Geodesic Active Regions: A New Framework to Deal with Frame Partition Problems in Computer Vision

This paper presents a novel variational framework for dealing with frame partition problems in computer vision by the propagation of curves. This framework integrates boundary- and region-based frame partition modules under a curve-based objective function, which aims at finding a set of minimal length curves that preserve three main properties: (i) they are regular and smooth, (ii) they are attracted by the boundary points (boundary-based information), (iii) and they create a partition that is optimal according to the expected region properties of the different hypotheses (region-based information). The defined objective function is minimized using a gradient descent method. According to the obtained motion equations, the set of initial curves is propagated toward the best partition under the influence of boundary- and region-based forces, and is constrained by a regularity force. The changes of topology are naturally handled thanks to the level set implementation. Furthermore, a coupled multiphase propagation that imposes the idea of mutually exclusive propagating curves and increases the robustness as well as the convergence rate is proposed. The proposed framework has been validated using three important applications in computer vision, the tasks of image and supervised texture segmentation in low-level vision and the task of motion estimation and tracking in motion analysis.

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

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

[3]  Paul Scheunders,et al.  Wavelet correlation signatures for color texture characterization , 1999, Pattern Recognit..

[4]  Jean-Michel Morel,et al.  Geometry and Color in Natural Images , 2002, Journal of Mathematical Imaging and Vision.

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

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

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

[8]  R. Deriche,et al.  Geodesic Active Regions for Texture Segmentation , 1998 .

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

[10]  Charles A. Bouman,et al.  A multiscale random field model for Bayesian image segmentation , 1994, IEEE Trans. Image Process..

[11]  Donald Geman,et al.  Bayes Smoothing Algorithms for Segmentation of Binary Images Modeled by Markov Random Fields , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[12]  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.

[13]  Johan Wiklund,et al.  Multidimensional Orientation Estimation with Applications to Texture Analysis and Optical Flow , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

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

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

[16]  S. Mallat.  A wavelet tour of signal processing , 1998 .

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

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

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

[20]  Rachid Deriche,et al.  Unsupervised Segmentation Incorporating Colour, Texture, and Motion , 2003, CAIP.

[21]  G. Aubert,et al.  Detection and tracking of moving objects using a new level set based method , 2000, Proceedings 15th International Conference on Pattern Recognition. ICPR-2000.

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

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

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

[25]  Alan L. Yuille,et al.  A common framework for image segmentation , 1990, International Journal of Computer Vision.

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

[27]  J. Morel,et al.  A multiscale algorithm for image segmentation by variational method , 1994 .

[28]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[29]  Josiane Zerubia,et al.  A Probabilistic Framework for Adaptive Texture Description , 2003 .

[30]  Rachid Deriche,et al.  Geodesic Active Regions for Motion Estimation and Tracking , 1999, ICCV.

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

[32]  J. Sethian,et al.  FRONTS PROPAGATING WITH CURVATURE DEPENDENT SPEED: ALGORITHMS BASED ON HAMILTON-JACOB1 FORMULATIONS , 2003 .

[33]  T. Kanade,et al.  Color information for region segmentation , 1980 .

[34]  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..

[35]  David Mumford,et al.  Statistics of natural images and models , 1999, Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149).