Bivariate statistical modeling of color and range in natural scenes

The statistical properties embedded in visual stimuli from the surrounding environment guide and affect the evolutionary processes of human vision systems. There are strong statistical relationships between co-located luminance/chrominance and disparity bandpass coefficients in natural scenes. However, these statistical relationships have only been deeply developed to create point-wise statistical models, although there exist spatial dependencies between adjacent pixels in both 2D color images and range maps. Here we study the bivariate statistics of the joint and conditional distributions of spatially adjacent bandpass responses on both luminance/chrominance and range data of naturalistic scenes. We deploy bivariate generalized Gaussian distributions to model the underlying statistics. The analysis and modeling results show that there exist important and useful statistical properties of both joint and conditional distributions, which can be reliably described by the corresponding bivariate generalized Gaussian models. Furthermore, by utilizing these robust bivariate models, we are able to incorporate measurements of bivariate statistics between spatially adjacent luminance/chrominance and range information into various 3D image/video and computer vision applications, e.g., quality assessment, 2D-to-3D conversion, etc.