Curve evolution and segmentation functionals: application to color images

Curve evolution has developed into an important tool in computer vision and has been applied to a wide variety of problems such as smoothing of shapes, shape analysis and shape recovery. The different versions of curve evolution used in computer vision together with the preprocessing step of constructing an edge-strength function can be integrated in the form of a new segmentation functional. The new functional permits junctions such as triple points to develop. The numerical solutions obtained retain sharp discontinuities or "shocks", thus providing sharp demarcation of object boundaries. The new segmentation functional is extended for application to vector-valued features such as color.

[1]  Guillermo Sapiro,et al.  Differential Invariant Signatures and Flows in Computer Vision: A Symmetry Group Approach , 1994, Geometry-Driven Diffusion in Computer Vision.

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

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

[4]  André Weil,et al.  The classical case , 1971 .

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

[6]  Benjamin B. Kimia,et al.  On the evolution of curves via a function of curvature , 1992 .

[7]  J. Shah,et al.  A computationally efficient shape analysis via level sets , 1996, Proceedings of the Workshop on Mathematical Methods in Biomedical Image Analysis.

[8]  Jayant Shah,et al.  A common framework for curve evolution, segmentation and anisotropic diffusion , 1996, Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[9]  Jayant Shah.  Uses of Elliptic Approximations in Computer Vision , 1996 .

[10]  Kaleem Siddiqi,et al.  Parts of Visual Form: Computational Aspects , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

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

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

[13]  Benjamin B. Kimia,et al.  Entropy scale-space , 1992 .

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

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

[16]  Guillermo Sapiro,et al.  Color Snakes , 1997, Comput. Vis. Image Underst..