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Communication Dans Un Congrès Année : 2011

Alternative method for Hamilton-Jacobi PDEs in image processing

Résumé

Multiscale signal analysis has been used since the early 1990s as a powerful tool for image processing, notably in the linear case. However, nonlinear PDEs and associated nonlinear operators have advantages over linear operators, notably preserving important features such as edges in images. In this paper, we focus on nonlinear Hamilton-Jacobi PDEs defined with adaptive speeds or, alternatively, on adaptive morphological fiters also called semi-flat morphological operators. Semi-flat morphology were instroduced by H. Heijmans and studied only in the case where the speed (or equivalently the filtering parameter) is a decreasing function of the luminance. It is proposed to extend the definition suggested by H. Heijmans in the case of non decreasing speeds. We also prove that a central property for defining morphological filters, that is the adjunction property, is preserved while dealing with our extended definitions. Finally experimental applications are presented on actual images, including connection of thin lines by semi-flat dilations and image filtering by semi-flat openings.
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Dates et versions

hal-01508512 , version 1 (14-04-2017)

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Aurélie Lagoutte, Hadrien Salat, Corinne Vachier. Alternative method for Hamilton-Jacobi PDEs in image processing. Image Processing: Algorithms and Systems IX, Jan 2011, San Francisco, CA, United States. pp.787010, ⟨10.1117/12.872591⟩. ⟨hal-01508512⟩
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