Abstract
This paper presents a 3D active contour model for boundary detection and tracking of non-rigid objects, which applies stereo vision and motion analysis to the class of energy-minimizing deformable contour models, known as snakes. The proposed contour evolves in three-dimensional space in reaction to a 3D potential function, which is derived by projecting the contour onto the 2D stereo images. The potential function is augmented by a kinetic term, which is related to the velocity field along the contour. This term is used to guide the inter-image contour displacement. The incorporation of inter-frame velocity estimates in the tracking algorithm is especially important for contours which evolve in 3D space, where the added freedom of motion can easily result in loss of tracking. The proposed scheme incorporates local velocity information seamlessly in the snake model, with little computational overhead, and does not require exogenous computation of the optical flow or related quantities in each image. The resulting algorithm is shown to provide good tracking performance with only one iteration per frame, which provides a considerable advantage for real time operation.
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Bascle, B., Bouthemy, P., Deriche, R., and Meyer, F. 1994. Tracking complex primitives in an image sequence. In Proc. 12th IAPR International Conference on Pattern Recognition (ICPR'94), Jerusalem, pp. 426–431.
Bascle, B. and Deriche, R. 1993a. Energy-based methods for 2D curve tracking, reconstruction and refinement of 3D curves and applications. In Geometric Methods in Computer Vision, SPIE Vol. 2031, B.C. Vemuri (Eds.), pp. 282–293.
Bascle, B. and Deriche, R. 1993b. Stereo matching, reconstruction and refinement of 3D curves using deformable contours. In Proc. IEEE Int. Conf. on Computer Vision, Berlin, pp. 421–430.
Berger, M.-O., Mozelle, G., and Laprie, Y. 1995. Cooperation of active contours and optical flow for tongue tracking in X-ray motion pictures. In Proc. 9th Scandinavian Conference on Image Analysis, Puerto Rico, pp. 1094–1099.
Bertalmio, M., Sapiro, G., and Randall, M.G. 2000. Morphing active contours. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(7):733–737.
Blake, A. and Isard, M. 1998. Active Contours. Springer: London.
Blake, A. and Yuille, A. 1992. Active Vision. MIT Press: Cambridge, MA.
Caselles, B. and Coll, B. 1996. Snakes in movement. SIAM Journal on Numerical Analysis, 33:2445–2456.
Caselles, V., Kimmel, R., and Sapiro, G. 1997. Geodesic active contours. International Journal of Computer Vision, 22(1):61–79.
Caselles, V., Kimmel, R., Sapiro, G., and Sbert, C. 1997. Minimal surfaces based object segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 19(4):394–398.
Cham, T. and Cipolla, R. 1997. Stereo coupled active contours. In Proc. IEEE Conf. on Computer Vision and Pattern Recognition, Puerto Rico, pp. 1094–1099.
Deriche, R., Bouvin, S., and Faugeras, O. 1998. Front propagation and level-set approach for geodesic active stereovision. In Third Asian Conference On Computer Vision, Hong Kong.
Faugeras, O. and Keriven, R. 1999. Variational principles, surface evolution, PDE's, level set methods and the stereo problem. IEEE Transactions on Image Processing, 7(3):336–344.
Goldenberg, R., Kimmel, R., Rivlin, E., and Rudzsky, M. 2001. Fast geodesic active contours. IEEE Transactions on Pattern Analysis and Machine Intelligence, 10(10):1467–1475.
Horn, B.K.P. 1986. Robot Vision. MIT Press: Cambridge, MA.
Jain, A.K., Zhong, Y., and Dubuisson-Jolly, M. 1998. Deformable template models: A review. Signal Processing, 71:109–129.
Kass, M., Witkin, A., and Terzopoulos, D. 1987. Snakes: Active contour models. International Journal of Computer Vision, 1(4):321– 331.
Kichenassami, S., Kumar, A., Olver, P., Tannenbaum, A., and Yezzi, A. 1996. Conformal curvature flows: From phase transitions to active vision. Arch. Rational Mech. Anal., 134:275–301.
McInerney, T. and Terzopoulos, D. 1996. Deformable models in medical image analysis: A survey. Medical Image Analysis, 1(2):91– 108.
Paragios, N. and Deriche, R. 1999. Geodesic active regions for motion estimation and tracking. In Proc. 7th IEEE Int. Conf. on Computer Vision, Kerkyra, Greece, pp. 688–694.
Paragios, N. and Deriche, R. 2000. Geodesic active contours and level sets for the detection and tracking of moving objects. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(3):266– 280.
Peterfreund, N. 1997. The velocity snake. In Proc. IEEE Non Rigid and Articulated Motion Workshop, Los Alamitos, CA, pp. 70–79.
Peterfreund, N. 1999. The velocity snake: Deformable contour for tracking in spatio-velocity space. Computer Vision and Image Understanding, 73(3):346–356.
Sapiro, G. 2001. Geometric Partial Differential Equations and Image Analysis. Cambridge University Press, New York.
Terzopoulos, D. and Szeliski, R. 1992. Tracking with kalman snakes. In Active Vision, A. Blake and A. Yuille (Eds.), MIT Press: Cambridge, MA.
Terzopoulos, D., Witkin, A., and Kass, M. 1988. Constraints on deformable models: Recovering 3D shape and nonrigid motion. Artificial Intelligence, 36:91–123.
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Zaritsky, R., Peterfreund, N. & Shimkin, N. Velocity-Guided Tracking of Deformable Contours in Three Dimensional Space. International Journal of Computer Vision 51, 219–238 (2003). https://doi.org/10.1023/A:1021853902673
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DOI: https://doi.org/10.1023/A:1021853902673