|
| This Article | ||
| ||
| Share | ||
| Bibliographic References | ||
| Add to: | ||
| | ||
| Search | ||
| ||
| ASCII Text | x | ||
| Marcelo Bertalmío, Guillermo Sapiro, Gregory Randall, "Morphing Active Contours," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 22, no. 7, pp. 733-737, July, 2000. | |||
| BibTex | x | ||
| @article{ 10.1109/34.865191, author = {Marcelo Bertalmío and Guillermo Sapiro and Gregory Randall}, title = {Morphing Active Contours}, journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {22}, number = {7}, issn = {0162-8828}, year = {2000}, pages = {733-737}, doi = {http://doi.ieeecomputersociety.org/10.1109/34.865191}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - JOUR JO - IEEE Transactions on Pattern Analysis and Machine Intelligence TI - Morphing Active Contours IS - 7 SN - 0162-8828 SP733 EP737 EPD - 733-737 A1 - Marcelo Bertalmío, A1 - Guillermo Sapiro, A1 - Gregory Randall, PY - 2000 KW - Partial differential equations KW - curve evolution KW - morphing KW - segmentation KW - tracking KW - topology. VL - 22 JA - IEEE Transactions on Pattern Analysis and Machine Intelligence ER - | |||
Abstract—A method for deforming curves in a given image to a desired position in a second image is introduced in this paper. The algorithm is based on deforming the first image toward the second one via a Partial Differential Equation (PDE), while tracking the deformation of the curves of interest in the first image with an additional, coupled, PDE. The tracking is performed by projecting the velocities of the first equation into the second one. In contrast with previous PDE-based approaches, both the images and the curves on the frames/slices of interest are used for tracking. The technique can be applied to object tracking and sequential segmentation. The topology of the deforming curve can change without any special topology handling procedures added to the scheme. This permits, for example, the automatic tracking of scenes where, due to occlusions, the topology of the objects of interest changes from frame to frame. In addition, this work introduces the concept of projecting velocities to obtain systems of coupled PDEs for image analysis applications. We show examples for object tracking and segmentation of electronic microscopy.
[1] L. Alvarez, P.L. Lions, and J.M. Morel, “Image Selective Smoothing and Edge Detection by Nonlinear Diffusion,” SIAM J. Numeric Analysis, vol. 29, pp. 845-866, 1992.
[2] M. Bertalmío, G. Sapiro, and G. Randall, “Region Tracking on Level-Sets Methods,” IEEE Trans. Medical Imaging, vol. 18, no. 5, pp. 448-451, May 1999.
[3] M. Black, G. Sapiro, D. Marimont, and D. Heeger, “Robust Anisotropic Diffusion,” IEEE Trans. Image Processing, vol. 7, no. 3, pp. 421-432, 1998.
[4] A. Blake and M. Isard, Active Contours. New York: Springer-Verlag, 1998.
[5] V. Caselles, R. Kimmel, and G. Sapiro, “Geodesic Active Contours,” Int'l J. Computer Vision, vol. 22, no. 1, pp. 61-79, 1997.
[6] V. Caselles, G. Sapiro, and D.H. Chung, “Vector Median Filters, Inf-Sup Operations, and Coupled PDE's: Theoretical Connections,” J. Math. Imaging and Vision, vol. 12, pp. 109-120, Apr. 2000.
[7] Y.G. Chen, Y. Giga, and S. Goto, “Uniqueness and Existence of Viscosity Solutions of Generalized Mean Curvature Flow Equations,” J. Differential Geometry, vol. 33, 1991.
[8] L.C. Evans and J. Spruck, “Motion of Level Sets by Mean Curvature, I,” J. Differential Geometry, vol. 33, 1991.
[9] M. Kass, A. Witkin, and D. Terzopoulos, “Snakes: Active Contour Models,” Int'l J. Computer Vision, vol. 1, pp. 321-331, 1988.
[10] S. Kichenassamy, A. Kumar, P. Olver, A. Tannenbaum, and A. Yezzi, “Conformal Curvature Flows: From Phase Transitions to Active Vision,” Archive for Rational Mechanics and Analysis, vol. 134, pp. 275-301, 1996.
[11] R. Malladi, J. Sethian, and B.C. Vemuri, "Shape Modeling with Front Propagation: A Level Set Approach," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, pp. 158-175, 1995.
[12] S. Osher and J.A. Sethian, “Fronts Propagating with Curvature-Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations,” J. Computing in Physics, vol. 79, pp. 12-49, 1988.
[13] N. Paragios and R. Deriche, “A PDE-Based Level-Set Approach for Detection and Tracking of Moving Objects,” Proc. Int'l Conf. Computer Vision '98, Jan. 1998.
[14] N. Paragios and R. Deriche, “Geodesic Active Regions for Motion Estimation and Tracking,” Proc. Int'l Conf. Computer Vision, Sept. 1999.
[15] N. Paragios and R. Deriche, ”Unifying Boundary and Region-Based Information for Geodesic Active Tracking,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, June 1999.
[16] P. Perona and J. Malik, "Scale-Space and Edge Detection Using Anisotropic Diffusion," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 12, no. 7, pp. 629639, July 1990.
[17] Geometry-Driven Diffusion in Computer Vision, B.M. ter Haar Romeny, ed. Kluwer, 1994.
[18] M. Proesmans, E. Pauwels, and L. van Gool, “Coupled Geometry-Driven Diffusion Equations for Low-Level Vision,” Geometry Driven Diffusion in Computer Vision, B. Romeny, ed., The Netherlands: Kluwer, 1994.
[19] B. Tang, G. Sapiro, and V. Caselles, “Diffusion of General Data on Non-Flat Manifolds via Harmonic Maps Theory: The Direction Diffusion Case,” Int'l J. Computer Vision, to appear.
[20] L. Vazquez, G. Sapiro, and G. Randall, “Segmenting Neurons in Electronic Microscopy via Geometric Tracing,” Proc. IEEE Int'l Conf. Information Processing, Oct. 1998.

