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Can Oluk, Wilson S. Geisler; Ideal Observers for the Estimation of Disparity in Random-Pixel Stereograms. Journal of Vision 2020;20(11):578. doi: https://doi.org/10.1167/jov.20.11.578.
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© ARVO (1962-2015); The Authors (2016-present)
Random-pixel stereograms (Julesz, 1960) are routinely used to isolate and study the binocular mechanisms of 3D perception. These stereograms consist of textures where the pixels have gray levels that are statistically independent and identically distributed (IID textures). Typically, the distributions are either Bernoulli (binary) or Gaussian. We derived the ideal observers for these two cases, where the task is to estimate the absolute disparity when the IID texture is a different unknown random sample on each trial, and where “internal noise” is represented by adding some level of independent Gaussian pixel noise that is uncorrelated in the left and right images. The parameters of the IID probability distribution, the standard deviation of internal noise, and the prior over disparity were assumed to be known to the observer.
We compared the performance of the ideal observer with three standard computational observers: cross-correlation (CC), squared error (SE), and normalized cross-correlation (NCC). Simulations show that the NCC observer generally performs better than the CC observer and slightly better than the SE observer. Furthermore, the NCC observer closely approximates the ideal observer if the local patch is sufficiently big. The NCC observer more closely approximates the ideal observer for the IID Gaussian texture than for the IID Bernoulli texture. The overall conclusion is that the NCC observer generally performs close to the ideal observer. Code and demonstrations can be found here: https://github.com/CanOluk/OptimalDisparityEstimation.
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