A Study of a Convex Variational Diffusion Approach for Image Segmentation and Feature Extraction |
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Authors: | Christoph Schnörr |
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Affiliation: | (1) FB Informatik, AB KOGS, Universität Hamburg, Vogt-Kölln-Strasse 30, D-22527 Hamburg, Germany |
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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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Keywords: | variational segmentation adaptive smoothing nonlinear regularization feature extraction |
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