Geodesic Active Contours
 Vicent Caselles,
 Ron Kimmel,
 Guillermo Sapiro
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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 “snakes” 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.
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 Title
 Geodesic Active Contours
 Journal

International Journal of Computer Vision
Volume 22, Issue 1 , pp 6179
 Cover Date
 19970201
 DOI
 10.1023/A:1007979827043
 Print ISSN
 09205691
 Online ISSN
 15731405
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 dynamic contours
 variational problems
 differential geometry
 Riemannian geometry
 geodesics
 curve evolution
 topology free boundary detection
 Industry Sectors
 Authors

 Vicent Caselles ^{(1)}
 Ron Kimmel ^{(2)}
 Guillermo Sapiro ^{(3)}
 Author Affiliations

 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. HewlettPackard Labs, 1501 Page Mill Road, Palo Alto, CA, 94304