Minimal Surfaces Based Object Segmentation

A geometric approach for 3D object segmentation and representation is presented. The segmentation is obtained by deformable surfaces moving towards the objects to be detected in the 3D image. The model is based on curvature motion and the computation of surfaces with minimal areas, better known as minimal surfaces. The space where the surfaces are computed is induced from the 3D image (volumetric data) in which the objects are to be detected. The model links between classical deformable surfaces obtained via energy minimization, and intrinsic ones derived from curvature based flows. The new approach is stable, robust, and automatically handles changes in the surface topology during the deformation.

[1]  Vicent Caselles,et al.  What is the Best Causal Scale Space for Three-Dimensional Images? , 1996, SIAM J. Appl. Math..

[2]  V. Caselles,et al.  What is the best causal scale-space for 3D images , 1994 .

[3]  Richard Szeliski,et al.  Modeling surfaces of arbitrary topology with dynamic particles , 1993, Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[4]  Laurent D. Cohen,et al.  Using Deformable Surfaces to Segment 3-D Images and Infer Differential Structures , 1992, ECCV.

[5]  Guillermo Sapiro,et al.  Invariant Geometric Evolutions of Surfaces and Volumetric Smoothing , 1997, SIAM J. Appl. Math..

[6]  S. Osher,et al.  Algorithms Based on Hamilton-Jacobi Formulations , 1988 .

[7]  Anthony J. Yezzi,et al.  A geometric snake model for segmentation of medical imagery , 1997, IEEE Transactions on Medical Imaging.

[8]  M. Gage,et al.  The heat equation shrinking convex plane curves , 1986 .

[9]  Tai Sing Lee,et al.  Region competition: unifying snakes, region growing, energy/Bayes/MDL for multi-band image segmentation , 1995, Proceedings of IEEE International Conference on Computer Vision.

[10]  Demetri Terzopoulos,et al.  Topologically adaptable snakes , 1995, Proceedings of IEEE International Conference on Computer Vision.

[11]  Benjamin B. Kimia,et al.  Image segmentation by reaction-diffusion bubbles , 1995, Proceedings of IEEE International Conference on Computer Vision.

[12]  Demetri Terzopoulos,et al.  Constraints on Deformable Models: Recovering 3D Shape and Nonrigid Motion , 1988, Artif. Intell..

[13]  Alfred M. Bruckstein,et al.  Finding Shortest Paths on Surfaces Using Level Sets Propagation , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[14]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[15]  Anthony J. Yezzi,et al.  Gradient flows and geometric active contour models , 1995, Proceedings of IEEE International Conference on Computer Vision.

[16]  D. Chopp.  Computing Minimal Surfaces via Level Set Curvature Flow , 1993 .

[17]  V. Caselles,et al.  A geometric model for active contours in image processing , 1993 .

[18]  P. Olver,et al.  Conformal curvature flows: From phase transitions to active vision , 1996, ICCV 1995.

[19]  Andrew Blake,et al.  Visual Reconstruction , 1987, Deep Learning for EEG-Based Brain–Computer Interfaces.

[20]  Baba C. Vemuri,et al.  Shape Modeling with Front Propagation: A Level Set Approach , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[21]  J. Sethian,et al.  A Fast Level Set Method for Propagating Interfaces , 1995 .

[22]  J. Sethian,et al.  A geometric approach to segmentation and analysis of 3D medical images , 1996, Proceedings of the Workshop on Mathematical Methods in Biomedical Image Analysis.

[23]  Laurent D. Cohen,et al.  Global Minimum for Active Contour Models: A Minimal Path Approach , 1996, Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[24]  Dimitris N. Metaxas,et al.  Dynamic 3D models with local and global deformations: deformable superquadrics , 1990, [1990] Proceedings Third International Conference on Computer Vision.

[25]  Ross T. Whitaker,et al.  Algorithms for implicit deformable models , 1995, Proceedings of IEEE International Conference on Computer Vision.

[26]  B KimiaBenjamin,et al.  Shapes, shocks, and deformations I , 1995 .

[27]  R. Osserman.  A survey of minimal surfaces , 1969 .

[28]  Laurent D. Cohen,et al.  Finite-Element Methods for Active Contour Models and Balloons for 2-D and 3-D Images , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[29]  Laurent D. Cohen,et al.  On active contour models and balloons , 1991, CVGIP Image Underst..

[30]  P. Lions,et al.  Axioms and fundamental equations of image processing , 1993 .

[31]  ISAAC COHEN,et al.  Using deformable surfaces to segment 3-D images and infer differential structures , 1992, CVGIP Image Underst..

[32]  R. Kimmel,et al.  Minimal surfaces: a geometric three dimensional segmentation approach , 1997 .

[33]  M. Grayson.  The heat equation shrinks embedded plane curves to round points , 1987 .