Color and depth priors in natural images

Natural scene statistics have played an increasingly important role in both our understanding of the function and evolution of the human vision system, and in the development of modern image processing applications. Because range (egocentric distance) is arguably the most important thing a visual system must compute (from an evolutionary perspective), the joint statistics between image information (color and luminance) and range information are of particular interest. It seems obvious that where there is a depth discontinuity, there must be a higher probability of a brightness or color discontinuity too. This is true, but the more interesting case is in the other direction--because image information is much more easily computed than range information, the key conditional probabilities are those of finding a range discontinuity given an image discontinuity. Here, the intuition is much weaker; the plethora of shadows and textures in the natural environment imply that many image discontinuities must exist without corresponding changes in range. In this paper, we extend previous work in two ways--we use as our starting point a very high quality data set of coregistered color and range values collected specifically for this purpose, and we evaluate the statistics of perceptually relevant chromatic information in addition to luminance, range, and binocular disparity information. The most fundamental finding is that the probabilities of finding range changes do in fact depend in a useful and systematic way on color and luminance changes; larger range changes are associated with larger image changes. Second, we are able to parametrically model the prior marginal and conditional distributions of luminance, color, range, and (computed) binocular disparity. Finally, we provide a proof of principle that this information is useful by showing that our distribution models improve the performance of a Bayesian stereo algorithm on an independent set of input images. To summarize, we show that there is useful information about range in very low-level luminance and color information. To a system sensitive to this statistical information, it amounts to an additional (and only recently appreciated) depth cue, and one that is trivial to compute from the image data. We are confident that this information is robust, in that we go to great effort and expense to collect very high quality raw data. Finally, we demonstrate the practical utility of these findings by using them to improve the performance of a Bayesian stereo algorithm.