Graph-based variational optimization and applications in computer vision. (Optimisation variationnelle discrète et applications en vision par ordinateur)
نویسنده
چکیده
Many computer vision applications such as image filtering, segmentation and stereovision can be formulated as optimization problems. Recently discrete, convex, globally optimal methods have received a lot of attention. Many graph-based methods suffer from metrication artifacts. Segmented contours are blocky in areas where contour information is lacking. In Chapter 2, we develop a discrete yet isotropic energy minimization formulation for the continuous maximum flow problem that prevents metrication errors. This new convex formulation leads us to a provably globally optimal solution. The interior point method can optimize the problem faster than existing continuous methods. The energy formulation is adapted and extended to multi-label problems in Chapter 3 and shows improvements over existing methods. Fast parallel proximal optimization tools have been tested and adapted for the optimization of this latest problem. In Chapter 4 we introduce a framework that generalizes several state-of-the-art graph-based segmentation algorithms, namely graph cuts, random walker, shortest paths, and watershed. This generalization allowed us to exhibit a new case, for which we developed a globally optimal optimization method: “Power watershed”. Our proposed power watershed algorithm computes a unique global solution to multilabeling problems, and is very fast. In Chapter 5, we further generalize and extend the framework to applications beyond image segmentation, for example image filtering optimizing an `0 norm energy, stereovision and fast and smooth surface reconstruction from a noisy cloud of 3D points.
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