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Minimal partitions and image classification using a gradient-free perimeter approximation

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dc.contributor.author Amstutz, Samuel
dc.contributor.author Novotny, Antonio André
dc.contributor.author Van Goethem, Nicolas
dc.date.accessioned 2013-07-03T10:35:29Z
dc.date.available 2013-07-03T10:35:29Z
dc.date.issued 2013-07-03
dc.identifier.uri http://preprints.sissa.it/xmlui/handle/1963/6976
dc.description.abstract In this paper a new mathematically-founded method for the optimal partitioning of domains, with applications to the classification of greyscale and color images, is proposed. Since optimal partition problems are in general ill-posed, some regularization strategy is required. Here we regularize by a non-standard approximation of the total interface length, which does not involve the gradient of approximate characteristic functions, in contrast to the classical Modica-Mortola approximation. Instead, it involves a system of uncoupled linear partial differential equations and nevertheless shows $\Gamma$-convergence properties in appropriate function spaces. This approach leads to an alternating algorithm that ensures a decrease of the objective function at each iteration, and which always provides a partition, even during the iterations. The efficiency of this algorithm is illustrated by various numerical examples. Among them we consider binary and multilabel minimal partition problems including supervised or automatic image classification, inpainting, texture pattern identification and deblurring. en_US
dc.language.iso en en_US
dc.publisher SISSA en_US
dc.title Minimal partitions and image classification using a gradient-free perimeter approximation en_US
dc.type Preprint en_US
dc.subject.keyword Image classification, deblurring, optimal partitions, perimeter approximation en_US
dc.subject.miur MAT/05 ANALISI MATEMATICA
dc.miur.area 1 en_US
dc.contributor.area Mathematics en_US


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