An active contour model for image segmentation based on elastic interaction

The task of image segmentation is to partition an image into non-overlapping regions based on intensity or textural information. The active contour methods provide an effective way for segmentation, in which the boundaries of the objects are detected by evolving curves. In this paper, we propose a new edge-based active contour method, which uses a long-range and orientation-dependent interaction between image boundaries and the moving curves while maintaining the edge fidelity. As a result, this method has a large capture range, and is able to detect sharp features of the images. The velocity field for the moving curves generated by this elastic interaction is calculated using the fast Fourier transform (FFT) method. Level set representation is used for the moving curves so that the topological changes during the evolution are handled automatically. This new method is derived based on the elastic interaction between line defects in solids (dislocations). Although it is derived originally for two dimensional segmentation, we also extend it to three dimensions. The features of the new method are examined by experiments on both synthetic images and medical images of blood vessels. Comparisons are made with the existing active contour methods.

[1]  Tony F. Chan,et al.  Active contours without edges , 2001, IEEE Trans. Image Process..

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

[3]  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..

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

[5]  Guillermo Sapiro,et al.  Geodesic Active Contours , 1995, International Journal of Computer Vision.

[6]  S. Osher,et al.  Regular Article: A PDE-Based Fast Local Level Set Method , 1999 .

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

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

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

[10]  Michel Barlaud,et al.  Inward and outward curve evolution using level set method , 1999, Proceedings 1999 International Conference on Image Processing (Cat. 99CH36348).

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

[12]  Junaed Sattar Snakes , Shapes and Gradient Vector Flow , 2022 .

[13]  S. Osher,et al.  A Level Set Formulation of Eulerian Interface Capturing Methods for Incompressible Fluid Flows , 1996 .

[14]  Tony F. Chan,et al.  A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model , 2002, International Journal of Computer Vision.

[15]  Thierry Blu,et al.  Efficient energies and algorithms for parametric snakes , 2004, IEEE Transactions on Image Processing.

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

[17]  Tony F. Chan,et al.  Active Contours without Edges for Vector-Valued Images , 2000, J. Vis. Commun. Image Represent..

[18]  Alan S. Willsky,et al.  Medical image segmentation via coupled curve evolution equations with global constraints , 2000, Proceedings IEEE Workshop on Mathematical Methods in Biomedical Image Analysis. MMBIA-2000 (Cat. No.PR00737).

[19]  Kaleem Siddiqi,et al.  Area and length minimizing flows for shape segmentation , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[20]  D CohenLaurent On active contour models and balloons , 1991 .

[21]  Jerry L. Prince,et al.  Generalized gradient vector flow external forces for active contours , 1998, Signal Process..

[22]  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..

[23]  J. D. Eshelby,et al.  Mathematical Theory of Dislocations and Fracture , 1975 .

[24]  S. Osher,et al.  A PDE-Based Fast Local Level Set Method 1 , 1998 .

[25]  S. Osher,et al.  The nonconvex multi-dimensional Riemann problem for Hamilton-Jacobi equations , 1991 .

[26]  S. Osher,et al.  High-order essentially nonsocillatory schemes for Hamilton-Jacobi equations , 1990 .

[27]  Nikos Paragios,et al.  Gradient vector flow fast geometric active contours , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[28]  Leonid M Pismen,et al.  Vortices in Nonlinear Fields: From Liquid Crystals to Superfluids, from Non-Equilibrium Patterns to Cosmic Strings , 1999 .

[29]  Yang Xiang,et al.  A level set method for dislocation dynamics , 2003 .

[30]  E. M. Lifshitz,et al.  Statistical physics. Pt.1, Pt.2 , 1980 .

[31]  Xue-Cheng Tai,et al.  A variant of the level set method and applications to image segmentation , 2006, Math. Comput..

[32]  Yongmin Kim,et al.  Active contour model with gradient directional information: directional snake , 2001, IEEE Trans. Circuits Syst. Video Technol..

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

[34]  R. W. Fox,et al.  Introduction to fluid mechanics, 3rd edition , 1985 .

[35]  Wang Hai-bing,et al.  High-order essentially non-oscillatory schemes for Hamilton-Jacobi equations , 2006 .

[36]  E Weinan,et al.  Dynamics of vortices in Ginzburg-Landau theories with applications to superconductivity , 1994 .

[37]  Jens Lothe John Price Hirth,et al.  Theory of Dislocations , 1968 .

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

[39]  Jacob Rubinstein,et al.  Motion of Vortex lines in the Ginzburg-Landau model , 1991 .

[40]  A. D. Young,et al.  An Introduction to Fluid Mechanics , 1968 .

[41]  Alexandre J. Chorin,et al.  Vorticity and turbulence , 1994 .

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

[43]  John Porrill,et al.  Statistical Snakes: Active Region Models , 1994, BMVC.

[44]  Yang Xiang,et al.  Level set simulations of dislocation-particle bypass mechanisms , 2004 .

[45]  Rémi Ronfard,et al.  Region-based strategies for active contour models , 1994, International Journal of Computer Vision.

[46]  Danping Peng,et al.  Weighted ENO Schemes for Hamilton-Jacobi Equations , 1999, SIAM J. Sci. Comput..