Geodesic
Sparsity-inducing variational shape partitioning
Electronic transactions on numerical analysis, Tome 46 (2017), pp. 36-54
We propose a sparsity-inducing multi-channel multiple region model for the efficient partitioning of a mesh into salient parts. Our approach is based on rewriting the Mumford-Shah models in terms of piece-wise smooth/constant functionals that incorporate a non-convex regularizer for minimizing the boundary lengths. The solution of this optimization problem, obtained by an efficient proximal forward backward algorithm, is used by a simple thresholding/clusterization procedure to segment the shape into the required number of parts. Therefore, it is not necessary to further solve the optimization problem for a different number of partitioning regions. Experimental results show the effectiveness and efficiency of our proposals when applied to both single- and multi-channel (shape characterizing) functions.
Classification : 65M10, 78A48
Keywords: mesh decomposition, variational segmentation, non-convex minimization, spectral clustering 
@article{ETNA_2017__46__a11,
     author = {Morigi,  Serena and Huska,  Martin},
     title = {Sparsity-inducing variational shape partitioning},
     journal = {Electronic transactions on numerical analysis},
     pages = {36--54},
     year = {2017},
     volume = {46},
     zbl = {1357.78009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2017__46__a11/}
}
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%A Huska,  Martin
%T Sparsity-inducing variational shape partitioning
%J Electronic transactions on numerical analysis
%D 2017
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%F ETNA_2017__46__a11
Morigi,  Serena; Huska,  Martin. Sparsity-inducing variational shape partitioning. Electronic transactions on numerical analysis, Tome 46 (2017), pp. 36-54. http://geodesic.mathdoc.fr/item/ETNA_2017__46__a11/