When Convex Analysis Meets Mathematical Morphology on Graphs

Abstract : In recent years, variational methods, i.e., the formulation of problems under optimization forms, have had a great deal of success in image processing. This may be accounted for by their good performance and versatility. Conversely, mathematical morphology (MM) is a widely recognized methodology for solving a wide array of image processing-related tasks. It thus appears useful and timely to build bridges between these two fields. In this article, we propose a variational approach to implement the four basic, structuring element-based operators of MM: dilation, erosion, opening, and closing. We rely on discrete calculus and convex analysis for our formulation. We show that we are able to propose a variety of continuously varying operators in between the dual extremes, i.e., between erosions and dilation; and perhaps more interestingly between openings and closings. This paves the way to the use of morphological operators in a number of new applications.
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Communication dans un congrès
Mathematical Morphology and Its Applications to Signal and Image Processing, May 2015, Reykjavik, Iceland. Springer, 9082, pp.473-484, 2015, Lecture Note In Computer Sciences. <10.1007/978-3-319-18720-4_40>
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Contributeur : Laurent Najman <>
Soumis le : vendredi 26 juin 2015 - 15:24:57
Dernière modification le : jeudi 13 octobre 2016 - 14:05:01
Document(s) archivé(s) le : vendredi 9 octobre 2015 - 18:50:58

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Laurent Najman, Jean-Christophe Pesquet, Hugues Talbot. When Convex Analysis Meets Mathematical Morphology on Graphs. Mathematical Morphology and Its Applications to Signal and Image Processing, May 2015, Reykjavik, Iceland. Springer, 9082, pp.473-484, 2015, Lecture Note In Computer Sciences. <10.1007/978-3-319-18720-4_40>. <hal-01168801>

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