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Tracking Deformable Objects in the Plane Using an Active Contour Model
June 1993 (vol. 15 no. 6)
pp. 617-634
The problems of segmenting a noisy intensity image and tracking a nonrigid object in the plane are discussed. In evaluating these problems, a technique based on an active contour model commonly called a snake is examined. The technique is applied to cell locomotion and tracking studies. The snake permits both the segmentation and tracking problems to be simultaneously solved in constrained cases. A detailed analysis of the snake model, emphasizing its limitations and shortcomings, is presented, and improvements to the original description of the model are proposed. Problems of convergence of the optimization scheme are considered. In particular, an improved terminating criterion for the optimization scheme that is based on topographic features of the graph of the intensity image is proposed. Hierarchical filtering methods, as well as a continuation method based on a discrete sale-space representation, are discussed. Results for both segmentation and tracking are presented. Possible failures of the method are discussed.
[1] 617A. A. Amini, T. E. Weymouth, and R. C. Jain, "Using dynamic programming for solving variational problems in vision,"IEEE Trans. Patt. Anal. Machine Intell., vol. 12, pp. 855-867, Sept. 1990.[2] K. -J. Bathe,Finite Element Procedures in Engineering Analysis. Englewood Cliffs, NJ: Prentice-Hall, 1982, Civil Eng., Eng. Mechanics Series.[3] A. Benson and D. J. Evans, "A normalized algorithm for the solution of positive definite symmetric quindiagonal systems of linear equations,"ACM Trans. Math. Software, vol. 3, pp. 96-103, Mar. 1977.[4] M. -O. Berger, "Active contour models and growing methods," Tech. Rep. CRIN 90-R-081, Centre de Recherche en Informatique de Nancy, Vandøeuvre-les-Nancy, France, Dec. 1989.[5] A. Blake and A. Zisserman,Visual Reconstruction. Cambridge, MA: MIT Press, 1987.[6] A. Boyarsky and P. B. Noble, "A marker chain characterization of human neutrophil locomotion under neutral and chemotactic conditions,"Can. J. Physiol. Pharmacol., vol. 55, pp. 1-6, 1977.[7] P. J. Burt, "Fast filter transforms for image processing,"Comput. Graphics Image Processing, vol. 16, pp. 20-51, 1981.[8] S. Chandran, T. Maejima, and S. Miyazaki, "Global minima via dynamic programming: Energy minimizing active contours," inProc. SPIE Conf. Geometric Methods Comput. Vision `91(San Diego, CA), July 1991, pp. 391-402, vol. SPIE-1570.[9] P. G. Ciarlet,Introduction to Numerical Linear Algebra and Optimization. Cambridge. Cambridge: Cambridge University Press, 1988.[10] L. D. Cohen, "On active contour models and balloons,"Comput. Vision Graphics Image Processing: Image Understanding, vol. 53, pp. 211-218, Mar. 1991.[11] L. D. Cohen and I. Cohen, "A finite element method applied to new active contour models and 3d reconstruction from cross sections,"Proc. ICCV, pp. 587-591, 1990.[12] C. David and S. W. Zucker, "Potentials, valleys, and dynamic global coverings,"Int. J. Comput. Vision, vol. 5, pp. 219-238, Dec. 1990.[13] A. de Boisfleury-Chevance, B. Rapp, and H. Gruler, "Locomotion of white blood cells: A biophysical analysis,"Blood Cells, vol. 15, pp. 315-333, 1989.[14] A. R. Dill, M. D. Levine, and P. B. Noble, "Multiple resolution skeletons,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-9, pp. 495-504, July 1987.[15] F. P. Ferrie, M. D. Levine, and S. W. Zucker, "Cell tracking: A modeling and minimization approach,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-4, pp. 277-291, May 1982.[16] F. Ferrie, J. Lagarde, and P. Whaite, "Darboux frames, snakes, and super-quadrics: Geometry from the bottom-up," inProc. Workshop Interpretation 3D Scenes, 1989, pp. 170-176.[17] P. Fua and Y. Leclerc, "Model driven edge detection,"Machine vision Applications, vol. 3, no. 1, pp. 45-56, 1990.[18] C. Garbay, "Image structure representation and processing: A discussion of some segmentation methods in cytology,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-8, pp. 140-146, Mar. 1986.[19] D. Gauthier, M. D. Levine, and P. B. Noble, "Principles of object detection for an automated cell tracking system," inImage Analysis in Biology(D.-P. Häder, Ed.). Boca Raton, FL: CRC, 1992, pp. 9-28, ch. 2.[20] S. Inout,Video Microscopy. New York: Plenum, 1986.[21] M. Kass, A. Witkin, and D. Terzopoulos, "Snakes: Active contour models," inProc. First Int. Conf. Comput. Vision(London), 1987, pp. 259-268.[22] J. M. Lackie,Cell Movement and Cell Behaviour. London: Allen and Unwin, 1986.[23] M. D. Levine,Vision in Man and Machine. New York: McGraw-Hill, 1985, Comput. Eng. Series.[24] M. D. Levine, P. B. Noble, and Y. M. Youssef, "Understanding blood cell motion,"Comput. Graphics Image Processing, vol. 21, pp. 58-84, Jan. 1983.[25] M. D. Levine, Y. M. Youssef, P. B. Noble, and A. Boyarsky, "The quantification of blood cell motion by a method of automatic digital picture processing,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI- 2, pp. 444-450, Sept. 1980.[26] F. Leymarie, "Tracking and describing deformable objects using active contour models," McRCIM Tech. Rep. CIM-90-9, McGill Res. Cent. Intell. Machines, McGill Univ. Montréal, Canada, Feb. 1990; Master's thesis, Electrical Eng. Dept.[27] F. Leymarie and M. D. Levine, "Shape features using curvature morphology," inProc. SPIE Conf. Intell. Robots Comput. Vision VIII: Algorithms Techniques(D. P. Casasent, Ed.) (Philadelphia), Nov. 1989, pp. 536-547, vol. SPIE-1192, part 2.[28] F. Leymarie and M. D. Levine, "Simulating the grassfire transform using an active contour model,"IEEE Trans. Patt. Anal. Machine Intell., vol. 14, pp. 56-75, Jan. 1992.[29] U. Montanari, "On the optimal detection of curves in noisy pictures,"Comm. ACM, vol. 14, pp. 335-345, 1971.[30] P. B. Noble and M. D. Levine,Computer-Assisted Analyses of Cell Locomotion and Chemotaxis. Boca Raton, FL: CRC, 1986.[31] W. R. Oliver, "Cell locomotion as shape change,"Blood Cells, vol. 15, pp. 334-342, 1989.[32] A. Pentland and S. Scarloff, "Closed-form solutions for physically based shape modeling and recognition,"IEEE Trans. Patt. Anal. Machine Intell., vol. 13, pp. 715-729, July 1991.[33] R. Samadani, "Adaptive snakes: Control of damping and material parameters," inProc. SPIE Conf. Geometric Methods Comput. Vision `91(San Diego, CA), July 1991, pp. 202-213, vol. SPIE-1570.[34] G. L. Scott, "The alternative snake--and other animals," in1987 Stockholm Workshop Comput. Vision(J. -O. Eklundh, Ed.) (Stockholm, Sweden), 1987.[35] D. M. Shotton, "Review: Video-enhanced light microscopy and its applications in cell biology,"J. Cell Sci., vol. 89, pp. 129-150, Feb. 1988, pt. 2.[36] G. D. Smith,Numerical Solution of Partial Differential Equations: Finite Difference Methods. Oxford: Clarendon, 1985, Oxford Applied Math. Comput. Sci. Series, 3rd ed.[37] L. H. Staib and J. S. Duncan, "Parametrically deformable contour models," inProc. I989 Conf. Comput. Vision Patt. Recogn.(San Diego, CA), June 1989, pp. 98-103.[38] G. W. Stewart,Introduction to Matrix Computations. New York: Academic, 1973, Comput. Sci. Appl. Math. Series.[39] D. Terzopoulos, "The role of constraints and discontinuities in visiblesurface reconstruction," inProc. 8th Int. Joint Conf. Artificial Intell.(Kalsruhe, Germany), Aug. 1983, pp. 1073-1077, vol. 2.[40] D. Terzopoulos, "Matching deformable models to images: Direct and iterative solutions," inTopical Mtg. Machine Vision Techn. Dig. Series(Washington, DC), Mar. 1987, pp. 164-167, vol. 12, Opt. Soc. Amer.[41] D. Terzopoulos, "On matching deformable models to images," inTopical Mtg. Machine Vision Techn. Dig. Series(Washington, DC), Mar. 1987, pp. 16C-163, vol. 12, Opt. Soc. Amer.[42] A. P. Witkin, D. Terzopoulos, and M. Kass, "Signal matching through scale space," inProc. 5th Nat. Conf. Artificial Intell.(Philadelphia), 1986, pp. 714-719.[43] K. Wu, D. Gauthier, and M. D. Levine, "Cell segmentation revisited," McRCIM Tech. Rep. CIM-91-4, McGill University, Montréal, Canada, Oct. 1991.[44] S.W. Zucker, C. David, L. Dobbins, and L. Iverson, "The organization of curve detection: Coarse tanget fields and fine spline coverings," inProc. 2nd ICCV, Tarpon Springs, FL, 1988, pp. 568-577.
Index Terms:
image segmentation; hierarchical filtering; deformable objects; active contour model; noisy intensity image; tracking; nonrigid object; snake; cell locomotion; segmentation; convergence; optimization; terminating criterion; topographic features; continuation method; discrete sale-space representation; convergence; filtering and prediction theory; graph theory; image segmentation; optimisation; tracking
Citation:
F. Leymarie, M.D. Levine, "Tracking Deformable Objects in the Plane Using an Active Contour Model," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 15, no. 6, pp. 617-634, June 1993, doi:10.1109/34.216733