ISSN:
1573-7683
Keywords:
variational segmentation
;
adaptive smoothing
;
nonlinear regularization
;
feature extraction
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We analyze a variational approach to image segmentation that is based on a strictly convex non-quadratic cost functional. The smoothness term combines a standard first-order measure for image regions with a total-variation based measure for signal transitions. Accordingly, the costs associated with “discontinuities” are given by the length of level lines and local image contrast. For real images, this provides a reasonable approximation of the variational model of Mumford and Shah that has been suggested as a generic approach to image segmentation. The global properties of the convex variational model are favorable to applications: Uniqueness of the solution, continuous dependence of the solution on both data and parameters, consistent and efficient numerical approximation of the solution with the FEM-method. Various global and local properties of the convex variational model are analyzed and illustrated with numerical examples. Apart from the favorable global properties, the approach is shown to provide a sound mathematical model of a useful locally adaptive smoothing process. A comparison is carried out with results of a region-growing technique related to the Mumford-Shah model.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1008278718907
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