Abstract
The joint analysis of motions and deformations is crucial in a number of computer vision applications. In this paper, we introduce a non-linear stochastic filtering technique to track the state of a free curve. The approach we propose is implemented through a particle filter which includes color measurements characterizing the target and the background respectively. We design a continuous-time dynamics that allows us to infer inter-frame deformations. The curve is defined by an implicit level-set representation and the stochastic dynamics is expressed on the level-set function. It takes the form of a stochastic differential equation with Brownian motion of low dimension. Specific noise models lead to traditional evolution laws based on mean curvature motions, while other forms lead to new evolution laws with different smoothing behaviors. In these evolution models, we propose to combine local motion information extracted from the images and an incertitude modeling of the dynamics. The associated filter we propose for curve tracking thus belongs to the family of conditional particle filters. Its capabilities are demonstrated on various sequences with highly deformable objects.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Cremers, D., Soatto, S.: Motion competition: A variational framework for piecewise parametric motion segmentation. IJCV 62(3), 249–265 (2005)
Goldenberg, R., Kimmel, R., Rivlin, E., Rudzsky, M.: Fast geodesic active contours. IEEE Trans. on Image Processing 10(10), 1467–1475 (2001)
Kimmel, R., Bruckstein, A.M.: Tracking level sets by level sets: a method for solving the shape from shading problem. Comput. Vis. Image Underst. 62(1), 47–58 (1995)
Niethammer, M., Tannenbaum, A.: Dynamic geodesic snakes for visual tracking. In: CVPR (1), pp. 660–667 (2004)
Osher, S., Sethian, J.A.: Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics 79, 12–49 (1988)
Paragios, N., Deriche, R.: Geodesic active regions: a new framework to deal with frame partition problems in computer vision. J. of Visual Communication and Image Representation 13, 249–268 (2002)
Sethian, J.: Level set methods: An act of violence - evolving interfaces in geometry, fluid mechanics, computer vision and materials sciences (1996)
Cremers, D.: Dynamical statistical shape priors for level set based tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 28(8), 1262–1273 (2006)
Leventon, M., Grimson, E., Faugeras, O.: Statistical shape influence in geodesic active contours. In: CVPR (2000)
Paragios, N.: A level set approach for shape-driven segmentation and tracking of the left ventricle. IEEE Trans. on Med. Imaging 22(6) (2003)
Cremers, D., Soatto, S.: Variational space-time motion segmentation. In: ICCV 2003: Proceedings of the Ninth IEEE International Conference on Computer Vision, Washington, DC, USA, p. 886. IEEE Computer Society, Los Alamitos (2003)
Papadakis, N., Mmin, E.: A variational technique for time consistent tracking of curves and motion. Journal of Mathematical Imaging and Vision 31(1), 81–103 (2008)
Jiang, T., Tomasi, C.: Level-set curve particles. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006. LNCS, vol. 3953, pp. 633–644. Springer, Heidelberg (2006)
Rathi, Y., Vaswani, N., Tannenbaum, A., Yezzi, A.: Tracking deforming objects using particle filtering for geometric active contours. IEEE Trans. Pattern Analysis and Machine Intelligence 29(8), 1470–1475 (2007)
Pérez, P., Hue, C., Vermaak, J., Gangnet, M.: Color-based probabilistic tracking. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2350, pp. 661–675. Springer, Heidelberg (2002)
Juan, O., Keriven, R., Postelnicu, G.: Stochastic motion and the level set method in computer vision: Stochastics active contours. International Journal of Computer Vision 69(1), 7–25 (2006)
Arnaud, E., Mmin, E.: Partial linear gaussian model for tracking in image sequences using sequential monte carlo methods. IJCV 74(1), 75–102 (2007)
Jazwinski, A.H.: Stochastic Processes and Filtering Theory. Academic Press, London (1970)
Liu, J.S., Chen, R.: Sequential Monte Carlo methods for dynamic systems. Journal of the American Statistical Association 93(443), 1032–1044 (1998)
Karatzas, I., Shreve, S.E.: Brownian Motion and Stochastic Calculus. Graduate Texts in Mathematics. Springer, Heidelberg (2004)
Oksendal, B.: Stochastic Differential Equations: An Introduction with Applications (Universitext). Springer, Heidelberg (2005)
Chan, T., Vese, L.: An active contour model without edges. In: Nielsen, M., Johansen, P., Fogh Olsen, O., Weickert, J. (eds.) Scale-Space 1999. LNCS, vol. 1682, pp. 141–151. Springer, Heidelberg (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Avenel, C., Mémin, E., Pérez, P. (2009). Tracking Closed Curves with Non-linear Stochastic Filters. In: Tai, XC., Mørken, K., Lysaker, M., Lie, KA. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2009. Lecture Notes in Computer Science, vol 5567. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02256-2_48
Download citation
DOI: https://doi.org/10.1007/978-3-642-02256-2_48
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02255-5
Online ISBN: 978-3-642-02256-2
eBook Packages: Computer ScienceComputer Science (R0)