WEBERâ€™S LAW AND THE STATISTICS OF THE NATURAL ENVIRONMENT
Weberâ€™s law is one of the most fundamental properties of visual processing. This raises the question of why and how the underlying neural circuitry has developed. Here we propose that the emergence of Weberâ€™s law can be seen as a by-product of a more general evolutionary strategy for the development of sensory systems: the adaptation to the statistical regularities of natural scenes. Many basic properties of early vision have already been successfully explained within this framework. Here we extend this approach by measuring the joint statistics of neighbouring pixels of natural images under varying illumination conditions. We demonstrate that a linear decorrelating transform would leave significant statistical dependencies between the responses. We then show that the removal of these dependencies can be achieved by learning from the statistics a nonlinear gain control mechanism which can be implemented as ROG (ratio of Gaussian) filter. Weberâ€™s law is a direct consequence of this nonlinear operation. One single basic principle, the reduction of statistical dependencies between sensory messages, thus seems to be sufficient to derive all essential processing properties of early vision.