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Skeletal curves of 3D astrocyte samples

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Języki publikacji
EN
Abstrakty
EN
The paper discusses the concept of simple (and non-simple) elements for the generation of topologic skeletons, their transformation into abstract curve graphs, and the analysis of such graphs. The definition of a branching index of a point on a curve is fundamental in curve theory (in Euclidean space), and leads to important subjects of curve analysis. This paper derives analogous notions, such as branching index, branch element, and junction, for digital curves, which allow us to introduce new concepts for analyzing complex digital curves in a 3D space. The paper provides new theoretical insights, and also discusses an application project (the description of astrocytes in 3D confocal images of human brain tissue). This work was originally initiated by a particular research project at the Medical School of The University of Auckland. Medical experts developed the hypothesis that features of astrocytes in confocal volume scans are useful for defining states between normal and abnormal tissue. The calculation of skeletal curves, as proposed and studied in this paper, provides a valuable tool for calculating such features.
Słowa kluczowe
Rocznik
Strony
105--129
Opis fizyczny
Bibliogr. 21 poz., rys., tab., wykr.
Twórcy
autor
  • CITR, University of Auckland, Tamaki Campus, Building 731 Auckland, New Zealand
Bibliografia
  • [1] Aleksandrov P. S.: Combinatorial topology, Volume 1. Graylock Press, New York, 1956.
  • [2] Kim E. C.: Three-dimensional digital line segments. IEEE Trans. Pattern Analysis and Machine Intelligence, 5, 231-234, 1983.
  • [3] Kovalevsky V.: Finite topology as applied to image analysis. Computer Vision, Graphics, and Image Processing, 46, 141-161, 1989.
  • [4] Lee T., Kashyap R. L., Chu C.: Building skeleton models via 3D medial surface/axis thinning algorithms. Graphical Models and Image Processing, 56: 462- 478, 1994.
  • [5] Debled-Rennesson L, Reveilles J.-P.: A linear algorithm for segmentation of digital curves. Int. J. Pattern Recognition Artificial Intelligence, 9:635-662, 1995.
  • [6] Kong T. Y.: On topology preservation in 2-D and 3-D thinning. Int. J. for Pattern Recognition and Artificial Intelligence, 9: 813-844, 1995.
  • [7] Brassard G., Bratley P.: Fundamentals of algorithmics. Prentice-Hall, New Jersey, 1996.
  • [8] Palagyi K., Kuba A.: A 3D 6-subiteration thinning algorithm for extracting medial lines. Pattern Recognition Letters, 19: 613-627, 1998.
  • [9] Palagyi K., Kuba A.: Directional 3D thinning using 8 subiterations. In Proceedings: DGCI'99, pages 325-336, LNCS 1568, Springer, 1999.
  • [10] Lee L. Q., Lumsdaine A., Siek J. G.: The boost graph library. Addison Wesley Professional, 352 pages, 2001.
  • [11] Lohou C.: Contribution to the topological analysis of images: study of thinning algorithms for 2D or 3D images, according to either a digital topology approach or a discrete topology approach. Thesis, Universite de Marne la Vallee, Paris, pages 1-365, 2001.
  • [12] Palagyi K., Sorantin E., Balogh E., Kuba A., Halmai C., Erdohelyi B., Hausegger K.: A sequential 3D thinning algorithm and its medical applications, in: Int. Conf. Information Processing in Medical Imaging, pages 409-415, LNCS 2082, Springer Berlin, 2001.
  • [13] Gau C. J., Kong T. Y.: 4D minimal non-simple sets. Discrete Geometry for Computer Imagery, pages 81-91, LNCS 2301, Springer, Berlin, 2002.
  • [14] Gau C. J., Kong T. Y.: Minimal non-simple sets in 4D binary images. Graphical Models, 65: 112-130, 2003.
  • [15] Klette G.: A comparative discussion of distance transformations and simple deformations in digital image processing. Machine Graphics & Vision, 12: 235-256, 2003.
  • [16] Klette G.: Simple points in 2D and 3D binary images. Proceedings of CAIP 2003, pages 57-64, LNCS 2756, Springer, Berlin.
  • [17] Palagyi K., Tschirren J., Sonka M.: Quantitative analysis of intrathoracic airway trees: methods and validation. in: Int. Conf. Information Processing in Medical Imaging, pages 222-232, LNCS 2732, Springer, 2003.
  • [18] Klette R., Rosenfeld A.: Digital geometry - geometrie methods for digital picture analysis. Morgan Kaufmann, San Francisco, 2004.
  • [19] Klette G., Pan M.: 3D topological thinning by identifying non-simple voxels, Proc. 10th IWCIA, pages 164-175, LNCS3322, Springer, Berlin, 2004.
  • [20] Borgefors G.: Digital distance transforms in 2D, 3D, and 4D. Handbook of Pattern Recognition and Computer Vision, pages 157-177, 2005.
  • [21] Klette G., Pan M.: Characterization of curve-like structures in 3D medical Images In Proc. IVCNZ, pages 164-175, Dunedin, 2005
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BWA1-0032-0006
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