Center for Neural Science and Courant Institute for Mathematical Sciences, New York University
Cortical Normalization Models and the Statistics of Visual Images
I present a parametric statistical model for visual images in the wavelet transform domain. The model characterizes the joint densities of coefficients corresponding to basis functions at adjacent spatial locations, adjacent orientations, and adjacent spatial scales. The model is consistent with the statistics of a wide variety of images, including photographs of indoor and outdoor scenes, medical images, and synthetic (graphics) images, and has been used successfully in applications of compression, noise removal, and texture synthesis. The model also suggests a nonlinear method of removing these dependencies, which I call ``normalized component analysis'', in which each wavelet coefficient is divided by a linear combination of coefficient magnitudes at adjacent locations, orientations and scales. This analysis provides a theoretical justification for recent divisive normalization models of striate visual cortex. Furthermore, the statistical measurements may be used to determine the weights that are used in computing the normalization signal. The resulting model makes specific predictions regarding non-specific suppression and adaptation behaviors of cortical neurons, and thus offer the opportunity to test directly (through physiological measurements) the ecological hypothesis that visual neural computations are optimally matched to the statistics of images.