Abstract
We introduce a polyhedral representation of surfaces for analysis and recognition of three-dimensional digital images. Our representation is based on combinatorial topology. By using a discrete version of combinatorial topology we also present an algorithm for reconstruction of a polyhedron in a discrete space from a set of lattice points.
The first author has been on leave from School of Information Science, JAIST, Japan, thanks to the JSPS postdoctoral fellowships for research abroad from October 2000.
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References
Rosenfeld, A. (1970): Connectivity in digital pictures. Journal of the Association for Computing Machinery 17 1, 146–160
Artzy, E., Frieder, G., Herman, G. T. (1981): The theory, design, implementation, and evaluation of a three-dimensional boundary detection algorithm. Computer Graphics Image Processing 15 1–24
Kong, T. Y., Rosenfeld, A. (1989): Digital topology: introduction and survey. Computer Vision Graphics and Image Processing 48, 357–393
Hausdor, F. (1937): Set theory. Chelsea Publishing Company
Alexandrov, P. S. (1956): Combinatorial topology I. Graylock Press
Stillwell, J. (1993): Classical topology and combinatorial group theory. Springer
Kong, T. Y., Roscoe, A. W., Rosenfeld, A. (1992): Concepts of digital topology. Topology and its Applications 46, 219–262
Voss, K. (1993): Discrete images, objects, and functions in Z 3. Springer-Verlag
Tourlakis, G., Mylopoulos, J. (1973): Some results in computational topology. Journal of the Association for Computing Machinery 20 3, 439–455
Lorensen, W. E., Cline, H. E. (1987): Marching cubes: a high-resolution 3d surface construction algorithm. Computer Graphics (SIGGRAPH’ 87) 21 4 163–169
Kenmochi, Y., Imiya, A., Ichikawa, A. (1998): Boundary extraction of discrete objects. Computer Vision and Image Understanding 71 3, 281–293
Clifford, W. K. (1956): The postulates of the science of space. The world of mathematics, Simon and Schuster, New York
Kovalevsky, V. A. (1989): Finite topology as applied to image analyses. Computer Vision Graphics and Image Processing 46, 141–161
Morgenthaler, D. G., Rosenfeld, A. (1981): Surfaces in three-dimensional images. Information and Control 51, 227–247
Couprie, M., Bertrand, G. (1998): Simplicity surfaces: a new definition of surfaces in Z3. SPIE Vision Geometry VII 3454, 40–51
Françcon, J. (1995): Discrete combinatorial surfaces. CVGIP: Graphical Models and Image Processing 57 1, 20–26
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© 2001 Springer-Verlag Berlin Heidelberg
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Kenmochi, Y., Imiya, A. (2001). Discrete Polyhedrization of a Lattice Point Set. In: Bertrand, G., Imiya, A., Klette, R. (eds) Digital and Image Geometry. Lecture Notes in Computer Science, vol 2243. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45576-0_9
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DOI: https://doi.org/10.1007/3-540-45576-0_9
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