This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Veinerization: A New Shape Description for Flexible Skeletonization
May 1998 (vol. 20 no. 5)
pp. 505-521

Abstract—Despite the intuitive interpretation of the skeleton as the "center line of the shape," it is surprisingly hard to get skeletonization algorithms that simultaneously produce all the "good" properties we expect (e.g., well-centered, well-connected, rotation-invariant, efficient, robust, accurately reflecting the shape). In this paper, we introduce the new concept of "veinerization," which produces a graph that contains all the "topological" information needed to derive a wide variety of skeletons. Theoretically, the main contribution is to provide a homogeneous framework for integration of the major concepts described in other related works on digital skeletonization. In practice, the new aspect of this approach is to provide the user with different criteria for selecting the most suitable skeleton for a given application; e.g., the user can select a suitable threshold for obtaining the desirable balance between "having a skeleton without noisy prunes" and "having a skeleton that reflects the initial shape." This algorithm has been tested on numerous kinds of patterns, including pathological ones like fractal sets well-known for the complexity of their shapes.

[1] C. Arcelli, "A Condition for Digital Points Removal," Signal Processing, vol. 1, pp. 283-285, July 1979.
[2] C. Arcelli, G. Sanniti di Baja, "A Width Independant Fast Thinning Algorithm," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 7, no. 4, pp. 463-474, July 1985.
[3] H. Blum, "A Transformation for Extracting New Parameter of Shape," Models for the Perception of Speech and Visual Form.Cambridge, Mass.: MIT Press, 1967.
[4] G. Borgefors, "Distance Transformation in Digital Images," CVGIP, vol. 34, pp. 344-371, 1986.
[5] J.M. Chassery and A. Montanvert, "Géométrie Discréte en Analyse d'Images," Hermes, ed. Paris, 1991.
[6] Y.K. Chu and C.Y. Suen, "An Alternate Smoothing and Stripping Algorithm for Thinning Digital Binary Patterns" Signal Processing, vol. 11, pp. 207-222, 1986.
[7] P.E. Danielsson, "Euclidean Distance Mapping," Computer Graphics and Image Processing, vol. 14, pp. 227-248, 1980.
[8] E.S. Deutsch, "Thinning Algorithms on Rectangular, Hexagonal and Triangular Arrays," Comm. ACM, vol. 15, pp. 827-837, 1972.
[9] Y. Ge and J.M. Fitzpatrick, "On the Generation of Skeletons From Discrete Euclidean Distance Maps," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 18, pp. 1,055-1,066, 1996.
[10] C.H. Hilditch, "Linear Skeletons From Square Cupboard," Machine Intelligence, vol. 4, B. Meltzer and D. Mitchie, eds., pp. 403-420.Edinburgh: Edinburgh Univ. Press, 1969.
[11] B.K. Jang and R.T. Chin, "Reconstructable Parallel Thinning," Thinning Methodologies for Pattern Recognition, C.Y. Suen P.S.P. Wang, eds., pp 181-218. World Scientifc Publishing, 1994.
[12] P.C.K. Kwok, "A Thinning Algorithm by Contour Generation," Comm. ACM, vol. 31, no. 11, pp. 1,314-1,324, 1988.
[13] L. Lam, S.W. Lee, and C.Y. Suen, “Thinning Methodologies: A Comprehensive Survey,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 14, pp. 869-885, 1992.
[14] S.W. Lee, L. Lam, and C.Y. Suen, "A Systematic Evaluation of Skeletonization Algorithms," Thinning Methodologies for Pattern Recognition, C.Y. Suen and P.S.P. Wang, eds., pp. 239-262. World Scientifc Publishing, 1994.
[15] H. Ma, "A Comparative Study of Thinning Algorithms in Pattern Processing," Master's major report of computer science, Dept of Computer Science, Concordia Univ., Nov. 1983.
[16] B.B. Mandelbrot, "Fractal Aspects of the Iterations of z→λz(1$-$z) for Complexλ, z," Ann. N.Y. Acad. Sci., vol. 357, pp. 249-259,New York, 1980.
[17] G. Matheron, "Examples of Topological Properties of Skeletons," Image Analysis and Mathematical Morphology, vol. 2, Theoretical Advances, pp. 217-238.London: Academic Press, 1988.
[18] F. Meyer, "Skeletons in Digital Spaces," Image Analysis and Mathematical Morphology. vol. 2, Theoretical Advances, pp. 257-296.London: Academic Press, 1988.
[19] F. Meyer, "Cytologie Quantitative et Morphologie Mathématique," PhD thesis, Ecoles de Mines de Paris, Paris 1979.
[20] C.W. Niblack, P.B. Gibbons, and D.W. Capson, "Generating Skeletons and Centerlines From the Distance Transform," CVGIP: Graphical Models and Image Processing, vol. 54, no. 5, pp 420-437, Sept. 1992.
[21] R. Ogniewicz, "Discrete Voronoi Skeletons," PhD thesis, 1993, Hartung Gore Verlag, Konstanz.
[22] R. Ogniewicz and O. Kübler, "Hierarchic Voronoi Skeletons," Pattern Recognition, vol. 28, no. 3, pp. 343-359, 1995.
[23] D.W. Paglerioni, "Distance Transforms, Properties and Machine Vision Application," CVGIP, Graphical Models and Image Processing, vol. 54, no. 1, pp. 56-74, Jan. 92.
[24] M.P. Deseilligny, "Lecture Automatique de Cartes," PhD dissertation, "UniversitéParis V-RenéDescartes, vol. 2, pp. 25-59,Paris, Oct. 1994.
[25] R. Plamondon, C.Y. Suen, M. Bourdeau, and C. Barriere, "Methodologies for Evaluating Thinning Algorithms for Character Recognition," Int'l J. Pattern Recognition and Artificial Intelligence, vol. 7, no. 5, pp. 1,247-1,270, Oct. 1993.
[26] R. Plamondon, M. Bourdeau, C. Chouinard, and C.Y. Suen, "Validation of Preprocessing Algorithms: A Methodology and Its Application to the Design of a Thinning Algorithm for Handwritten Characters," Proc. Second Int'l Conf. Document Analysis and Recognition (ICDAR'93), pp 262-269,Tsukuba, Japan, Oct. 1993.
[27] A. Rosenfeld, "Digital Geometry," Pictures Languages, pp. 7-37.New-York: Academic Press, 1979.
[28] D. Rutovitz, "Pattern Recognition," J. Royal Statistical Soc., vol. 129, pp. 504-530, 1966.
[29] R. Stefanelli and A. Rosenfeld, "Some Parallel Thinning Algorithms for Digital Pictures," J. ACM, vol. 18, pp. 255-264, 1971.
[30] C.Y. Suen and C. Nadal, "An Algorithm for Thinning Handwritten Characters," Tech. Rep. CENPARMI, Concordia Univ., 1991.
[31] G. Sanniti di Baja and E. Thiel, "A Skeletonization Algorithm Running on Path-Based Distance Maps," Image and Vision Computting, 1034, vol. 14, pp 47-57, Feb. 1996.
[32] S. Suzuki and K. Abe, "Binary Picture Thinning by an Iterative Parallel Two-Subcycle Operation," Pattern Recognition, vol. 10, no. 3, pp. 297-397, 1987.
[33] S. Suzuki, N. Ueda, and J. Sklansky, "Graph-Based Thinning for Binary Images," Thinning Methodologies for Pattern Recognition, C.Y. Suen and P.S.P. Wang, eds., pp. 45-66. World Scientifc Publishing, 1994.
[34] H. Talbot and L. Vincent, "Euclidean Skeletons and Conditional Bisectors," SPIE, vol. 1818, Visual Communication and Image Processing, pp 862-876 1992.
[35] H. Tamura, "A Comparison of Line Thinning Algorithms From Digital Geometry View Point," Proc Fourth Int'l Joint Conf. Pattern Recognition, pp 715-719, 1978.
[36] S. Tsuruoka, F. Kimura, M. Yoshimura, S. Yokoi, and Y. Miyake, "Thinning Algorithms for Digital Pictures and Their Application to Handprinted Character Recognition," Trans. IECE Japan, pp 525-532, 1983.
[37] T.Y. Zhang and C.Y. Suen, "A Fast Parallel Algorithm for Thinning Digital Pattern," Comm. ACM, vol. 27, pp 236-239, 1984.
[38] L. Vincent, "Algorithmes MorphologiquesàBase de Files d'Attentes et de Lacets. Extension aux Graphes," PhD dissertation of "Ecole Nationale Supérieure des Mines de Paris," pp 85-129, 1990.

Index Terms:
Digital skeleton, veinerization, skeletonization, context adaptation, digital topology, graphs, fractal sets.
Citation:
Marc Pierrot Deseilligny, Georges Stamon, Ching Y. Suen, "Veinerization: A New Shape Description for Flexible Skeletonization," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 20, no. 5, pp. 505-521, May 1998, doi:10.1109/34.682180
Usage of this product signifies your acceptance of the Terms of Use.