Journal of Applied Mathematics
Volume 2010 (2010), Article ID 761783, 19 pages
Research Article

An Overview of the Topological Gradient Approach in Image Processing: Advantages and Inconveniences

1Dammam University, Faculty of Sciences, PO Box 838, 31113 Dammam, Saudi Arabia
2ENIT-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 boundary measurements. This paper aims at reviewing this methodology through various applications in image processing; 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 show the efficiency of the topological gradient approach for modelling and solving different image analysis problems. However, the topological gradient approach presents a major drawback: the identified edges are not connected and then the results obtained particularly for the segmentation problem can be degraded. To overcome this inconvenience, we propose an alternative solution by combining the topological gradient approach with the watershed technique. The numerical results obtained using the coupled method are very interesting.