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<p><b>Abstract</b>—Deformable models are a useful modeling paradigm in computer vision. A deformable model is a curve, a surface, or a volume, 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. With low-level computer vision and image processing techniques, such as optical flow, we extract relevant information from images. Then, we use this information to change the parameters of the model iteratively until we find a good approximation of the object in the images. When we have multiple computer vision algorithms providing distinct sources of information (<it>cues</it>), 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 (<scp>dag</scp>) to describe the position and Jacobian of each point of deformable models. This representation is dynamic, flexible, and allows computational optimizations that would be difficult to do otherwise. We then describe a new method for statistical cue integration method for tracking deformable models that scales well with the dimension of the parameter space. We use <it>affine forms</it> and <it>affine arithmetic</it> to represent and propagate the cues and their regions of confidence. We show that we can apply the <it>Lindeberg</it> theorem to approximate each cue with a Gaussian distribution, and can use a <it>maximum-likelihood estimator</it> to integrate them. Finally, we demonstrate the technique at work in a 3D deformable face tracking system on monocular image sequences with thousands of frames.</p>
Statistical cue integration, deformable model tracking, affine arithmetic, face tracking, directed acyclic graphs, deformable model representation.

S. K. Goldenstein, C. Vogler and D. Metaxas, "Statistical Cue Integration in DAG Deformable Models," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 25, no. , pp. 801-813, 2003.
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