Minimal surfaces: a geometric three dimensional segmentation approach

作者: Vicent Caselles , Ron Kimmel , Guillermo Sapiro , Catalina Sbert

DOI: 10.1007/S002110050294

关键词:

摘要: A novel geometric approach for three dimensional object segmentation is presented. The scheme based on deformable surfaces moving towards the objects to be detected. We show that this model related computation of minimal area (local surfaces). space where these are computed induced from image in which general also shows relation between classical obtained via energy minimization and ones derived curvature flows surface evolution framework. stable, robust, automatically handles changes topology during deformation. Results existence, uniqueness, stability, correctness solution presented as well. Based an efficient numerical algorithm evolution, we present a number examples detection real synthetic images.

参考文章(52)
R. Malladi, J. A. Sethian, B. C. Vemuri, Evolutionary fronts for topology-independent shape modeling and recovery european conference on computer vision. ,vol. 800, pp. 3- 13 ,(1994) , 10.1007/3-540-57956-7_1
Matthew A. Grayson, The heat equation shrinks embedded plane curves to round points Journal of Differential Geometry. ,vol. 26, pp. 285- 314 ,(1987) , 10.4310/JDG/1214441371
Benjamin B. Kimia, Allen Tannenbaum, Steven W. Zucker, Toward a computational theory of shape: an overview european conference on computer vision. pp. 402- 407 ,(1990) , 10.1007/BFB0014889
M. Gage, R. S. Hamilton, The heat equation shrinking convex plane curves Journal of Differential Geometry. ,vol. 23, pp. 69- 96 ,(1986) , 10.4310/JDG/1214439902
Peter Olver, Guillermo Sapiro, Allen Tannenbaum, Differential Invariant Signatures and Flows in Computer Vision: A Symmetry Group Approach Geometry-Driven Diffusion in Computer Vision. pp. 255- 306 ,(1994) , 10.1007/978-94-017-1699-4_11
Manfredo Perdigão do Carmo, Differential geometry of curves and surfaces ,(1976)
Laurent D. Cohen, Ron Kimmel, Global Minimum for Active Contour Models: A Minimal Path Approach International Journal of Computer Vision. ,vol. 24, pp. 57- 78 ,(1997) , 10.1023/A:1007922224810
Guillermo Sapiro, Ron Kimmel, Doron Shaked, Benjamin B Kimia, Alfred M Bruckstein, IMPLEMENTING CONTINUOUS-SCALE MORPHOLOGY VIA CURVE EVOLUTION Pattern Recognition. ,vol. 26, pp. 1363- 1372 ,(1993) , 10.1016/0031-3203(93)90142-J
G. Sapiro, A. Tannenbaum, On Affine Plane Curve Evolution Journal of Functional Analysis. ,vol. 119, pp. 79- 120 ,(1994) , 10.1006/JFAN.1994.1004
David Adalsteinsson, James A. Sethian, A Fast Level Set Method for Propagating Interfaces Journal of Computational Physics. ,vol. 118, pp. 269- 277 ,(1995) , 10.1006/JCPH.1995.1098