Towards a Closed Form Second-Order Natural Scene Statistics Model

Previous work on natural scene statistics (NSS)-based image models has focused primarily on characterizing the univariate bandpass statistics of single pixels. These models have proven to be powerful tools driving a variety of computer vision and image/video processing applications, including depth estimation, image quality assessment, and image denoising, among others. Multivariate NSS models descriptive of the joint distributions of spatially separated bandpass image samples have, however, received relatively little attention. Here, we develop a closed form bivariate spatial correlation model of bandpass and normalized image samples that completes an existing 2D joint generalized Gaussian distribution model of adjacent bandpass pixels. Our model is built using a set of diverse, high-quality naturalistic photographs, and as a control, we study the model properties on white noise. We also study the way the model fits are affected when the images are modified by common distortions.