Three-Dimensional Natural Scene Statistics: Dependencies between Luminance and Range Contrasts

Abstract

Computing relative or absolute range (egocentric distance) is difficult because, of course, neither is specified in any direct way by the 2D retinal image. If, however, there was a relationship between range and luminance or color, perhaps it could be exploited to yield fast, initial estimates of range from the retinal image per se. We studied the statistical dependence between range (and disparity) contrast and luminance contrast across random point-pairs in natural scenes, and found that changes in range and luminance are highly dependent. We collected high resolution range maps of natural scenes co-registered with luminance (RGB) images using a Riegl terrestrial scanner, co-mounted camera, and in-house software. Various alternative preprocessing stages were used to simulate the early stages of visual processing (e.g. foveation). Our basic approach was to randomly sample pairs of points in the scenes to determine if the change in range or luminance or both exceeded some criterion. We then 1) compared the conditional density of range edges given luminance edges to the (unconditioned) density of range edges and 2) compared the joint distribution of range and luminance contrast to the product of their marginal distributions. We found a robust statistical dependence between range and luminance. Additionally, we computed difference surface maps (between the joint distributions and product-of-marginals predicted by independence). These difference surfaces reveal which regions of luminance and range change exhibit the strongest statistical dependencies. The statistical dependence between luminance and range allows the construction of models where one can assign a probability of occurrence of a range edge given a luminance edge at a particular point in a scene. In principle, such a mechanism could also be used by biological visual system to serve as priors when reconstructing the 3D environment from 2D image data. Meeting abstract presented at VSS 2012