The Current State of Bayesian Image Analysis
Raymond Hoffmann
Medical College of Wisconsin
Edgar A. Deyoe
Radiology, Medical College of Wisconsin
Data: The Visual Field Map (VFM) is obtained by activating the visual cortex in the brain with a dynamic target presented to the subject. Changes in the visual system can be simulated with images that have different size wedges (0, 18, 27, 36, 45 and 90 degrees) removed from a circular disk which is presented to the subject's eye. The output of the visual system is a set of activated voxels (from 295 to 619) in the visual cortex determined by functional MRI, which then is used to induce a figure on a virtual circular retina using an (r, theta) representation for the location. The virtual retina will have more points in the center as does the real retina. Methods: A Bayesian non-parametric spatial model, a spatial Dirichlet Process model, is used to model the ratio of two different images induced by the two different angular wedges. Gelfand, Kottas and MachEachern (JASA, 2005) introduced a Dirichlet Process as a prior mixing distribution on the family of densities DP(v G). Under the null hypothesis of no difference, the ratio of the two densities will have a constant posterior density. Deviations from this will be used to indicate the probability of a perturbed visual system.