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Many tasks in image processing, e.g. segmentation, surface reconstruction, are naturally expressed as energy minimization problems, in which the free variables are shapes, such as curves in 2d or surfaces in 3d. Iterative shape optimization can be used to solve these problems, but can have difficulties, such as slow convergence, sensitivity to initialization, robustness issues. We have developed a framework that leverages 2nd order shape derivatives of the shape energies for a shape-Newton algorithm, and implemented it efficiently with a finite element discretization. Our algorithm shows superior performance on real examples, compared with traditional approaches.