New bivariate statistical model of natural image correlations

We perform bivariate statistical analysis and modeling of the joint distributions of spatially adjacent sub-band responses for both luminance/chrominance and range data in natural scenes. In particular, we introduce a multivariate generalized Gaussian distribution and an exponentiated sine function to model the underlying statistics and correlations. The experimental results show that the bivariate statistics relating spatially adjacent pixels in both 2D color images and range maps are well described by the proposed models. We validate the robustness of the proposed bivariate models using a multi-variate statistical hypothesis test, and further demonstrate their effectiveness with application to a prototype depth estimation algorithm.