A Variational Approach for Object Contour Tracking

In this paper we describe a new framework for the tracking of closed curves described through implicit surface modeling. The approach proposed here enables a continuous tracking along an image sequence of deformable object contours. Such an approach is formalized through the minimization of a global spatio-temporal continuous cost functional stemming from a Bayesian Maximum a posteriori estimation of a Gaussian probability distribution. The resulting minimization sequence consists in a forward integration of an evolution law followed by a backward integration of an adjoint evolution model. This latter pde include also a term related to the discrepancy between the curve evolution law and a noisy observation of the curve. The efficiency of the approach is demonstrated on image sequences showing deformable objects of different natures.

[1]  Andrew F. Bennett,et al.  Inverse Methods in Physical Oceanography: Frontmatter , 1992 .

[2]  Thomas S. Huang,et al.  Image processing , 1971 .

[3]  P. Courtier,et al.  Variational Assimilation of Meteorological Observations With the Adjoint Vorticity Equation. Ii: Numerical Results , 2007 .

[4]  Daniel Cremers,et al.  Diffusion Snakes: Introducing Statistical Shape Knowledge into the Mumford-Shah Functional , 2002, International Journal of Computer Vision.

[5]  Rachid Deriche,et al.  Geodesic Active Regions: A New Framework to Deal with Frame Partition Problems in Computer Vision , 2002, J. Vis. Commun. Image Represent..

[6]  F. L. Dimet,et al.  Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects , 1986 .

[7]  Andrew F. Bennett,et al.  Inverse Methods in Physical Oceanography: Bibliography , 1992 .

[8]  P. Courtier,et al.  Variational Assimilation of Meteorological Observations With the Adjoint Vorticity Equation. I: Theory , 2007 .

[9]  A. Tannenbaum,et al.  Dynamic geodesic snakes for visual tracking , 2004, CVPR 2004.

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

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

[12]  Natan Peterfreund,et al.  Robust Tracking of Position and Velocity With Kalman Snakes , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[13]  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..

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

[15]  Abdol-Reza Mansouri,et al.  Region Tracking via Level Set PDEs without Motion Computation , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

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

[17]  Patrick Pérez,et al.  Dense estimation and object-based segmentation of the optical flow with robust techniques , 1998, IEEE Trans. Image Process..

[18]  Philippe Réfrégier,et al.  Influence of the noise model on level set active contour segmentation , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[19]  O. Faugeras,et al.  Statistical shape influence in geodesic active contours , 2002, 5th IEEE EMBS International Summer School on Biomedical Imaging, 2002..

[20]  N. Paragios.  A level set approach for shape-driven segmentation and tracking of the left ventricle , 2003, IEEE Transactions on Medical Imaging.