Chordal Axis on Weighted Distance Transforms
Abstract
Chordal Axis (CA) is a new representation of planar shapes introduced by Prasad in [1], useful for skeleton computation, shape analysis, characterization and recognition. The CA is a subset of chord and center of discs tangent to the contour of a shape, derivated from Medial Axis (MA). Originally presented in a computational geometry approach, the CA was extracted on a constrained Delaunay triangulation of a discretely sampled contour of a shape. Since discrete distance transformations allow to efficiently compute the center of distance balls and detect discrete MA, we propose in this paper to redefine the CA in the discrete space, to extract on distance transforms in the case of chamfer norms, for which the geometry of balls is well-known, and to compare with MA.
Keywords
image analysis shape description chordal axis medial axis discrete geometry chamfer or weighted distancesReferences
- 1.Prasad, L.: Morphological analysis of shapes. CNLS Newsletter 139 (1997)Google Scholar
- 2.Blum, H.: A transformation for extracting new descriptors of shape. In: Wathen-Dunn, W. (ed.) Models for the Perception of Speech and Visual Form, pp. 362–380. MIT Press, Cambridge (1967)Google Scholar
- 3.Pfaltz, J., Rosenfeld, A.: Computer representation of planar regions by their skeletons. Comm. of ACM 10, 119–125 (1967)CrossRefGoogle Scholar
- 4.Montanari, U.: Continuous skeletons from digitized images. Journal of the ACM 16(4), 534–549 (1969)MATHCrossRefGoogle Scholar
- 5.Attali, D., Montanvert, A.: Semicontinuous skeletons of 2d and 3d shapes. In: Aspects of Visual Form Processing, pp. 32–41. World Scientific, Singapore (1994)Google Scholar
- 6.Prasad, L.: Rectification of the chordal axis transform and a new criterion for shape decomposition. In: 11th DGCI, Poitiers (2005)Google Scholar
- 7.Remy, E., Thiel, E.: Medial Axis for Chamfer Distances: computing LUT and Neighbourhoods in 2D or 3D. Pattern Recognition Letters 23(6), 649–661 (2002)MATHCrossRefGoogle Scholar
- 8.Remy, E., Thiel, E.: Exact Medial Axis with Euclidean Distance. Image and Vision Computing 23(2), 167–175 (2005)CrossRefGoogle Scholar
- 9.Borgefors, G.: Distance transformations in arbitrary dimensions. Computer Vision, Graphics and Image Processing 27, 321–345 (1984)CrossRefGoogle Scholar
- 10.Rosenfeld, A., Pfaltz, J.L.: Sequential operations in digital picture processing. Journal of ACM 13(4), 471–494 (1966)MATHCrossRefGoogle Scholar
- 11.Borgefors, G.: Distance transformations in digital images. Computer Vision, Graphics and Image Processing 34, 344–371 (1986)CrossRefGoogle Scholar
- 12.Thiel, E.: Géométrie des distances de chanfrein. HDR, Univ. de la Méditerranée, Aix-Marseille 2 (2001), http://www.lif-sud.univ-mrs.fr/~thiel/hdr
- 13.Attali, D., Sanniti di Baja, G., Thiel, E.: Skeleton simplification through non significant branch removal. Image Processing and Communications 3(3-4), 63–72 (1997)Google Scholar