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Journal of Applied MathematicsVolume 2010 2010, Article ID 761783, 19 pages

Research Article

Dammam University, Faculty of Sciences, PO Box 838, 31113 Dammam, Saudi Arabia

ENIT-LAMSIN, Université de Tunis El Manar, BP 37, 1002 Tunis-Bélvédère, Tunisia

Received 27 July 2010; Accepted 21 November 2010

Academic Editor: Ke Chen

Copyright © 2010 Lamia Jaafar Belaid. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Image analysis by topological gradient approach is a technique based upon the historic application of the topological asymptotic expansion to crack localization problem from boundarymeasurements. This paper aims at reviewing this methodology through various applications in imageprocessing; in particular image restoration with edge detection, classification and segmentation problems for both grey level and color images is presented in this work. The numerical experiments showthe efficiency of the topological gradient approach for modelling and solving different image analysisproblems. However, the topological gradient approach presents a major drawback: the identifiededges are not connected and then the results obtained particularly for the segmentation problem canbe degraded. To overcome this inconvenience, we propose an alternative solution by combining thetopological gradient approach with the watershed technique. The numerical results obtained usingthe coupled method are very interesting.

Autor: Lamia Jaafar Belaid



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