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Proceedings Paper

Alternative method for Hamilton-Jacobi PDEs in image processing
Author(s): A. Lagoutte; H. Salat; C. Vachier
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Paper Abstract

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.

Paper Details

Date Published: 4 February 2011
PDF: 10 pages
Proc. SPIE 7870, Image Processing: Algorithms and Systems IX, 787010 (4 February 2011); doi: 10.1117/12.872591
Show Author Affiliations
A. Lagoutte, ENS Cachan, CNRS (France)
H. Salat, ENS Cachan, CNRS (France)
C. Vachier, ENS Cachan, CNRS (France)

Published in SPIE Proceedings Vol. 7870:
Image Processing: Algorithms and Systems IX
Jaakko T. Astola; Karen O. Egiazarian, Editor(s)

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