In this talk we describe two different approaches to nonlinear image analysis and segmentation. The first of these, which can be thought of as a limiting form of so-called anisotropic diffusions results in a coupled set of differential equations with discontinuous right-hand sides. At each point in the evolution of this system, the image has been partitioned into a set of disjoint regions (starting from the trivial partition in which every pixel is a distinct region), and there is one DE for each such region. Thanks to the form of the RHS, the evolution causes regions to merge, producing a nested sequence of segmentations. Experimental results demonstrate the robustness of this algorithm to severe image degradations such as speckle. We will also describe the mathematical properties of these evolutions, their ties to robust edge-preserving priors, and the use of such an evolution for ML segmentation.
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