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Wilson Geisler, Jeffrey Perry; Combining Perceptual Estimates Using Recursive Conditional Means (RCM). Journal of Vision 2013;13(9):1266. doi: https://doi.org/10.1167/13.9.1266.
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© ARVO (1962-2015); The Authors (2016-present)
Many tasks performed by real and artificial visual systems involve combining multiple noisy estimates of a given variable (e.g., depth) to obtain a more accurate estimate of the variable. In the classic approach, estimates are obtained independently (e.g., in parallel) and then combined linearly, where the weight on each estimate is its relative reliability. We describe a more powerful and computationally efficient approach, where estimates are obtained and combined recursively. This approach is demonstrated for estimates based on natural image statistics in the specific task of denoising images corrupted with multiplicative (Poisson-like) noise, but the approach is applicable to many visual processing tasks. First consider the classic approach for the case where each estimate is a Bayesian optimal estimate given a particular set of observed variables (a "context"). If the goal (cost function) is to minimize squared estimation error, then each optimal estimate is simply the conditional mean of the unknown variable given the context, and the reliability of each estimate is the inverse of the conditional variance given the context. As mentioned above these estimates are combined linearly to get the final estimate. Now consider the RCM approach. In this case, each estimate is also a Bayesian optimal estimate based on a context. However, the estimates obtained from the first context serve as part of the second context; the estimates from the second context serve as part of the third context; and so on. We show that the RCM approach performs better than the classic approach, does not require knowing conditional variances, and yields denoising performance that exceeds the state-of-the-art algorithms in the image processing literature. Importantly, the RCM approach is simple and could be implemented hierarchically with plausible neural circuits. Thus, it represents a viable new alternative for how sensory estimates are combined in neural systems.
Meeting abstract presented at VSS 2013
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