Statistical Cue Integration of DAG Deformable Models

Deformable models are an important tool in computer vision. A deformable model is a curve (in two dimensions) or a surface (in three dimensions), whose shape, position, and orientation are controlled through a set of parameters. They can represent manufactured objects, human faces and skeletons, and even bodies of fluid. Deformable models restrict the family of possible solutions in tracking and fitting applications. With low-level computer vision and image processing techniques, such as optical flow, we extract relevant information from the image(s). Then, we use this information to change the parameters of the model iteratively until we find a good approximation of the object in the image(s). When we have multiple computer vision algorithms providing distinct sources of information (cues), we have to deal with the difficult problem of combining these sometimes conflicting contributions in a sensible way. In this paper, we introduce the use of a directed acyclic graph (DAG) to describe the position and Jacobian of each point on the surface of deformable models. We then describe a new method of statistical cue integration method for tracking and and fitting deformable models. We use affine forms and affine arithmetic to represent and propagate the cues and their regions of confidence. We show when and how we can apply the Lindeberg theorem to justify the use of a Gaussian distribution to approximate each cue. We describe two methods to find such approximations, and use the Berry-Esseen theorem to evaluate the error of such approximation. We finally use a maximum likelihood estimator to integrate the Gaussian distributions describing the different cues. Finally, we demonstrate the technique at work in a 3D deformable face tracking system.