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Nonlocal PdEs on graphs for active contours models with applications to image segmentation and data clustering

Olivier Lezoray 1 Abderrahim Elmoataz 1 Vinh Thong Ta 2
1 Equipe Image - Laboratoire GREYC - UMR6072
GREYC - Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen
Abstract : We propose a transcription on graphs of recent continuous global active contours proposed for image segmentation to address the problem of binary partitioning of data represented by graphs. To do so, using the framework of Partial difference Equations (PdEs), we propose a family of nonlocal regularization functionals that verify the co-area formula on graphs. The gradients of a sub-graph are introduced and their properties studied. Relations, for the case of a sub-graph, between the introduced nonlocal regularization functionals and nonlocal discrete perimeters are exhibited and the co-area formula on graphs is introduced. Finally, nonlocal global minimizers can be considered on graphs with the associated energies. Experiments show the benefits of the approach for nonlocal image segmentation and high dimensional data clustering.
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Olivier Lezoray, Abderrahim Elmoataz, Vinh Thong Ta. Nonlocal PdEs on graphs for active contours models with applications to image segmentation and data clustering. International Conference on Acoustics, Speech, and Signal Processing, 2012, Kyoto, Japan. pp.873 - 876-, ⟨10.1109/ICASSP.2012.6288023⟩. ⟨hal-00708972⟩

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