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We present a modification of the Mumford–Shah functional and its cartoon limit which allows the incorporation of statistical shape knowledge in a single energy functional. We show segmentation results on artificial and real–world images with and without prior shape information. In the case of occlusion and strongly cluttered background the shape prior significantly improves segmentation. Finall...

Hierarchies, such as the tree of shapes, are popular representations for image simplification and segmentation thanks to their multiscale structures. Selecting meaningful level lines (boundaries of shapes) yields to simplify image while preserving intact salient structures. Many image simplification and segmentation methods are driven by the optimization of an energy functional, for instance th...

The Deligne–Mumford moduli space is the space M̄g,n of isomorphism classes of stable nodal Riemann surfaces of arithmetic genus g with n marked points. A marked nodal Riemann surface is stable if and only if its isomorphism group is finite. We introduce the notion of a universal unfolding of a marked nodal Riemann surface and show that it exists if and only if the surface is stable. A natural co...

this paper describes a new video segmentation method obtained by minimizing an extension of Mumford-Shah functional used for 2D+time partitions. This extension permits to write the MumfordShah functional as an amultiscale energy, which is minimized on a 2D+time persistent hierarchy. The building of this hierarchy based on connected components of spatio-temporal regions.

In this paper, we propose a method for computing partial functional correspondence between non-rigid shapes. We use perturbation analysis to show how removal of shape parts changes the Laplace-Beltrami eigenfunctions, and exploit it as a prior on the spectral representation of the correspondence. Corresponding parts are optimization variables in our problem and are used to weight the functional...

Matching of rigid shapes is an important problem in numerous applications across the boundary of computer vision, pattern recognition and computer graphics communities. A particularly challenging setting of this problem is partial matching, where the two shapes are dissimilar in general, but have significant similar parts. In this paper, we show a rigorous approach allowing to find matching par...