Geodesic Active Regions and Level Set Methods for Supervised Texture Segmentation

This paper presents a novel variational framework to deal with frame partition problems in Computer Vision. This framework exploits boundary and region-based segmentation modules under a curve-based optimization objective function. The task of supervised texture segmentation is considered to demonstrate the potentials of the proposed framework. The textured feature space is generated by filtering the given textured images using isotropic and anisotropic filters, and analyzing their responses as multi-component conditional probability density functions. The texture segmentation is obtained by unifying region and boundary-based information as an improved Geodesic Active Contour Model. The defined objective function is minimized using a gradient-descent method where a level set approach is used to implement the obtained PDE. According to this PDE, the curve propagation towards the final solution is guided by boundary and region-based segmentation forces, and is constrained by a regularity force. The level set implementation is performed using a fast front propagation algorithm where topological changes are naturally handled. The performance of our method is demonstrated on a variety of synthetic and real textured frames.

[1]  John F. Canny,et al.  A Computational Approach to Edge Detection , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[2]  Ibrahim M. Elfadel,et al.  Gibbs Random Fields, Cooccurrences, and Texture Modeling , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[3]  James A. Sethian,et al.  A real-time algorithm for medical shape recovery , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[4]  Theodosios Pavlidis,et al.  Segmentation by Texture Using Correlation , 1983, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[5]  Josiane Zerubia,et al.  A Level Set Model for Image Classification , 1999, International Journal of Computer Vision.

[6]  S.R. Yhann,et al.  Boundary localization in texture segmentation , 1995, IEEE Trans. Image Process..

[7]  Robert T. Schultz,et al.  Volumetric layer segmentation using coupled surfaces propagation , 1998, Proceedings. 1998 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No.98CB36231).

[8]  Michael Unser,et al.  Texture classification and segmentation using wavelet frames , 1995, IEEE Trans. Image Process..

[9]  O. Faugeras,et al.  Variational principles, surface evolution, PDE's, level set methods and the stereo problem , 1998, 5th IEEE EMBS International Summer School on Biomedical Imaging, 2002..

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

[11]  T. Chan,et al.  A Variational Level Set Approach to Multiphase Motion , 1996 .

[12]  Olivier Faugeras,et al.  Reconciling Distance Functions and Level Sets , 2000, J. Vis. Commun. Image Represent..

[13]  Song-Chun Zhu,et al.  Filters, Random Fields and Maximum Entropy (FRAME): Towards a Unified Theory for Texture Modeling , 1998, International Journal of Computer Vision.

[14]  Anthony J. Yezzi,et al.  A curve evolution approach to smoothing and segmentation using the Mumford-Shah functional , 2000, Proceedings IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2000 (Cat. No.PR00662).

[15]  Anil K. Jain,et al.  Unsupervised texture segmentation using Gabor filters , 1990, 1990 IEEE International Conference on Systems, Man, and Cybernetics Conference Proceedings.

[16]  Charles A. Bouman,et al.  Multiple Resolution Segmentation of Textured Images , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[17]  Jian Fan,et al.  Texture Classification by Wavelet Packet Signatures , 1993, MVA.

[18]  R. Deriche,et al.  Coupled Geodesic Active Regions for Image Segmentation , 1999 .

[19]  Song-Chun Zhu,et al.  Equivalence of Julesz and Gibbs texture ensembles , 1999, Proceedings of the Seventh IEEE International Conference on Computer Vision.

[20]  N. Paragios,et al.  Gradient vector flow fast geodesic active contours , 2001, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001.

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

[22]  Andrew K. C. Wong,et al.  A texture information-directed region growing algorithm for image segmentation and region classification , 1988, Comput. Vis. Graph. Image Process..

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

[24]  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.

[25]  V. Savchenko,et al.  Shape Modeling , 2002 .

[26]  Rachid Deriche,et al.  Geodesic active contours for supervised texture segmentation , 1999, Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149).

[27]  Dennis Gabor,et al.  Theory of communication , 1946 .

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

[29]  Paul A. Viola,et al.  Texture recognition using a non-parametric multi-scale statistical model , 1998, Proceedings. 1998 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No.98CB36231).

[30]  Olivier D. Faugeras,et al.  Codimension-two geodesic active contours for the segmentation of tubular structures , 2000, Proceedings IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2000 (Cat. No.PR00662).

[31]  Rachid Deriche,et al.  Geodesic active regions and level set methods for motion estimation and tracking , 2005, Comput. Vis. Image Underst..

[32]  Wilson S. Geisler,et al.  Multichannel Texture Analysis Using Localized Spatial Filters , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[33]  Rachid Deriche,et al.  Geodesic Active Regions for Tracking , 1999, ICCV 1999.

[34]  William M. Wells,et al.  Model Based Segmentation of Clinical Knee MRI , 1998 .

[35]  M. Unser.  Local linear transforms for texture measurements , 1986 .

[36]  D. Mumford,et al.  Statistical and computational theories for image segmentation, texture modeling and object recognition , 1996 .

[37]  Alfred M. Bruckstein,et al.  Tracking Level Sets by Level Sets: A Method for Solving the Shape from Shading Problem , 1995, Comput. Vis. Image Underst..

[38]  Stanley Osher,et al.  Level Set Methods , 2003 .

[39]  Michael Isard,et al.  Active Contours , 2000, Springer London.

[40]  Ruzena Bajcsy,et al.  Segmentation of range images as the search for geometric parametric models , 1995, International Journal of Computer Vision.

[41]  C.-C. Jay Kuo,et al.  Texture analysis and classification with tree-structured wavelet transform , 1993, IEEE Trans. Image Process..

[42]  J. Tsitsiklis,et al.  Efficient algorithms for globally optimal trajectories , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[43]  Edward H. Adelson,et al.  Shiftable multiscale transforms , 1992, IEEE Trans. Inf. Theory.

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

[45]  Anil K. Jain,et al.  Markov Random Field Texture Models , 1983, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[46]  Haluk Derin,et al.  Modeling and Segmentation of Noisy and Textured Images Using Gibbs Random Fields , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[47]  Mark S. Kaiser,et al.  Markov Random Field Models , 2014 .

[48]  Rachid Deriche,et al.  Using Canny's criteria to derive a recursively implemented optimal edge detector , 1987, International Journal of Computer Vision.

[49]  G. Sapiro,et al.  Geometric partial differential equations and image analysis [Book Reviews] , 2001, IEEE Transactions on Medical Imaging.

[50]  B. S. Manjunath,et al.  Edge flow: A framework of boundary detection and image segmentation , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[51]  Bayya Yegnanarayana,et al.  Segmentation of Gabor-filtered textures using deterministic relaxation , 1996, IEEE Trans. Image Process..

[52]  Rachid Deriche,et al.  Image Sequence Restoration: A PDE Based Coupled Method for Image Restoration and Motion Segmentation , 1998, ECCV.

[53]  Guillermo Sapiro,et al.  Morphing active contours: a geometric approach to topology-independent image segmentation and tracking , 1998, Proceedings 1998 International Conference on Image Processing. ICIP98 (Cat. No.98CB36269).

[54]  Patrick C. Chen,et al.  Segmentation by texture using a co-occurrence matrix and a split-and-merge algorithm☆ , 1979 .

[55]  C J Taylor,et al.  The use of active shape models for making thickness measurements of articular cartilage from MR images , 1997, Magnetic resonance in medicine.

[56]  Dennis F. Dunn,et al.  Optimal Gabor filters for texture segmentation , 1995, IEEE Trans. Image Process..

[57]  Anil K. Jain,et al.  Texture classification and segmentation using multiresolution simultaneous autoregressive models , 1992, Pattern Recognit..

[58]  Rama Chellappa,et al.  Unsupervised Texture Segmentation Using Markov Random Field Models , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

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

[60]  John F. Haddon,et al.  Image Segmentation by Unifying Region and Boundary Information , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[61]  Michael Werman,et al.  Texture segmentation using a diffusion region growing technique , 1990, Pattern Recognit..

[62]  Roman Goldenberg,et al.  Fast Geodesic Active Contours , 1999, Scale-Space.

[63]  Olivier D. Faugeras,et al.  Segmentation of Bone in Clinical Knee MRI Using Texture-Based Geodesic Active Contours , 1998, MICCAI.

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

[65]  Rachid Deriche,et al.  Geodesic Active Contours and Level Sets for the Detection and Tracking of Moving Objects , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

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

[67]  Jia-Lin Chen,et al.  Unsupervised texture segmentation using multichannel decomposition and hidden Markov models , 1995, IEEE Trans. Image Process..

[68]  R. Deriche,et al.  Les EDP en traitement des images et vision par ordinateur , 1995 .

[69]  Max A. Viergever,et al.  Efficient and reliable schemes for nonlinear diffusion filtering , 1998, IEEE Trans. Image Process..

[70]  Jerry L. Prince,et al.  Gradient vector flow: a new external force for snakes , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

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

[72]  Michal Haindl,et al.  Unsupervised Texture Segmentation , 1998, SSPR/SPR.

[73]  Benjamin B. Kimia,et al.  Shock-Based Reaction-Diffusion Bubbles for Image Segmentation , 1995, CVRMed.

[74]  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..

[75]  Graham Jones,et al.  Image segmentation using texture boundary detection , 1994, Pattern Recognit. Lett..

[76]  Rolf Adams,et al.  Seeded Region Growing , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

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

[78]  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.

[79]  Georgios Tziritas,et al.  Bayesian Level Sets for Image Segmentation , 2002, J. Vis. Commun. Image Represent..

[80]  Yunmei Chen,et al.  On the incorporation of shape priors into geometric active contours , 2001, Proceedings IEEE Workshop on Variational and Level Set Methods in Computer Vision.

[81]  G. Aubert,et al.  Video object segmentation using Eulerian region-based active contours , 2001, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001.

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

[83]  Alex Pentland,et al.  Automatic extraction of deformable part models , 1990, International Journal of Computer Vision.

[84]  L. Vese,et al.  A level set algorithm for minimizing the Mumford-Shah functional in image processing , 2001, Proceedings IEEE Workshop on Variational and Level Set Methods in Computer Vision.

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

[86]  Olivier D. Faugeras,et al.  Variational principles, surface evolution, PDEs, level set methods, and the stereo problem , 1998, IEEE Trans. Image Process..

[87]  S. Mallat.  Multiresolution approximations and wavelet orthonormal bases of L^2(R) , 1989 .

[88]  Richard O. Duda,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.

[89]  Guillermo Sapiro,et al.  Vector-valued active contours , 1996, Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

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

[91]  Rama Chellappa,et al.  Learning Texture Discrimination Rules in a Multiresolution System , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

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

[93]  Olivier D. Faugeras,et al.  Statistical shape influence in geodesic active contours , 2000, Proceedings IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2000 (Cat. No.PR00662).

[94]  Donald Geman,et al.  Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images , 1984 .

[95]  Glenn Healey,et al.  Markov Random Field Models for Unsupervised Segmentation of Textured Color Images , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[96]  R. Deriche,et al.  Geodesic active regions for motion estimation and tracking , 1999, Proceedings of the Seventh IEEE International Conference on Computer Vision.

[97]  Alireza Khotanzad,et al.  Unsupervised Segmentation of Textured Images by Edge Detection in Multidimensional Feature , 1989, IEEE Trans. Pattern Anal. Mach. Intell..