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Geodesic Active Contours
Authors:Caselles  Vicent  Kimmel  Ron  Sapiro  Guillermo
Affiliation:(1) Department of Mathematics and Informatics, University of Illes Balears, 07071 Palma de Mallorca, Spain;(2) Department of Electrical Engineering, Technion, I.I.T., Haifa, 32000, Israel;(3) Hewlett-Packard Labs, 1501 Page Mill Road, Palo Alto, CA, 94304
Abstract:A novel scheme for the detection of object boundaries is presented. The technique is based on active contours evolving in time according to intrinsic geometric measures of the image. The evolving contours naturally split and merge, allowing the simultaneous detection of several objects and both interior and exterior boundaries. The proposed approach is based on the relation between active contours and the computation of geodesics or minimal distance curves. The minimal distance curve lays in a Riemannian space whose metric is defined by the image content. This geodesic approach for object segmentation allows to connect classical ldquosnakesrdquo based on energy minimization and geometric active contours based on the theory of curve evolution. Previous models of geometric active contours are improved, allowing stable boundary detection when their gradients suffer from large variations, including gaps. Formal results concerning existence, uniqueness, stability, and correctness of the evolution are presented as well. The scheme was implemented using an efficient algorithm for curve evolution. Experimental results of applying the scheme to real images including objects with holes and medical data imagery demonstrate its power. The results may be extended to 3D object segmentation as well.
Keywords:dynamic contours  variational problems  differential geometry  Riemannian geometry  geodesics  curve evolution  topology free boundary detection
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