- International Journal of Computer Vision...

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Unformatted text preview: International Journal of Computer Vision 22(1), 61–79 (1997) c 1997 Kluwer Academic Publishers. Manufactured in The Netherlands. Geodesic Active Contours VICENT CASELLES Department of Mathematics and Informatics, University of Illes Balears, 07071 Palma de Mallorca, Spain [email protected] RON KIMMEL Department of Electrical Engineering, Technion, I.I.T., Haifa 32000, Israel [email protected] GUILLERMO SAPIRO Hewlett-Packard Labs, 1501 Page Mill Road, Palo Alto, CA 94304 [email protected] Received October 17, 1994; Revised February 13, 1995; Accepted July 5, 1995 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 “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. Keywords: dynamic contours, variational problems, differential geometry, Riemannian geometry, geodesics, curve evolution, topology free boundary detection 1. Introduction Since original work by Kass et al. (1988), extensive research was done on “snakes” or active contour mo- dels for boundary detection. The classical approach is based on deforming an initial contour C towards the boundary of the object to be detected. The deformation is obtained by trying to minimize a functional designed so that its (local) minimum is obtained at the boundary of the object. These active contours are examples of the general technique of matching deformable models to image data by means of energy minimization (Blake and Zisserman, 1987; Terzopoulos et al., 1988). The energy functional is basically composed of two com- ponents, one controls the smoothness of the curve and another attracts the curve towards the boundary. This energy model is not capable of handling changes in the topology of the evolving contour when direct im- plementations are performed. Therefore, the topology of the final curve will be as the one of C (the initial 62...
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