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Center for Nonlinear Studies |
The information contained in an image ("What does the image represent?") also has a geometric interpretation ("Where does the image reside in the ambient signal space?"). It is often enlightening to consider this geometry in order to better understand the processes governing the specification, discrimination, or understanding of an image. This work concentrates on manifold-based models for image processing imposed, for example, by the geometric regularity of objects in images. We will discuss applications in computer vision, where we face a surprising barrier -- the image manifolds arising in many interesting situations are in fact nondifferentiable. Although this appears to complicate the process of parameter estimation, we identify a multiscale tangent structure to these manifolds that permits a coarse-to-fine Newton method. We will also discuss applications in the emerging field of Compressive Sensing, where in certain cases a manifold model can supplant sparsity as the key for image recovery from incomplete information.
Host: DDMA Speaker Series