In recent years, bandpass statistical models of natural, photographic images of the world have been used with great success to solve highly diverse problems involving image representation, image repair, image quality assessment (IQA), and image compression. One missing element has been a reliable and generic model of spatial image correlation that reflects the distributions of oriented and relatively oriented spatial structures. We have developed such a model for bandpass pristine images and have generalized it here to also capture the spatial correlation structure of bandpass distorted images. The model applies well to both luminance and depth images. As a demonstration of the usefulness of the generalized model, we develop a new no-reference stereoscopic/3D IQA framework, dubbed stereoscopic/3D blind image naturalness quality index, which utilizes both univariate and generalized bivariate natural scene statistics (NSS) models. We first validate the robustness and effectiveness of these novel bivariate and correlation NSS features extracted from distorted stereopairs, then demonstrate that they are predictive of distortion severity. Our experimental results show that the resulting 3D image quality predictor based in part on the new model outperforms state-of-the-art full- and no-reference 3D IQA algorithms on both symmetrically and asymmetrically distorted stereoscopic image pairs.