A comparison of natural-image-based models of simple-cell coding

Models such as that of Olshausen and Field (O&F, 1997 Vision Research 37 3311-3325) and principal components analysis (PCA) have been used to model simple-cell receptive fields, and to try to elucidate the statistical principles underlying visual coding in area V1. They connect the statistical structure of natural images with the statistical structure of the coding used in V1. The O&F model has created particular interest because the basis functions it produces resemble the receptive fields of simple cells. We evaluate these models in terms of their sparseness and dispersal, both of which have been suggested as desirable for efficient visual coding. However, both attributes have been defined ambiguously in the literature, and we have been obliged to formulate specific definitions in order to allow any comparison between models at all. We find that both attributes are strongly affected by any preprocessing (e.g. spectral pseudo-whitening or a logarithmic transformation) which is often applied to images before they are analysed by PCA or the O&F model. We also find that measures of sparseness are affected by the size of the filters--PCA filters with small receptive fields appear sparser than PCA filters with larger spatial extent. Finally, normalisation of the means and variances of filters influences measures of dispersal. It is necessary to control for all of these factors before making any comparisons between different models. Having taken these factors into account, we find that the code produced by the O&F model is somewhat sparser than the code produced by PCA. However, the difference is rather smaller than might have been expected, and a measure of dispersal is required to distinguish clearly between the two models.