Statistics of gradient directions in natural images.

Interest in finding statistical regularities in natural images has been growing since the advent of information theory and the advancement of the efficient coding hypothesis that the human visual system is optimised to encode natural visual stimuli. In this thesis, a statistical analysis of gradient directions in an ensemble of natural images is reported. Information-theoretic measures have been used to compute the amount of dependency which exists between triples of gradient directions at separate image locations. Control experiments are performed on other image classes: phase randomized natural images, whitened natural images, and Gaussian noise images. The main results show that for an ensemble of natural images the average amount of de pendency between two and three gradient directions is the same as for an ensemble of phase randomized natural images. This result does not extend to i) the amount dependency between gradient magnitudes, ii) gradient directions at high gradient magnitude locations, or iii) individual natural images. Furthermore, no significant synergetic dependencies are found between triples of gradient directions in an ensemble natural images a synergetic dependency is an increase in dependency between a pair of gradient directions given the interaction of a third gradient direction. Additional experiments are performed to establish both the generality and specificity of the main results by studying the gradient direction dependencies of ensembles of noise (random phases) images with varying power law power spectra. The results of the additional experiments indicate that, for ensembles of images with varying power law power spectra, the amount of dependency between two and three gradient directions is determined by the ensemble's mean power spectrum rather than the phase spectrum. A framework is also presented for future work and preliminary results are provided for the dependency between second order derivative measurements (shape index) for up to 9-point configurations