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

[摘要] 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.

[学科分类] 应用数学