A Fully Global Approach to Image Segmentation via Coupled Curve Evolution Equations

In this paper, we develop a novel region-based approach to snakes designed to optimally separate the values of certain image statistics over a known number of region types. Multiple sets of contours deform according to a coupled set of curve evolution equations derived from a single global cost functional. The resulting active contour model, in contrast to many other edge and region based models, is fully global in that the evolution of each curve depends at all times upon every pixel in the image and is directly coupled to the evolution of every other curve regardless of their mutual proximity. As such evolving contours enjoy a very wide “field of view,” endowing the algorithm with a robustness to initial contour placement above and beyond the significant improvement exhibited by other region based snakes over earlier edge based snakes.

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

[2]  J. Sethian.  Level set methods : evolving interfaces in geometry, fluid mechanics, computer vision, and materials science , 1996 .

[3]  Kaleem Siddiqi,et al.  Area and length minimizing flows for shape segmentation , 1998, IEEE Trans. Image Process..

[4]  D. Mumford,et al.  Optimal approximations by piecewise smooth functions and associated variational problems , 1989 .

[5]  W. Fleming,et al.  Controlled Markov processes and viscosity solutions , 1992 .

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

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

[8]  P. Lions,et al.  User’s guide to viscosity solutions of second order partial differential equations , 1992, math/9207212.

[9]  R. LeVeque.  Numerical methods for conservation laws , 1990 .

[10]  Joachim Weickert,et al.  Scale-Space Theories in Computer Vision , 1999, Lecture Notes in Computer Science.

[11]  Tony F. Chan,et al.  An Active Contour Model without Edges , 1999, Scale-Space.

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

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

[14]  Josiane Zerubia,et al.  A Level Set Model for Image Classification , 1999, Scale-Space.

[15]  James S. Duncan,et al.  Game-Theoretic Integration for Image Segmentation , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[16]  Rachid Deriche,et al.  Geodesic active regions for supervised texture segmentation , 1999, Proceedings of the Seventh IEEE International Conference on Computer Vision.

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

[18]  Yiannis Aloimonos,et al.  Active vision , 2004, International Journal of Computer Vision.

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

[20]  S. Osher.  Riemann Solvers, the Entropy Condition, and Difference , 1984 .

[21]  P. Lions.  Generalized Solutions of Hamilton-Jacobi Equations , 1982 .

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

[23]  James S. Duncan,et al.  Deformable boundary finding in medical images by integrating gradient and region information , 1996, IEEE Trans. Medical Imaging.

[24]  Demetri Terzopoulos,et al.  Energy Constraints on Deformable Models: Recovering Shape and Non-Rigid Motion , 1987, AAAI.

[25]  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.

[26]  M. James.  Controlled markov processes and viscosity solutions , 1994 .

[27]  Alan L. Yuille,et al.  Region Competition: Unifying Snakes, Region Growing, and Bayes/MDL for Multiband Image Segmentation , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[28]  Dana H. Ballard,et al.  Computer Vision , 1982 .

[29]  Rachid Deriche,et al.  Coupled Geodesic Active Regions for Image Segmentation: A Level Set Approach , 2000, ECCV.

[30]  Yvan G. Leclerc,et al.  Constructing simple stable descriptions for image partitioning , 1989, International Journal of Computer Vision.

[31]  Demetri Terzopoulos,et al.  Snakes: Active contour models , 2004, International Journal of Computer Vision.

[32]  Anthony J. Yezzi,et al.  A statistical approach to snakes for bimodal and trimodal imagery , 1999, Proceedings of the Seventh IEEE International Conference on Computer Vision.

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

[34]  James A. Sethian,et al.  Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid , 2012 .