Modeling and estimation of shape deformation for topology-preserving object tracking

SIAM Journal on Imaging Sciences

Volumn 7, Issue 1, 2014, Pages 427-455

  Staneva, Valentina ^a   Younes, Laurent ^a  

^a Johns Hopkins University   (United States)

Author keywords

Diffeomorphic flow; Gaussian random fields; Particle filtering; Reproducing kernel Hilbert space; Sub Riemannian geometry

Indexed keywords

ESTIMATION; GAUSSIAN DISTRIBUTION; MONTE CARLO METHODS; SIGNAL FILTERING AND PREDICTION; TARGET TRACKING; TOPOLOGY;

DIFFEOMORPHIC FLOWS; GAUSSIAN RANDOM FIELDS; PARTICLE FILTERING; REPRODUCING KERNEL HILBERT SPACES; SUB-RIEMANNIAN GEOMETRY;

DEFORMATION;

EID: 84897560304     PISSN: None     EISSN: 19364954     Source Type: Journal    
DOI: 10.1137/130919714     Document Type: Article

References (37)

1. A. Agrachev, D. Barilari, and U. Boscain, Introduction to Riemannian and Sub-Riemannian Geometry, Preprint SISSA 09/2012/M, Scuola Internazionale Superiore di Studi Avanzati, Trieste, Italy, 2013.
2. S. Allassonniére, A. Trouvé, and L. Younes, Geodesic shooting and diffeomorphic matching via textured meshes, in Energy Minimization Methods in Computer Vision and Pattern Recognition, Lecture Notes in Comput. Sci. 3757, A. Rangarajan, B. Vemuri, and A. L. Yuille, eds., Springer, Berlin, Heidelberg, 2005, pp. 365-381.
3. N. Aronszajn, Theory of reproducing kernels, Trans. Amer. Math. Soc., 68 (1950), pp. 337-404.
4. F. Arrate, J. T. Ratnanather, and L. Younes, Diffeomorphic active contours, SIAM J. Imaging Sci., 3 (2010), pp. 176-198.
5. S. Arulampalam, S. Maskell, N. Gordon, and T. Clapp, A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking, IEEE Trans. Signal Process., 50 (2002), pp. 174-188.
6. M. Bauer, P. Harms, and P. W. Michor, Sobolev metrics on shape space of surfaces, J. Geom.Mech., 3 (2011), pp. 389-438.
7. Y. K. Belyaev, Analytic random processes, Theory Probab. Appl., 4 (1959), pp. 402-407.
8. B. Bonnard and M. Chyba, Singular Trajectories and Their Role in Control Theory, Springer-Verlag, Berlin, 2003.
9. A. Chiuso and S. Soatto, Monte Carlo filtering on Lie groups, in Proceedings of the 39th IEEE Conference on Decision and Control, 2000, pp. 304-309.
10. D. Cremers, Dynamical statistical shape priors for level-set based tracking, IEEE Trans. Pattern Anal. Mach. Intell., 28 (2006), pp. 1262-1273.
11. D. Cremers, F. R. Schmidt, and F. Barthel, Shape priors in variational image segmentation: Convexity, Lipschitz continuity and globally optimal solutions, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2008, pp. 1-60.
12. A. Doucet, N. de Freitas, and N. Gordon, eds., Sequential Monte Carlo Methods in Practice, Springer, New York, 2001.
13. S. Durrleman, M. Prastawa, G. Gerig, and S. Joshi, Optimal data-driven sparse parameterization of diffeomorphisms for population analysis, in Information Processing in Medical Imaging, Lecture Notes in Comput. Sci. 6801, G. Székely and H. K. Hahn, eds., Springer-Verlag, Berlin, Heidelberg, 2011, pp. 123-134.
14. W. H. Fleming and R. W. Rishel, Deterministic and Stochastic Optimal Control, Springer-Verlag, Berlin, New York, 1975.
15. P. Getreuer, Chan-Vese Segmentation, Image Processing On Line, Vol. 2012, http://dx.doi.org/10.5201/ipol.2012.g-cv (8 August 2012).
16. W. R. Gilks and C. Berzuini, Following a moving target-Monte Carlo inference for dynamic Bayesian models, J. R. Stat. Soc. Ser. B Stat. Methodol., 63 (2001), pp. 127-146.
17. J. Glaunès, A. Trouvé, and L. Younes, Modeling planar shape variation via Hamiltonian flows of curves, in Statistics and Analysis of Shapes, Model. Simul. Sci. Eng. Technol., Birkhäuser Boston, Boston, MA, 2005, pp. 335-361.
18. Y. E. Gliklikh, Necessary and sufficient conditions for global-in-time existence of solutions of ordinary, stochastic, and parabolic differential equations, Abstr. Appl. Anal., 2006 (2006), 39786.
19. M. Isard and A. Blake, Condensation-Conditional density propagation for visual tracking, Int. J. Comput. Vis., 29 (1998), pp. 5-28.
20. J. Kwon, M. Choi, C. Chun, and F. C. Park, Particle filtering on the Euclidean group, in Proceedings of the IEEE International Conference on Robotics and Automation, 2007, pp. 3552-3557.
21. J. Kwon and F. C. Park, Visual tracking via particle filtering on the affine group, Int. J. Robot. Res., 29 (2010), pp. 198-217.
22. I. J. Ndiour, O. Arif, J. Teizer, and P. A. Vela, A probabilistic observer for visual tracking, in Proceedings of the IEEE American Control Conference, 2010, pp. 4558-4563.
23. J. Ortega, Asymptotic behavior of Gaussian random fields, Z. Wahrsch. Verw. Gebiete, 59 (1982), pp. 169-177.
24. P. Radau, Y. Lu, K. Connelly, G. Paul, A. J. Dick, and G. A. Wright, Evaluation framework for algorithms segmenting short axis cardiac MRI, The MIDAS Journal, (2009). Private Issue: Cardiac MR Left Ventricle Segmentation Challenge.
25. Y. Rathi, N. Vaswani, A. Tannenbaum, and A. Yezzi, Particle filtering for geometric active contours with application to tracking moving and deforming objects, in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Vol. 2, 2005, pp. 2-9.
26. H. Snoussi and C. Richard, Monte Carlo tracking on the Riemannian manifold of multivariate normal distributions, in Proceedings of the IEEE Digital Signal Processing Workshop, 2009, pp. 280-285.
27. C. Snyder, T. Bengtsson, P. Bickel, and J. Anderson, Obstacles to high-dimensional particle filtering, Mon. Wea. Rev., 136 (2008), pp. 4629-4640.
28. S. Sommer, M. Nielsen, S. Darkner, and X. Pennec, Higher-order momentum distributions and locally affine LDDMM registration, SIAM J. Imaging Sci., 6 (2013), pp. 341-367.
29. H. Soneson, J. F. A. Ubachs, M. Ugander, H. Arheden, and E. Heiberg, An improved method for automatic segmentation of the left ventricle in myocardial perfusion SPECT, J. Nucl. Med., 50 (2009), pp. 205-213.
30. G. Sundaramoorthi, A. Mennucci, S. Soatto, and A. Yezzi, Tracking deforming objects by filtering and prediction in the space of curves, in Proceedings of the 48th IEEE Conference on Decision and Control, held jointly with the 28th Chinese Control Conference, 2009, pp. 2395-2401.
31. N. Vaswani, Particle filters for infinite (or large) dimensional state spaces-Part 2, in Proceedings of the 2006 IEEE International Conference on Acoustics, Speech and Signal Processing, Vol. 3, 2006, pp. 29-32.
32. N. Vaswani, Y. Rathi, A. Yezzi, and A. Tannenbaum, Deform PF-MT: Particle filter with mode tracker for tracking non-affine countour deformations, IEEE Trans. Image Process., 19 (2010), pp. 841-857.
33. N. Vaswani, A. Yezzi, Y. Rathi, and A. Tannenbaum, Particle filters for infinite (large) dimensional state spaces-Part 1, in Proceedings of the 2006 IEEE International Conference on Acoustics, Speech and Signal Processing, Vol. 3, 2006, pp. 29-32.
34. F.-X. Vialard and A. Trouvé, Shape splines and stochastic shape evolutions: A second-order point of view, Quart. Appl. Math., 70 (2010), pp. 219-251.
35. A. J. Yezzi and S. Soatto, Deformotion: Deforming motion, shape average and the joint registration and approximation of structures in images, Int. J. Comput. Vis., 53 (2003), pp. 153-167.
36. L. Younes, Shapes and Diffeomorphisms, Springer-Verlag, Berlin, 2010.
37. L. Younes, Constrained diffeomorphic shape evolution, Found. Comput. Math., 12 (2012), pp. 295-325.