Abstract
The eccentricity transform associates to each point of a shape the distance to the point farthest away from it. The transform is defined in any dimension, for open and closed manyfolds, is robust to Salt & Pepper noise, and is quasi-invariant to articulated motion. This paper presents and algorithm to efficiently compute the eccentricity transform of a polygonal shape with or without holes. In particular, based on existing and new properties, we provide an algorithm to decompose a polygon using parallel steps, and use the result to derive the eccentricity value of any point.
Chapter PDF
References
Rosenfeld, A.: A note on ’geometric transforms’ of digital sets. Pattern Recognition Letters 1(4), 223–225 (1983)
Gorelick, L., Galun, M., Sharon, E., Basri, R., Brandt, A.: Shape representation and classification using the poisson equation. In: CVPR (2), pp. 61–67 (2004)
Kropatsch, W.G., Ion, A., Haxhimusa, Y., Flanitzer, T.: The eccentricity transform (of a digital shape). In: 13th International Conference on Discrete Geometry for Computer Imagery, Szeged, Hungary, October 25-27, pp. 437–448. Springer, Heidelberg (2006)
Ogniewicz, R.L., Kübler, O.: Hierarchic Voronoi Skeletons. Pattern Recognition 28(3), 343–359 (1995)
Siddiqi, K., Shokoufandeh, A., Dickinson, S., Zucker, S.W.: Shock graphs and shape matching. International Journal of Computer Vision 30, 1–24 (1999)
Paragios, N., Chen, Y., Faurgeras, O.: 6. In: Handbook of Mathematical Models in Computer Vision, pp. 97–111. Springer, Heidelberg (2006)
Soille, P.: Morphological Image Analysis. Springer, Heidelberg (1994)
Harary, F.: Graph Theory. Addison-Wesley, Reading (1969)
Diestel, R.: Graph Theory. Springer, New York (1997)
Klette, R., Rosenfeld, A.: Digital Geometry. Morgan Kaufmann, San Francisco (2004)
Ion, A., Peyré, G., Haxhimusa, Y., Peltier, S., Kropatsch, W.G., Cohen, L.: Shape matching using the geodesic eccentricity transform - a study. In: 31st OAGM/AAPR, Schloss Krumbach, Austria, OCG (May 2007)
Maisonneuve, F., Schmitt, M.: An efficient algorithm to compute the hexagonal and dodecagonal propagation function. Acta Stereologica 8(2), 515–520 (1989)
Ion, A., Peltier, S., Haxhimusa, Y., Kropatsch, W.G.: Decomposition for efficient eccentricity transform of convex shapes. In: Kropatsch, W.G., Kampel, M., Hanbury, A. (eds.) CAIP 2007, Springer, Heidelberg (2007)
Suri, S.: The all-geodesic-furthest neighbor problem for simple polygons. In: Symposium on Computational Geometry, pp. 64–75 (1987)
Khuller, S., Raghavachari, B.: Basic Graph Algorithms. CRC Press (1998)
Sethian, J.: Level Sets Methods and Fast Marching Methods, 2nd edn. Cambridge Univ. Press, Cambridge (1999)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kropatsch, W.G., Ion, A., Peltier, S. (2007). Computing the Eccentricity Transform of a Polygonal Shape. In: Rueda, L., Mery, D., Kittler, J. (eds) Progress in Pattern Recognition, Image Analysis and Applications. CIARP 2007. Lecture Notes in Computer Science, vol 4756. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76725-1_31
Download citation
DOI: https://doi.org/10.1007/978-3-540-76725-1_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-76724-4
Online ISBN: 978-3-540-76725-1
eBook Packages: Computer ScienceComputer Science (R0)