Statistical models on human shapes with application to Bayesian image segmentation and gait recognition

In this dissertation we develop probability models for human shapes and apply those probability models to the problems of image segmentation and human identification by gait recognition. To build probability models on human shapes, we consider human shape to be realizations of random variables on a space of simple closed curves and a space of elastic curves. Both of these spaces are quotient spaces of infinite dimensional manifolds. Our probability models arise through Tangent Principal Component Analysis, a method of studying probability models on manifolds by projecting them onto a tangent plane to the manifold. Since we put the tangent plane at the Karcher mean of sample shapes, we begin our study by examining statistical properties of Karcher means on manifolds. We derive theoretical results for the location of Karcher means on certain manifolds, and perform a simulation study of properties of Karcher means on our shape space. Turning to the specific problem of distributions on human shapes we examine alternatives for probability models and find that kernel density estimators perform well. We use this model to sample shapes and to perform shape testing. The first application we consider is human detection in infrared images. We pursue this application using Bayesian image segmentation, in which our proposed human in an image is a maximum likelihood estimate obtained using a prior distribution on human shapes and a likelihood arising from a divergence measure on the pixels in the image. We then consider human identification by gait recognition. We examine human gait as a cyclo-stationary process on the space of elastic curves and develop a metric on processes based on the geodesic distance between sequences on that space. We develop and demonstrate a framework for gait recognition based on this metric, which includes the following elements: automatic detection of gait cycles, interpolation to register gait cycles, computation of a mean gait cycle, and identification by matching a test cycle to the nearest member of a training set. We perform the matching both by an exhaustive search of the training set and through an expedited method using cluster-based trees and boosting.