The Redundancy Reduction Hypothesis by Barlow and Attneave suggests a link between the statistics of natural images and the physiologically observed structure and function in the early visual system. In particular, algorithms and probabilistic models like Independent Component Analysis, Independent Subspace Analysis and Radial Factorization, which allow for redundancy reduction mechanism, have been used successfully to generate several features of the early visual system such as bandpass filtering, contrast gain control, and orientation selective filtering when applied to natural images.Here, we propose a new family of probability distributions, called Lp-nested symmetric distributions, that comprises all of the above algorithms for natural images. This general class of distributions allows us to quantitatively asses (i) how well the assumptions made by all of the redundancy reducing models are justified for …