more
robust analysis compared to existing non-contact tonometers.
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5.3 Future Directions
We have created an air puff generator and analysis system which clearly models
varying deformation of porcine eyes. We now look toward ways to develop this novel
proof of concept into a widely accessible product. Due to time and resource con-
straints, as well as research restrictions throughout a large portion of 2020, several
aspects of this experiment would benefit from more robust development, experimen-
tation, and analysis.
The nearest future goals are those which further test the validity and usefulness
of our experimental setup. These shorter term research goals would require either the
same supplies currently used in the setup with additional time for experimentation
or a small number of additional measurement tools such a pressure sensor calibrated
for a specific range of pressures.
Beyond these shorter goals are tasks which will compare our system to modern
tonometry techniques and display our method?s unique advantages or disadvantages.
Several tonometers require deformation to be precisely in the center of the cornea
to isolate a specific two-dimensional cross section of the eye. Our method should be
able to classify non-centered deformations through tensor analysis of the produced
deformation mapping, but will require extensive research to confirm.
Finally, other steps need to be taken to solidify our method as a realistic and
equitable diagnostic tool. These steps include further research into the tolerance of
varying air puff intensities as well as in vivo experimentation.
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5.3.1 Puff Generation
As seen in our methodology, we have used two sources of air puffs with vary-
ing puff monitors. In the setup used for the majority of our analysis, we simply
connected to a variable air supply and did not monitor the actual air pressure that
reaches the eye. It is essential to know the pressure of the air impacting the eye
in order to properly characterize IOP. Solely regulating output air pressure of an
air puff does not provide enough quantitative control for this purpose, as the air
pressure exiting a nozzle is proportional to but vastly different from the force and
pressure of that air hitting a cornea.
Because we will never be able to directly measure the force on the eye, we need
to finely control output pressure of air and create a relationship between that output
pressure and the pressure felt by a cornea at a specific distance. By purchasing and
integrating a pressure sensor correctly calibrated to the range of pressures we work
with, one can create this relationship between output air pressure, deformation, and
IOP, and further validate the precision of our air puff generation.
5.3.2 Robust Modeling
Our goal is to lay the foundation for a product that will help reduce the
economic barrier between patients and modern tonometry devices, and to introduce
new technological advances in machine learning into ophthalmic practices. There
are several branches of this experiment that lay directly ahead which will help place
our experiment in context with current tonometry techniques and drive it forward
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into the realm of realism.
5.3.2.1 Establishing Agreement with Existing Tonometers
Using air puffs to deform eyes for the purpose of measuring IOP is not new;
there are several commonly used tonometers that all use this method, notably the
Corvis series of tonometers. These tonometers are all proprietary and have not
published detailed writings about why they use the puff pressure and shape that
they use. Because air-puff tonometers have been found to be a suitable method
for wide-scale screenings of IOP, it is prudent to compare our imaging and analysis
system to other tonometers under the same air puff and corneal conditions [135].
We began this process while designing our air puff system; we used a micro-
phone to imprecisely classify the intensity and duration of a Corvis air puff as a
model for our system. Once we acquire a pressure sensor and validate the precision
of our own puffs, a close next step would be to again measure the Corvis air puff
in an attempt to replicate its intensity and duration with increased accuracy and
precision. By calibrating our system to release the same puffs as the Corvis system,
we will be able to compare our deformation mapping with the deformation classified
by the Corvis software to compare our output IOPs.
This process will also allow us to more effectively compare our model?s ad-
vantages with advantages of other air puff tonometers. For example, if our system
is able to accurately model deformation and accurately determine the IOP of pa-
tients using lower pressures than in existing tonometers, our system can decrease
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discomfort and invasiveness and can be tailored to sensitive patients.
5.3.2.2 Realism Tests
This subsection discusses potential research endeavors to begin testing efficacy
and application of our model to more realistic scenarios and would help us determine
which parts of our neural network to rework in order to best account for variance in
human eyes. There are two types of these future goals. The first type are research
endeavors involving testing on humans to better understand comfort in relation to
our experimental setup and air puff. The second type involves researching more
abstract human conditions such as age, gender, race, corneal thickness, and other
specific eye attributes that may change the results of our system.
One common motivation for developing new tonometry techniques is limiting
any potential invasiveness or discomfort during the measurement. Contact tonom-
etry may result in small scratches on the cornea which cause discomfort for several
hours, and receiving a strong enough puff of air to displace an eye is uncomfort-
able. One of our goals is to devise a device which has advanced enough imaging
and processing to permit lower air pressures in order to reduce discomfort as much
as possible during measurement. In order to accurately judge the needs and wants
of potential users, it would be beneficial to survey community members throughout
a range of air puff pressures to determine at which point if any air puffs become
uncomfortable in order to maximize cost, comfort, and efficacy.
Broader than just reaching out to community members in order to judge dis-
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comfort from air puffs is the acknowledgement of different needs of different people.
It is important to create this device head on with the idea of increasing equity, so it
will be crucial to research further differences in parameters which may impact IOP
output of our model from age, gender, and race, which may be more easily known,
to corneal thickness, curvature (astigmatism), and eye size, which may be unknown
prior to measurement.
One way our model may have a flexibility advantage is its ability to train
on specific data. If this type of imaging system is used with many people and
types of eyes, different models could be trained for different communities using
transfer learning in order to maintain best results.This specificity of modeling would
be beneficial for several reasons. The usefulness from the model comes from it
transforming many images to a deformation map of the cornea throughout the air
puff, but if factors such as age, gender, or corneal thickness impact the images we
record, then the network will incorrectly map them. In addition, for eyes of different
shapes from, for example, astigmatism, our model will not recognize which eyes are
astigmatic and which are not, and will create deformation mappings which would
most likely assume that the eye is not astigmatic if the majority of its training
samples are not from patients with astigmatism.
5.3.2.3 Device Implementation and Design
Our experimental setup was designed with the potential of easily being con-
verted into a distributable tonometer product while still maintaining its core prop-
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erties. At its core, our design is composed of one stationary camera, one stationary
projector, and one air pressure source. Our current experimental setup has the air
source positioned in line with the eye, at a distance of 40 mm. The camera and
projector are positioned at roughly 45? angles to either side of the air source at a
distance of approximately 80 mm each. As such, this kind of setup could easily
be assembled into a single device containing all three elements that could rest on a
tabletop.
We will briefly compare our tonometer to other tonometers, both contact and
non-contact. One of the most state of the art and widely used non-contact tonome-
ters is the Corvis tonometer, which uses a more complex imaging system. Corvis
tonometers use rotating cameras which quickly move on a circular track around
the eye, a feature that adds potential failure points as well as cost and complexity.
Corvis tonometers also are of similar dimension to our setup. Corvis systems also
use a thin slit illuminator in conjunction with their imaging system. This thin illu-
minator is in contrast to our compact pattern projector, which is larger in scale than
the illuminator. In order to make our design as compact as the Corvis, we would
need to shrink our projector while still meeting the constraints that it projects a
bright pattern while lacking a color wheel. The Corvis is a significant investment for
any establishment to obtain. Thus, the large price results in many ophthalmologist
places renting the machines rather than buying them outright. A more user-friendly
tonometer option is the iCare Home tonometer, which costs $1000 . This product,
though much smaller and lighter than our design, uses contact tonometry and con-
stantly requires new materials, which leads to increasing cost of ownership over time.
86
When compared to our design, it is much more expensive.
The method for obtaining measurements will also differ in clinical settings from
our porcine tests. A fully operational unit will need to include ergonomic features
and calibration steps. Similar to current non-contact tonometers, an adjustable chin-
face stage is required to properly position the cornea of the patient. Because our
neural network-based approach is more robust against off-center puffs and differences
in the camera and projector alignment, the alignment of the cornea of a patient
requires much less accuracy than traditional methods. This should enable us to
both reduce the cost of our overall design, as well as make it more user-friendly and
easy to use. Our current system requires calibration with a flat plate to ensure the
camera and projector are in focus.
A future design could include a more flexible lens configuration which would
reduce the depth-of-field effect and make the requirements for focusing the device
more flexible as well. Furthermore, the strength of the network in extracting a
pattern from a distorted image may also be leveraged to bring a slightly out of focus
image into focus, even further reducing the calibration requirements.
In addition, the final product will need a user interface so it can be controlled
by a technician or user. Traditionally, the physician will adjust settings on the
opposite side of the tonometer, either on an attached computer or directly through
the tonometer, as is in the Corvis ST. Our product could include several options:
first, similar to the Corvis, the tonometer could have a screen and knobs on the
opposite side for a physician or other person to use. This would increase the cost of
the machine, but prevent the requirement of additional purchases to fully utilize the
87
equipment. Next, the product could connect to a computer or phone via a wired
or wireless connection. Studies have shown that similar networks to ours can easily
run on cell phones, and these controls would remove the need to include expensive
non-essential software in each tonometer.
5.4 Conclusion
The experimental and simulated results demonstrate the viability of neural
networks for use in tonometry. We constructed two neural networks, which to-
gether are able to predict a three dimensional corneal deformation map based on
real footage. The first neural network cleanly extracts a checkerboard pattern as
projected onto the cornea. Using simulated footage, we demonstrate that this net-
work can extract the pattern successfully in spite of imperfections such as reflections
and image focusing errors. The second neural network converts this pattern into
a three dimensional topographical mapping. This process was also verified using
simulated data, justifying experimental analysis of the model. Experimentally, the
deformation predictions were shown to behave similarly to ground truth measure-
ments. We are able to obtain a clear correlation between the deformation predicted
by the model and the IOP, meaning that this method could realistically be applied
to extract IOP measurements in the future.
Further experimental analysis must be done to improve the robustness of the
experiments and to compare the advantages and disadvantages of this method to
current tonometry techniques. However, our existing implementation suggests that
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neural networks can be used to determine corneal topography with comparatively
low levels of computation. Additionally, we are able to construct a three dimen-
sional mapping, potentially improving the flexibility of individual measurements.
We believe this to be a unique and promising new method of tonometry with the
potential to improve the accessibility of glaucoma screening technology, acting as
one step to equitably reduce the impact of this preventable disease.
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Appendix A: Racial Equity Impact Analysis
In addition to building a solely technical solution, our research project, like
many others, has a goal of establishing a lasting positive impact on society. In order
to systematically examine how different groups will be impacted by our research,
we have conducted a Racial Equity Impact Analysis (REIA) [136].
Our project seeks to remove barriers, both cost and convenience, from ocular
tonometry with the goal of making it easier to more frequently monitor IOP. In
particular, our method is designed to help monitor risk for Primary Open-Angle
Glaucoma (POAG), the most common form of Open-Angle Glaucoma (OAG), it-
self the most common form of glaucoma, accounting for approximately 70 to 90%
of all glaucoma cases [137, 138]. However, notably there are other less common
forms of primary and secondary glaucoma such as normal-tension glaucoma that
disproportionately affects individuals of Japanese ancestry, angle-closure glaucoma,
congenital glaucoma which occur in newborn babies, and pigmentary glaucoma that
primarily impacts young, Caucasian males [138].
In this analysis we will examine differences in POAG for people of various
heritages, ages, gender, as well as other factors and consider possible impacts that
our research can have. Though we briefly discuss the state of OAG in nations
90
outside of the United States, much of our focus in this assessment will be on racial
equity impact within the United States. We also discuss potential applications of
our project in real-world communities; however, much of this discussion is beyond
the scope of our project.
A.1 Background
A.1.1 Identifying Stakeholders
Currently in 2020, among the age pool with the greatest prevalence in glau-
coma (ages 40 to 80) there were approximately 76.0 million cases of glaucoma world-
wide, up from an estimated 64.3 million in 2013, and projected to increase to 11.8
million in the year 2040 [139], impacting every nation, with certain demographic
populations at greater risk than others. Because these statistics do not include in-
dividuals younger than forty years old or older than eighty years old, we expect a
greater number in truth than aforementioned. Part of identifying stakeholders for
our project relies on knowing the change in risk factors between different racial,
ethnic, gender, age, and habitation groups, as our research will have more impact
on groups with higher risk for POAG. In addition, as our research seeks to lower
barriers for all individuals in accessing regular IOP checkups, we will focus on high-
risk populations such as low-income communities and underdeveloped or socioe-
conomically disadvantaged communities within high-income areas. Many of these
disproportionately impacted communities do not have reliable access to tonometers
or ophthalmologists.
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A.1.1.1 Risk Factor Impact On Prevalence of POAG/OAG
Many studies on the prevalence of glaucoma, OAG, and POAG exist, each with
a slightly different focus or result. Many studies commonly recognize that increasing
age increases risk for OAG anywhere from 50 to 150% per decade [139?141] for all
groups. In fact, studies that examine the influences of socio-demographic factors
such as age, gender, race, or ethnicity begin measuring prevalence at age forty
[139, 140, 142]. Studies generally agree that glaucoma occurs in 2 to 5% of adults
around age forty and 8 to 10% of adults aged eighty and above [139,142?144].
Many studies agree that OAG disproportionately affects racial minorities within
the United States [18]. Within the past 20 years, more effort has been made to dis-
tinguish aspects of glaucoma development in racial minority populations throughout
the United States, typically the Black, Hispanic, and more recently, Asian popula-
tions. For example, one study showed that although Black populations demonstrate
a higher prevalence for glaucoma overall than Caucasian populations, Caucasian
populations have a faster increase of risk in glaucoma than Black and Asian popu-
lations, with the odds ratio of OAG increasing by about 2 per decade for Caucasian
populations and about 1.6 per decade for Black and Asian populations [140]. Other
studies have shown that blindness from glaucoma is at least six times more prevalent
in Black Americans than in Caucasian Americans, and that glaucoma prevalence is
three times higher in Black Americans and Hispanic Americans with Mexican an-
cestry compared to non-Hispanic Caucasian Americans [141]
Socio-demographic factors aside from race should be considered that also may
92
influence the odds of developing glaucoma. Two frequently studied factors are sex
and geographic area. Many studies agree that men are more likely to develop glau-
coma than women, by about 1.5 times [139,140]. Also, a correlation has been found
between urban and rural populations, where individuals living in urban areas are
1.58 times more likely to develop glaucoma than those living in rural areas [139].
A.1.1.2 Other Stakeholders To Consider
There are many other stakeholders to consider aside from socio-demographic
groups that have a higher risk of having or developing glaucoma.
One of the most important aspects of managing glaucoma after diagnosis
are follow-up appointments to monitor glaucomatous progression and administer
medicine [145]. Patients more adherent to a determined follow-up medical schedule
have more favorable outcomes than those who are not [146].
One study conducted in Baltimore, Maryland found three of the largest fac-
tors correlated with inconsistent follow-ups were Black race, Latino ethnicity, and
unfamiliarity with treatment duration [146]. Similarly, one study conducted across
many sites throughout Canada found that the presence of misunderstandings, hesi-
tancy, and lack of formal education led to increases in noncompliance with following
prescribed medication and treatment procedures, such as patients improperly self-
administering eye drops [145].
Therefore, we perceive that the problem is on a much grander scale than sim-
ply a genetic, socioeconomic, or geographic predisposition to developing glaucoma.
93
Many people do not have enough education to understand the treatment process,
and unknowingly allow their glaucoma to progress. This lack of education or un-
derstanding can often be associated with the disproportionate disadvantages certain
socio-demographic groups and communities often have. For instance, socioeconomic
status (SES) is a significant factor that influences the accessibility of resources, level
of education, level of cognitive competency, financial security, and other privileges
and opportunities [147]. In fact, low SES does not only contribute to fewer op-
portunities for wealth accumulation and financial security in afflicted individuals,
but also lower education attainment, poverty, and poor health [147]. In addition,
deep gaps between SES in both the United States and at the global level must be
addressed and mitigated to benefit society as a whole. SES collectively contributes
to and allows for the lingering resource, financial, quality of life, and lastly but
utmost, health distribution inequities that negatively affect the human population
globally [147].
These factors are deeply intertwined with many other factors such as demo-
graphics, politics, economics, education, psychological health and well-being, and
many others, making it an extremely difficult singular issue to tackle [147]. In fact,
many adolescents raised in a household with lower SES will have a (1) slower cogni-
tive development and lower literacy rate, reducing realization that glaucoma leads
to vision loss, as well as the prevalence of noncompliance in following ophthalmol-
ogists? or health professionals? recommendations, (2) greater accrued financial debt
and lower financial income, posing an economic barrier to diagnostic and treatment
options, (3) reduced accessibility to resources and/or leisure time due to working
94
to survive, leading to high levels of psychological stress, potentially making one
hesitant to receiving regular check-ups, or simply ignoring symptoms because they
do not have the time, knowledge, or finances to make an appointment and receive
healthcare [145?147].
Additionally, some people do not have the means to access health care or other
societal infrastructures, such as undocumented immigrants, uninsured patients, and
incarcerated individuals. [148] These indigent individuals have been deprived of or
denied access to healthcare. For example, Jacob Wilensky, MD mentions
?Care of glaucoma patients with limited financial resources is both chal-
lenging and frustrating. These patients are more time-consuming and
costly to treat, but generate less or even no compensation. These pa-
tients need care, and we need to provide that care?
during his address to the joint meeting of the American Academy of Ophthalmology
and the Pan-American Association of Ophthalmology [148]. The major problem is a
disconnect between the needs of the ophthalmologists and these patients. Ophthal-
mologists should provide care to all glaucomatous patients in need, yet even in this
country, there are individuals who have an additional barrier blocking them from
the healthcare that they require.
According to Teresa C. Chen, MD, an associate professor of ophthalmology
at the Harvard Medical School, Massachusetts Eye and Ear Infirmary Glaucoma
Service, ?The current global economic crisis underscores the urgent need for a better
solution for both the physician and, most importantly, the patient? [148]. Hence, we
95
would like to bring to attention this deeply ingrained problem in the United States
where doctors? economic interests and professional responsibilities may be at odds
when it comes to treating patients who cannot afford care. Tackling this problem
would require an overhaul of the current global and national healthcare system,
which adds an additional challenge should our proposed system be implemented in
the future.
Problems with healthcare accessibility are not limited to indigent individuals,
but also apply to the general American population. According to a 2016 Common-
wealth Fund International Health Policy Survey, around 33% of Americans went
without recommended care, did not see a doctor when sick, or did not buy pre-
scription pills [149]. Furthermore, the United States has an incarceration rate of
716 out of 100,000 individuals, which is approximately five times greater than the
United Kingdom with the second highest incarceration rate of 147 out of 100,000
individuals [150]. The United States also has a large population of undocumented
immigrants, which make up ?10.5 million to 12 million, or approximately 3.2%?3.6%
of the population.? [150] Incarcerated individuals and undocumented immigrants do
not have adequate access to healthcare. Most incarcerated individuals are dispropor-
tionately black, when compared with the racial distribution in the general American
population. The Bureau of Justice Statistics reports that of state prisoners, 35%
are Caucasian, 38% are Black, and 12% are Hispanic [151]. Often undocumented
immigrants have lower educational attainment, as a majority of the undocumented
population are from Mexico or Central America, which have by far the smallest
proportion of individuals with a bachelor?s degree: 7% and 11% respectively, in
96
2018 [152]. Additionally, nearly all were non-white, as ?of 9.75 million people,
about 700,000 were white (not Hispanic)?, according to Pew [153]. Therefore, we
see race play a role in who makes up the population of incarcerated individuals or
undocumented immigrants.
There are clear disparities in healthcare treatment between different socio-
demographic communities around the United States. And beyond the general social
inequities that are found throughout all aspects of healthcare in the United States,
several studies have demonstrated specific inequities regarding glaucoma care and
blindness in different populations, spanning from race to insurance coverage, all of
which are part of the intricate web of identity.
Moving in this direction of healthcare accessibility, a study performed in 2018
analyzed the testing and treatment of people with commercial health insurance or
Medicaid recipients [18]. For those with newly-diagnosed OAG, the study found
those with Medicaid were 234% more likely to not receive any glaucoma testing in
the 15 months following initial diagnoses, a portion of time which is crucial for mon-
itoring the disease [154]. This difference was observed across all races and ethnicities
in the study, but the researchers found that it was most notable for Black people
when accounting for confounding factors, who had 291% higher odds of receiving
no glaucoma testing compared to Black people with commercial health insurance.
This is compared to the 198% higher odds of receiving no glaucoma testing for Cau-
casian people. This inequity demonstrates the great differences in ophthalmologic
care not only between races and ethnicities, but also between insurance providers,
exacerbating the difference in care between SES.
97
Many of these indigent individuals are also members of other socio-demographic
groups such as by race, gender, sexual orientation, and ableism, all of which will be
elaborated [147].
There are multiple groups to consider in terms of lower SES and their internal-
ized racial identity such as African Americans, Latinx Americans, Native Americans,
and Asian Americans. Bluestein elaborates in his book, ?The Psychology of Work-
ing: A New Perspective for Career Development, Counseling, and Public Policy?,
that the first two aforementioned groups often face challenges in which many em-
ployers and service providers will have a ?sense of fear, social distance, and at times
pure antagonism? towards these employees or consumers [155]. As for the latter two
groups often there is a perceived difference in cultural attributes and views towards
Western society and lifestyles. [155]. In the case of Asian Americans, there is specif-
ically a model minority myth, but case studies have shown that contrary to this
ideality, ?people from Asian backgrounds face racism, prejudice, and stereotyping
in their educational and working lives? [155].
Additionally, individuals of handicap or disabilities often can be associated
with lower SES. Many of these individuals also are perceived differently externally,
just like previously mentioned with racial identity and face similar difficulties in nav-
igating the American social infrastructure [155]. Also, members of the LGBTQIA+
communities will not only have similar challenges but also a perceived ?discrimina-
tion and stigma in the psychological experience of one?s working life? [155]. Many of
them are trying to navigate their identity and may be conflicted between their pro-
fessional work life and their personal identities. In essence, many socio-demographic
98
factors impact peoples? access to social infrastructure such as healthcare and are in-
timately related to SES.
There are also several studies that display the correlation between region and
visual impairment and blindness [156, 157]. In addition to broader disparities in
equality across large communities like nations or the world, there are regional differ-
ences in prevalence of visual impairment and blindness. One discussed correlation
for these differences is economic development in each region, which itself may be
correlated with factors such as race [158].
To conclude, there are many groups of people that would benefit from lowered
barriers to measurement of IOP?barriers ranging from long wait times to the much
more restrictive obstacles such as decreased literacy, inaccessibility to resources, and
financial instability that face individuals from a lower socioeconomic class [146].
These inequalities are well documented, both quantitatively and qualitatively. In
the United States, racial groups are impacted by OAG differently and race is a
factor in received care for glaucoma, yet institutional barriers also play a role in the
accessibility of glaucoma diagnosis and treatment.
A.1.2 Engaging Stakeholders
Recently, more studies have been done in order to particularly analyze the re-
lationship between glaucoma and traditionally under-studied populations. However,
due to the constraints of this research project, we have been unable to consult many
stakeholders due to our larger focus on the implementation of new technology.
99
It is our hope that, should our technology become fully fleshed out, we are
able to work with stakeholders in order to identify ways to best help communities
whether through outreach or collecting training data or other methods, but much
of engaging stakeholders has remained beyond the scope of our project.
A.1.3 Examining the Causes
As we have discussed in the previous section, there is agreement that there are
inequalities in the treatment and prevalence of visual impairment, blindness, and
OAG. Several pieces on this topic discuss the idea of a Social Gradient, which ?refers
to the fact that inequalities in population health status are related to inequalities
in social status? [159].
There are many complex and related causes for the development and impact of
a Social Gradient with respect to glaucoma and eye-related care. Especially for issues
such as diseases, where genetic disposition interacts with environmental factors for
development, progression, and harm, many causes are present. As we have described
in previous sections, several studies do believe that there are biological differences
between different groups, like racial and sex, which place people at greater risk for
glaucoma, taking other factors into account [140]. However, even when considering
genetic factors, environmental factors controllable by society act as causes as well.
For example, the fact that the rate of glaucoma is higher in urban settings than
rural settings can indirectly impact already marginalized populations that are more
likely to live in urban settings [139].
100
A.2 Our Project
Our project has the goal of being applicable in a variety of settings. We hope
that with a streamlined and forgiving design, our device helps expand the amount
of opportunities to monitor IOP.
A.2.1 Clarifying The Purpose
Our project seeks to help discover methods to accurately and inexpensively
monitor IOP in a way that does not require expertise. One benefit of developing
cheaper and less invasive methods of measuring IOP is that it would not require a
physician to be present in order to measure IOP. This would allow for communities
which do not have access to many physicians to have access to machines, and lower
the barrier to access these tools. This should reduce disparities in healthcare in
communities with less access because it would provide them with more opportunity
to monitor their health.
One way that our neural network may help reduce any existing discrimination
in this field is in its adaptable analysis. As an example, if an ophthalmologist is
trained to measure IOP from one ethnic group, then they risk a biased or inaccurate
measurement for the eyes of other ethnic groups due to genetic differences in the
structure of the cornea. Our neural network approach could offer adaptability to
different corneal parameters.
101
A.2.2 Considering Adverse Impacts
Every research project contains impacts, both foreseen and unforeseen. In ad-
dition, the adoption and implementation of a new technology such as this one could
have a large influence on how it impacts society, so we will explore adverse impacts
of both the technology itself and the possible implementations of the technology.
The main technologically differentiating factor of our product is its use of
machine learning via two neural networks. The first network ?cleans up? input
images, and the second network models the shape of the eye during the deformation
as a series of points in three dimensions. The main inputs that can change the results
of our neural networks are the shape of the eye, the intensity and placement of the
air puff, and the deformation of the eye from the air puff, which is tracked using
a green lattice projected onto the cornea. Again, although this method of tracking
deformation is novel, its output is functionally the same as current tonometers. With
that in mind, one adverse impact this could have is the way in which light reflects
off the eye. We have assumed throughout this process that although populations
may have different eye properties and propensities for diseases like glaucoma, in
general the amount of light reflected from eyes stays constant enough for us to map
the shape of eyes. This of course may not necessarily be the case. Different eye
colors may reflect different amounts of light, which in turn may skew the results
for different ethnic groups who are more likely to have a specific eye color, however
this was beyond the scope of our project. Additionally, there are documented racial
biases in AI that arise from the networks being trained on a narrow data set [160].
102
We believe that our system is more robust to such biases because it was trained on
only corneas, which display lower variance between racial and ethnic groups.
It is our goal to create a technology that is more accessible and usable than
existing tonometry systems, ideally removing the need for an ophthalmologist at
every tonometry reading. However, this could potentially cause adverse impacts.
Results from a survey of glaucoma patients in North India demonstrate that
many people who receive a diagnosis for glaucoma after getting their IOP mea-
sured through tonometers do not have enough education or literacy to adequately
understand their condition [161]. If people feel that with measurement tools, oph-
thalmologists are not needed, then they risk not fully understanding their condition
and receiving improper treatment. It should be noted, however, that consultation
with an ophthalmologist is still necessary. Though our proposed method allows for
glaucoma screening without the direct, hands-on support of a medical professional,
care should be taken to ensure that professionals remain available to assist in inter-
pretation of the results and subsequent treatment decisions. This system does not
replace the need for an ophthalmologist to diagnose and treat glaucoma, it merely
simplifies the screening process so that regular checkups are more widely available
to populations with the greatest needs.
A.2.3 Advancing Equitable Impacts
We will explore possible advanced equitable impacts in the same form as we
explored adverse impacts, first through the technology itself and next through im-
103
plementation.
As mentioned, deep neural networks have already shown great promise in
corneal disease classification and detection. Our project attempts to apply neural
networks to corneal topography and tonometry, and presents potential advantages
for accuracy and efficiency. To date, corneal topographers like the Placido topog-
rapher use algorithms that do not take all the information produced into account,
as in the case of the widely-used SimK algorithm, which attempts to reconstruct
corneal topography from only one of the several Placido rings. Current non-contact
tonometers also fail to consider all information available, as they rely on the two-
dimensional cross-sections produced by the Scheimpflug imaging technique and con-
sequently incur assumptions of radial symmetry to accurately analyze apex motion.
The Scheimpflug technique also introduces the need for a moving camera, which
adds additional complexity and cost to any device implementing it. As our method
produces a three-dimensional map of the cornea using a stationary camera, it re-
moves all assumptions about the geometry of a corneal deformation, and allows for
potential analysis methods that may accurately locate the apex of an applanation,
and incorporate the motion of the surrounding cornea to aid analysis. In addi-
tion, neural networks select spatially invariant, detailed features across an image,
and therefore may take all details about available patterns into account. This cre-
ates the potential for much more accurate analysis using our methods, with fewer
assumptions than in previous methods. In addition, the removal of the rotating
camera track allows for greater efficiency and less manufacturing complexity.
In order to truly provide positive impacts, the method of implementation of
104
this technology is crucial. We have proposed and developed a cheaper method to
more flexibly measure IOP in a way that may be easier to more equitably distribute
than currently available tonometers.
Currently we have only developed a bare-bones camera and projector system,
which requires a housing in the future. However, some components of this setup
can be adapted. The form of the projector grid is crucial, but the camera itself and
imaging software are able to be adapted to the needs of a given community up to a
certain point. As we have mentioned before, this can help to close the healthcare gap
for communities of color who are most at-risk of developing glaucoma. In the future,
if our research were to continue to develop, then it could eliminate the need for a
trained specialist to deliver a tonometry test, and this important health screening
practice could be given in a widely used general clinic or a smaller private practice
that serves those communities. The lowered cost of our proposed measurement
device also means that appointments could be cheaper and more facilities could
acquire the device, both leading to more accessible visual health care.
In addition, though the fitting of the neural network requires a large amount of
computing power, once fit, the network requires much less power to classify a single
image. Either way, the goal is to remove barriers to measuring IOP, and perhaps
it can be developed to the point where a user can operate the tonometer without a
medical care provider at all, if the computing system provides feedback.
Even if a medical care provider is still required, the added flexibility of mea-
surement removes some inequities in implementation: each measurement potentially
takes less time because the imaging system does not require careful centering, and
105
it is less likely to need repetition. Therefore, any given medical care provider can
accommodate a larger number of patients per day.
A.2.4 Examining Alternatives or Improvements
As previously mentioned, unity between technology and implementation is
crucial in order to make the most positive impact. With this in mind, there are
several improvements that can be considered.
The first step is to consult with people who specialize in racial equity and
inclusion in the healthcare field, particularly with eye care, such as ophthalmologists.
Additionally, we can talk to public healthcare and social workers that bridge the
gap between the patients and health professionals. Additionally, better educating
oneself on glaucoma and understanding its risks in causing preventable permanent
blindness and necessary treatments, as well as sharing this information with others
can help bring attention to glaucoma being a real issue. We want to increase the
awareness and health literacy, specifically around glaucoma so that even patients
who have been ignored and mistreated by the current American healthcare and
social infrastructure such as those from racial minority group to those who are
undocumented or on Medicaid can decide to get diagnosed and treated for glaucoma
earlier. Additionally, increasing awareness would allow for these patients to be more
compliant with all the treatment plans prescribed. Taking the step to lower the
barriers for these individuals to find ophthalmologists and have access to healthcare
would help lower the global crisis of people going permanently blind when glaucoma
106
is treatable when diagnosed early.
Lobbying the government and current American and global healthcare infras-
tructures to do more for people with greater obstacles to healthcare will help also
with enabling ophthalmologists to treat indigent individuals who cannot access or
afford healthcare. This would benefit society as a whole, so although a first-world
country, the United States would have a lower gap between people of different so-
cioeconomic and socio-demographic backgrounds, and that the United States does
not brag of a large institutional barrier to healthcare, even if the United States does
have many medicinal and technological research advancements in the world.
Next, another improvement would be to continually analyze our system in
relation to various socio-demographic groups, in order to provide scientific results
on the accuracy of our system as a function of race. Currently there is a wealth of
studies about occurrences of POAG between groups, however, there are not many
studies on the efficacy of measurement techniques on socio-demographic groups.
107
Appendix B: Relevant Code and Repositories
We have several GitHub repositories under the name https://github.com/
teamcontact. Our code for CheckMark may be found at https://github.com/
teamcontact/extract-checkers, and our code for DeepSquish may be found at
https://github.com/teamcontact/checker2cornea.
Diagrams of neural network architectures in this paper were generated using
Haris Iqbal?s PlotNeuralNet library, which may be found at https://github.com/
HarisIqbal88/PlotNeuralNet.
108
Appendix C: Modeling Process
C.1 Modeling
We scaled a hemisphere along the z-axis by a factor of 0.3, producing a flat-
tened surface with approximate similarities to a cornea. We neglected to give the
surface any thickness, as it would negligibly affect its reflective properties. The final
mesh had 241 vertices.
C.2 Lighting
Blender allows for the simulation of projected images using its shader node
editor. Specifically, one can link an image texture to the Strength input of the
Emission node of a Spot lamp. The scaling and offset of the projected texture can
be changed using a Mapping node, and the aperture size of the projector can be
simulated by changing the Size property of the lamp, for varying depths of field.
C.3 Deformations
We chose to create surface deformations using the Displace modifier. While
other methods exist to deform meshes, the Displace modifier modifies actual mesh
109
geometry, allowing for the export of Wavefront OBJ files and therefore a usable
ground truth. The Displace modifier deforms a surface based on the intensity of
an input texture, which may be either procedurally generated or image-based. We
chose to use procedurally generated noise textures, as they would allow us to create
arbitrary amounts of complex deformation data. In particular, we took advantage of
4D Perlin noise. By sampling along the time axis, we obtain a smooth, continuous
series of deformations.
C.4 Simulated Movement and Parameters
We trained the network to deal with variations in angle and distance. We ne-
glected to vary focal length, as the resulting changes in image structure are negligible
at such a shallow depth of field and can simply be simulated via data augmentation.
Our simulated camera has a focal length of 50 millimeters, and begins at a 45 angle
to the corneal surface, 3.68 meters away from the cornea (the cornea is modeled as a
circular surface with a radius of 1 meter). Using Blender?s Noise modifier, we apply
random rotations to the camera.
In a similar manner, we also randomly change the angle of projection onto
the cornea by randomizing the rotation of the simulated ?projector? relative to the
cornea. Additionally, we vary the scale of the projected grid.
110
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