Sparse mathematical morphology using non-negative matrix factorization

Jesus Angulo 1 Santiago Velasco-Forero 1
1 CMM - Centre de Morphologie Mathématique
Abstract : Sparse modelling involves constructing a succinct representation of initial data as a linear combination of a few typical atoms of a dictionary. This paper deals with the use of sparse representations to introduce new nonlinear operators which efficiently approximate the dilation/erosion. Non-negative matrix factorization (NMF) is a dimensional reduction (i.e., dictionary learning) paradigm particularly adapted to the nature of morphological processing. Sparse NMF representations are studied to introduce pseudo-morphological binary dilations/erosions. The basic idea consists in processing exclusively the image dictionary and then, the result of processing each image is approximated by multiplying the processed dictionary by the coefficient weights of the current image. These operators are then extended to grey-level images by means of the level-set decomposition. The performance of the present method is illustrated using families of binary shapes and face images.
Keywords : Current image Dictionary learning Dimensional reduction Face images Grey-level images Level sets Linear combinations Morphological processing Nonlinear operator Nonnegative matrix factorization Sparse representation Succinct representation
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https://hal-mines-paristech.archives-ouvertes.fr/hal-00658963
Contributeur : Bibliothèque Mines Paristech <>
Soumis le : mercredi 11 janvier 2012 - 16:29:17
Dernière modification le : lundi 12 novembre 2018 - 10:53:15

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Jesus Angulo, Santiago Velasco-Forero. Sparse mathematical morphology using non-negative matrix factorization. 10th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing, ISMM 2011, Jul 2011, Verbania-Intra, Italy. pp.1-12, ⟨10.1007/978-3-642-21569-8_1⟩. ⟨hal-00658963⟩

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