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Abstract

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 natural images, (ii) how large the contribution of each of these mechanisms (shape of filters, non-linear contrast gain control, subdivision into subspace) to redundancy reduction is. For ISA, we find that partitioning the space into different subspace only yields a competitive model when applied after contrast gain control. In this case, however, we find that the single filter responses are already almost independent. Therefore, we conclude that a partitioning into subspaces does not considerably improve the model which makes band-pass filtering (whitening) and contrast gain control (divisive normalization) the two most important mechanisms.