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2010 An Overview of the Topological Gradient Approach in Image Processing: Advantages and Inconveniences
Lamia Jaafar Belaid
J. Appl. Math. 2010: 1-19 (2010). DOI: 10.1155/2010/761783


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.


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Lamia Jaafar Belaid. "An Overview of the Topological Gradient Approach in Image Processing: Advantages and Inconveniences." J. Appl. Math. 2010 1 - 19, 2010.


Published: 2010
First available in Project Euclid: 12 August 2011

zbMATH: 1204.94012
MathSciNet: MR2746345
Digital Object Identifier: 10.1155/2010/761783

Rights: Copyright © 2010 Hindawi


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