Abstract
Branch indices of points on curves (introduced by Urysohn and Menger) are of basic importance in the mathematical theory of curves, defined in Euclidean space. This paper applies the concept of branch points in the 3D orthogonal grid, motivated by the need to analyze curve-like structures in digital images. These curve-like structures have been derived as 3D skeletons (by means of thinning). This paper discusses approaches of defining branch indices for voxels on 3D skeletons, where the notion of a junction will play a crucial role. We illustrate the potentials of using junctions in 3D image analysis based on a recent project of analyzing the distribution of astrocytes in human brain tissue.
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Debled-Rennesson, I., Reveilles, J.-P.: A linear algorithm for segmentation of digital curves. Int. J. Pattern Recognition Artificial Intelligence 9, 635–662 (1995)
Klette, G.: A comparative discussion of distance transformations and simple deformations in digital image processing. Machine Graphics & Vision 12, 235–256 (2003)
Klette, G.: Simple points in 2D and 3D binary images. In: Petkov, N., Westenberg, M.A. (eds.) CAIP 2003. LNCS, vol. 2756, pp. 57–64. Springer, Heidelberg (2003)
Klette, G., Pan, M.: 3D topological thinning by identifying non-simple voxels. In: Klette, R., Žunić, J. (eds.) IWCIA 2004. LNCS, vol. 3322, pp. 164–175. Springer, Heidelberg (2004)
Klette, G., Pan, M.: Characterization of curve-like structures in 3D medical images. In: Proc. Image Vision Computing New Zealand, pp. 164–175 (2005)
Klette, R., Rosenfeld, A.: Digital Geometry – Geometric Methods for Digital Picture Analysis. Morgan Kaufmann, San Francisco (2004)
Kong, T.Y.: On topology preservation in 2-D and 3-D thinning. Int. J. Pattern Recognition Artificial Intelligence 9, 813–844 (1995)
Palagyi, K., Sorantin, E., Balogh, E., Kuba, A., Halmai, C., Erdohelyi, B., Hausegger, K.: A sequential 3D thinning algorithm and its medical applications. In: Insana, M.F., Leahy, R.M. (eds.) IPMI 2001. LNCS, vol. 2082, pp. 409–415. Springer, Heidelberg (2001)
Palágyi, K., Kuba, A.: Directional 3D Thinning Using 8 Subiterations. In: Bertrand, G., Couprie, M., Perroton, L. (eds.) DGCI 1999. LNCS, vol. 1568, pp. 325–336. Springer, Heidelberg (1999)
Palagyi, K., Kuba, A.: A 3D 6-subiteration thinning algorithm for extracting medial lines. Pattern Recognition Letters 19, 613–627 (1998)
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© 2006 Springer-Verlag Berlin Heidelberg
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Klette, G. (2006). Branch Voxels and Junctions in 3D Skeletons. In: Reulke, R., Eckardt, U., Flach, B., Knauer, U., Polthier, K. (eds) Combinatorial Image Analysis. IWCIA 2006. Lecture Notes in Computer Science, vol 4040. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11774938_4
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DOI: https://doi.org/10.1007/11774938_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-35153-5
Online ISBN: 978-3-540-35154-2
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