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.
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Schnörr, C. A Study of a Convex Variational Diffusion Approach for Image Segmentation and Feature Extraction. Journal of Mathematical Imaging and Vision 8, 271–292 (1998). https://doi.org/10.1023/A:1008278718907
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DOI: https://doi.org/10.1023/A:1008278718907