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.