Statistical Cue Estimation for Model-based Shape and Motion Tracking

STATISTICAL CUE ESTIMATION FOR MODEL-BASED SHAPE AND MOTION TRACKING Siome Goldenstein Supervisor: Dimitris Metaxas Vision-based tracking of moving objects is important in many applications, ranging from sports and medicine to security and recognition of human action. In this dissertation we discuss novel methods for statistical deformable model tracking. Our main contribution is a method to estimate the probability distributions of the observations in a deformable model tracking system. This method offers the compelling advantage that it does not require us to make many of the traditional assumptions about the underlying probability distributions of the cues. Despite this advantage, it still is fast; the run time overhead over non-statistical approaches is only 5-10%. Our technique is based on the connection between affine forms, zonotopes, and Gaussian distributions. We use affine forms to bound and propagate confidences of image forces to confidences of the generalized forces in parameter space. Because its components are uniformly bounded, Lindeberg’s theorem tells us that we can use a Gaussian distribution to approximate the random variable of the generalized force, described by the resulting affine form. The Berry-Esseen theorem provides an upper bound for the error in the optimal Gaussian approximation, and helps us to determine how many image forces are necessary to obtain a good Gaussian approximation. Unlike many other statistical methods our technique is suited for systems with large number of degrees of freedom. We present two applications for the estimation of the cue distributions: automatic adaptive integration of different cues using a maximum likelihood estimator, and the distribution estimation of the observations for a predictive filter. In this dissertation we also introduce the use directed acyclic graphs as powerful data structure to represent and implement deformable models. It allows us the creation of powerful and complex models with very few primitives. Finally we show examples, evaluate and validate (both qualitatively and quantitatively) the benefits of our method in real face tracking experiments using a model with 11 degrees of freedom.