Abstract
We present a new approach to the algorithmic study of planar curves, with applications to estimations of contours in images. We construct spaces of curves satisfying constraints suited to specific problems, exploit their geometric structure to quantify properties of contours, and solve optimization and inference problems. Applications include new algorithms for computing planar elasticae, with enhanced performance and speed, and geometric algorithms for the estimation of contours of partially occluded objects in images.
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Bruckstein, A. and Netravali, N. 1990. On minimal energy trajectories. Computer Vision, Graphics and Image Processing, 49:283–296.
Chan, T., Shen, J., and Vese, L. 2003. Variational PDE Models in Image Processing. Notices Amer. Math. Soc., 50:14–26.
Cootes, T.F., Cooper, D., Taylor, C.J., and Graham, J. 1995. Active Shape Models—Their Training and Application. Computer Vision and Image Understanding, 61:38–59.
Do Carmo, M.P. 1976. Differential Geometry of Curves and Surfaces, Prentice Hall, Inc.
Euler, L. 1744. Methodus Inveniendi Lineas Curvas Maximi Minimive Proprietate Gaudentes, Sive Solutio Problematis Isoperimetrici Lattisimo Sensu Accepti. Bousquet, Lausannae e Genevae, E65A. O. O. Ser. I, 24.
Horn, B. 1983. The Curve of Least Elastic Energy. ACM Trans. Math. Software, 9:441–460.
Joshi, S., Srivastava, A., Mio, W., and Liu, X. 2004. Hierarchical Organization of Shapes for Efficient Retrieval. In Proc. ECCV 2004, LNCS, Prague, Czech Republic, pp. 570–581.
Kass, M., Witkin, A., and Terzopoulos, D. 1988. Snakes: Active Contour Models. International Journal of Computer Vision, 1: 321–331.
Kimia, B., Frankel, I., and Popescu, A. 2003. Euler Spiral for Shape Completion. International Journal of Computer Vision, 54:159–182.
Klassen, E., Srivastava, A., Mio, W., and Joshi, S. 2004. Analysis of Planar Shapes Using Geodesic Paths on Shape Spaces. Trans. Pattern Analysis and Machine Intelligence, 26:372–383.
Mio, W., Srivastava, A., and Klassen, E. 2004a. Interpolations with Elastica in Euclidean Spaces. Quarterly of Applied Mathematics, 62:359–378.
Mio, W., Srivastava, A., and Liu, X. 2004b. Learning and Bayesian Shape Extraction for Object Recognition. In Proc. ECCV 2004, LNCS, Prague, Czech Republic, pp. 62–73.
Mumford, D. 1994. Elastica and Computer Vision, Springer, New York. pp. 491–506.
Palais, R.S. 1963. Morse Theory on Hilbert Manifolds. Topology, 2:299–340.
Royden, H. 1988. Real Analaysis, Prentice Hall.
Sethian, J. 1996. Level Set Methods: Evolving Interfaces in Geometry, Fluid Mechanics, Computer Vision, and Material Science, Cambridge University Press.
Sharon, E., Brandt, A., and Basri, R. 2000. Completion Energies and Scale. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(10):1117–1131.
Weiss, I. 1988. 3D Shape Representation by Contours. Computer Vision, Graphics and Image Processing, 41:80–100.
Williams, L. and Jacobs, D. 1997. Local Parallel Computation of Stochastic Completion Fields. Neural Computation, 9:837–858.
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Mio, W., Srivastava, A. & Liu, X. Contour Inferences for Image Understanding. Int J Comput Vision 69, 137–144 (2006). https://doi.org/10.1007/s11263-006-6856-6
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DOI: https://doi.org/10.1007/s11263-006-6856-6