Abstract
We introduce the distance transform for surfaces in 3D images, i.e., the distance transform where every voxel in the surface is labelled with its geodesic distance to the closest voxel on the border of the surface. Then, the distance transform is used to identify the set of centres of maximal geodesic discs in the surface. The centres of maximal geodesic discs can be used to give a compact representation of any surface. In particular, they can provide a useful representation of the surface skeleton of solid volume objects.
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C. Arcelli and G. Sanniti di Baja. Finding local maxima in a pseudo-Euclidean distance transform. Computer Vision, Graphics and Image Processing, 43(3):361–367, Sept. 1988. 445, 448
G. Borgefors. On digital distance transforms in three dimensions. Computer Visionand Image Understanding, 64(3):368–376, 1996. 445
G. Borgefors, I. Nyström, and G. Sanniti di Baja. Connected components in 3D neighbourhoods. In M. Frydrych, J. Parkkinen, and A. Visa, editors, Proceedings of 10th Scandinavian Conference on Image Analysis (SCIA’97), pages 567–572, Lappeenranta, Finland, 1997. Pattern Recognition Society of Finland. 445
G. Borgefors, I. Nyström, and G. Sanniti di Baja. Computing skeletons in three dimensions. Pattern Recognition, 32(7):1225–1236, July 1999. 445, 446, 447
G. Borgefors, I. Nyström, G. Sanniti di Baja, and S. Svensson. Simplification of 3D skeletons using distance information. Accepted for publication in Proceedings of SPIE International Symposium on Optical Science and Technology: Vision Geometry IX (vol. 4117), 2000. 450
L. Dorst and P. W. Verbeek. The constrained distance transformation: a pseudo-Euclidean recursive implementation of the Lee algorithm. In I. T. Young, J. Biemond, R. P. W. Duin, and J. J. Gerbrands, editors, Signal Processing III: Theories and Applications, pages 917–920. Elsevier Science Publishers B. V. (North-Holland), 1986. 443
G. Malandain, G. Bertrand, and N. Ayache. Topological segmentation of discrete surfaces. International Journal of Computer Vision, 10(2):183–197, 1993. 445, 446
J. Piper and E. Granum. Computing distance transformations in convex and nonconvex domains. Pattern Recognition, 20(6):599–615, 1987. 447
I. Ragnemalm and S. Ablameyko. On the distance transform of line patterns. In K. A. Høgda, B. Braathen, and K. Heia, editors, Scandinavian Conference on Image Analysis (SCIA’93), pages 1357–1363. Norwegian Society for Image Processing and Pattern recognition, 1993. 443, 446
P. K. Saha and B. B. Chaudhuri. 3D digital topology under binary transformation with applications. Computer Vision and Image Understanding, 63(3):418–429, May 1996. 445, 446
G. Sanniti di Baja and S. Svensson. Surface skeletons detected on the D 6 distance transform. In F. J. Ferri, J. M. Iñetsa, A. Amin, and P. Pudil, editors, Proceedings of SSSPR 2000-Alicante: Advances in Pattern Recognition, pages 387–396, Alicante, Spain, 2000. Springer-Verlag, Berlin Heidelberg. Lecture Notes in Computer Science 1121. 446, 450
J.-I. Toriwaki, N. Kato, and T. Fukumura. Parallel local operations for a new distance transformation of a line pattern and their applications. IEEE Transactions on Systems, Man, and Cybernetics, 9(10):628–643, 1979. 443, 446
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di Baja, G.S., Svensson, S. (2000). Detecting Centres of Maximal Geodesic Discs on the Distance Transform of Surfaces in 3D Images. In: Borgefors, G., Nyström, I., di Baja, G.S. (eds) Discrete Geometry for Computer Imagery. DGCI 2000. Lecture Notes in Computer Science, vol 1953. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44438-6_36
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