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Bayesian Algorithms for Vision Acuity Tests
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David Nissan Cohen, M.Sc. Thesis Seminar
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Tuesday, 4.6.2019, 11:30
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Taub 601
Host:  Prof. Ran El-Yaniv
Visual acuity (VA) tests are widely used in ophthalmology to measure vision quality, but even modern tests still rely on an algorithm created in 1976 \cite{Bailey1976}. This algorithm is basically the original VA test algorithm from 1873 \cite{Snellen1873}, with minor modifications. The tests measure VA by requiring the examinee to identify different letters from a table that is positioned in a fixed distance. In this thesis, we present a novel way to assess VA by using a computerized software we developed, instead of the fixed tables that are currently used. Our method achieves better precision, even when presenting a smaller number of letters, thus creating a faster, more accurate VA test. To develop our software, we model the relation between the size of the presented letter and the probability of an examinee to identify it correctly. While this relation is key in many ophthalmology research (commonly referred to as "the S curve"), and some mathematical models have been used to model it, to the best of our knowledge, we are the first to empirically validate and compare these existing models. Additionally, we present a formalization for the existing VA test and provide the first known theoretical analysis for them. By doing so, we show a theoretical bias in the existing VA test and demonstrate this bias in clinical settings. Using these new insights, we developed a novel method to assess VA. Our method uses the examinee responses to the previously shown letters to create a Bayesian model of the examinee’s eyesight. Based on the Bayesian model, we calculate the next letter size by minimizing the expected entropy of the previous round model. Finally, we conducted a clinical study in which we compare our methods and the per letter methods, which is the gold standard for VA tests, showing a significant improvement in precision and number of letters presented per test.
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