Abstract
In this paper we introduce a deformable model based on cellular complexes. This model allows the representation of objects with different local dimensions, and has good topological properties.We define homotopic deformation on this model and prove that a local criterion can be used to characterize simple elements of the model. This criterion is used to build an homotopic deformable model that can be used for image processing.
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References
E. Artzy, G. Frieder, and G.T. Herman. The theory, design, implementation and evaluation of a three-dimensional surface detection algorithm. Computer Vision, Graphics and Image Processing: Graphical Models and Image Processing, 15:1–24, 1981.
Gilles Bertrand and Michel Couprie. Some structural properties of discrete surfaces. In Proceedings of DGCI’97, volume 1347 of LNCS, pages 113–124, 1997.
Gilles Bertrand and Grégoire Malandain. A new characterization of three-dimensional simple points. Pattern Recognition Letters, 15:169–175, February 1994.
Yann Cointepas, Isabelle Bloch, and Line Garnero. Cellular complexes: A tool for 3d homotopic segmentation in brain images. In Proceedings of ICIP’98, volume 3, pages 832–836, Chicago, 1998.
J. Françon. Discrete combinatorial surfaces. Computer Vision, Graphics and Image Processing: Graphical Models and Image Processing, 57:20–26, 1995.
Claude Godbillon. Eléments de topologie algébrique. Hermann, 1971.
Gabor T. Herman. Discrete multidimensional Jordan surfaces. Computer Vision, Graphics and Image Processing: Graphical Models and Image Processing, 54(6):507–515, 1992.
T.Y. Kong and A. Rozenfeld. Digital topology: Introduction and survey. Computer Vision, Graphics, and Image Processing, 48:357–393, 1989.
V.A. Kovalevsky. Discrete topology and contour definition. Pattern Recognition Letters, 2(5):281–288, 1984.
V.A. Kovalevsky. Finite topology as applied to image analysis. Computer Vision, Graphics, and Image Processing, 46:141–146, 1989.
Grégoire Malandain, Gilles Bertrand, and Nicolas Ayache. Topological segmentation of discrete surfaces. International Journal of Computer Vision, 10(2):183–197, 1993.
Réy Malgouyres. A definition of surfaces of Z 3. In Conference on Discrete Geometry for Computer Imaging, pages 23–34, 1994.
D.G. Morgenthaler and A. Rosenfeld. Surfaces in three-dimensional images. Information and control, 51:227–247, 1981.
J.R. Munkers. Elements of Algebraic Topology. Addison-Wesley, Menlo Park. CA, 1984.
T. Pavlidis. Structural Pattern Recognition. Springer-Verlag, New York, 1977.
Y.F. Tsao and K.S. Fu. A parallel thinning algorithm for 3-d pictures. Computer Vision, Graphics, and Image Processing, 17:315–331, 1981.
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© 1999 Springer-Verlag Berlin Heidelberg
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Cointepas, Y., Bloch, I., Garnero, L. (1999). A Discrete Homotopic Deformable Model Dealing with Objects with Different Local Dimensions. In: Bertrand, G., Couprie, M., Perroton, L. (eds) Discrete Geometry for Computer Imagery. DGCI 1999. Lecture Notes in Computer Science, vol 1568. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49126-0_20
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DOI: https://doi.org/10.1007/3-540-49126-0_20
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