Natural Image Coding in V1: How Much Use is Orientation Selectivity?
  Orientation selectivity is the most striking feature of simple cell coding in V1 which has been shown to emerge from the reduction of higher-order correlations in natural images in a large variety of statistical image models. The most parsimonious one among these models is linear Independent Component Analysis (ICA), whereas second-order decorrelation transformations such as Principal Component Analysis (PCA) do not yield oriented filters. Because of this finding it has been suggested that the emergence of orientation selectivity may be explained by higher-order redundancy reduction. In order to assess the tenability of this hypothesis, it is an important empirical question how much more redundancies can be removed with ICA in comparison to PCA, or other second-order decorrelation methods. This question has not yet been settled, as over the last ten years contradicting results have been reported ranging from less than five to more than hundred percent extra gain for ICA. Here, we aim at resolving this conflict by presenting a very careful and comprehensive analysis using three evaluation criteria related to redundancy reduction: In addition to the multi-information and the average log-loss we compute, for the first time, complete rate-distortion curves for ICA in comparison with PCA. Without exception, we find that the advantage of the ICA filters is surprisingly small. Furthermore, we show that a simple spherically symmetric distribution with only two parameters can fit the data even better than the probabilistic model underlying ICA. Since spherically symmetric models are agnostic with respect to the specific filter shapes, we conlude that orientation selectivity is unlikely to play a critical role for redundancy reduction. 
Jan Eichhorn, Fabian Sinz and Matthias Bethge