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Hierarchical Decomposition of Multiscale Skeletons
November 2001 (vol. 23 no. 11)
pp. 1296-1312

Abstract—This paper presents a new procedure to hierarchically decompose a multiscale discrete skeleton. The skeleton is a linear pattern representation that is generally recognized as a good shape descriptor. For discrete images, the discrete skeleton is often preferable. Multiresolution representations are convenient for many image analysis tasks. Our resulting skeleton decomposition shows two different types of hierarchy. The first type of hierarchy is one of different scales, as the original pattern is converted into an AND-pyramid and the skeleton is computed for each resolution level. The second type of hierarchy is established at each level of the pyramid by identifying and ranking skeleton subsets according to their permanence, where permanence is a property intrinsically related to local pattern thickness. To achieve the decomposition, both bottom-up and top-down analysis in the sense of moving from higher to lower resolution and vice versa are used. The bottom-up analysis is used to ensure that a part of the skeleton that is connected at a higher resolution level is also connected (if at all present) in the next, lower resolution level. The top-down analysis is used to build the permanence hierarchy ranking the skeleton components. Our procedure is based on the use of (3 × 3) local operations in digital images, so it is fast and easy to implement. This skeleton decomposition procedure is most effective on patterns having different thickness in different regions. A number of examples of decompositions of multiscale skeletons (with and without loops) will be shown. The skeletons are, in most cases, nicely decomposed into meaningful parts. The procedure is general and not limited to any specific application.

[1] Multiresolution Image Processing and Analysis. A. Rosenfeld, ed., Berlin: Springer Verlag, 1984.
[2] T.H. Hong and A. Rosenfeld, “Compact Region Extraction Using Weighted Pixel Linking in a Pyramid,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 6, pp. 222-229, 1984.
[3] S. Connelly and A. Rosenfeld, “A Pyramid Algorithm for Fast Curve Extraction,” Computer Vision, Graphics and Image Processing, vol. 49, pp. 332-345, 1990.
[4] A. Montanvert, P. Meer, and A. Rosenfeld, Hierarchical Image Analysis Using Irregular Tesselations IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, no. 4, pp. 307-316, Apr. 1991.
[5] H.H.S. Ip and S.W.C. Lam, “Alternative Strategies for Irregular Pyramid Construction,” Image and Vision Computing, vol. 14, pp. 297-304, 1996.
[6] P. Bottoni, L. Cinque, S. Levialdi, L. Lombardi, and P. Mussio, “Matching the Resolution Level to Salient Image Features,” Pattern Recognition, vol. 31, pp. 89-104, 1998.
[7] D. Chetverikov and A. Lerch, “A Multiresolution Algorithm for Rotation-Invariant Matching of Planar Shapes,” Pattern Recognition Letters, vol. 13, no. 9, pp. 669-676, 1992.
[8] V. Concepcion and H. Wechsler, “Detection and Localization of Objects in Time-Varying Imagery Using Attention, Representation and Memory Pyramids,” Pattern Recognition, vol. 29, no. 9, pp. 1543-1557, 1996.
[9] M. Pelillo, K. Siddiqi, and S.W. Zucker, “Matching Hierarchical Structures Using Association Graphs,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 11, pp. 1105-1120, 1999.
[10] S. Pizer, D. Fritsch, V. Johnson, and E. Chaney, Segmentation, Registration, and Measurement of Shape Variation via Image Object Shape IEEE Trans. Medical Imaging, 2000.
[11] K. Siddiqi, A. Shokoufandeh, S. Dickinson, and S. Zucker, Shock Graphs and Shape Matching Int'l J. Computer Vision, vol. 35, no. 1, pp. 13-32, Nov. 1999.
[12] S.C. Zhu and A.L. Yuille, “FORMS: A Flexible Object Recognition and Modeling System,” Int'l J. Computer Vision, vol. 20, no. 3, Dec. 1996
[13] H. Blum and R.N. Nagel, “Shape Description Using Weighted Symmetric Axis Features,” Pattern Recognition, vol. 10, pp. 167-180, 1978.
[14] G. Sanniti di Baja and E. Thiel, “(3,4)-Weighted Skeleton Decomposition for Pattern Representation and Description,” Pattern Recognition, vol. 27, pp. 1039-1049, 1994.
[15] C. Arcelli and G. Sanniti di Baja, “A Width-Independent Fast Thinning Algorithm,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 7, pp. 463-474, 1985.
[16] R.L. Ogniewicz, “Discrete Voronoi Skeletons,” PhD thesis, Hartung-Gorre Verlag, Konstanz, Germany, 1993.
[17] S.C. Zhu, “Stochastic Computation of Medial Axis in Markov Random Field,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 11, pp. 1,158-1,169, Nov. 1999.
[18] H. Rom and G. Medioni, “Hierarchical Decomposition and Axial Shape Description,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 15, pp. 973-981, 1993.
[19] A.R. Dill, M.D. Levine, and P.B. Noble, “Multiple Resolution Skeletons,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 9, pp. 495-504, 1987.
[20] S.M. Pizer, W.R. Oliver, and S.H. Bloomberg, “Hierarchical Shape Description via the Multiresolution Symmetric Axis Transform,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 9, pp. 505-511, 1987.
[21] G. Borgefors and G. Sanniti di Baja, “Multiresolution Skeletonization in Binary Pyramids,” Proc. 13th Int'l Conf. Pattern Recognition, vol. D, pp. 570-574, 1996.
[22] G. Borgefors, G. Ramella, and G. Sanniti di Baja, “Using Top-Down and Bottom-Up Analysis for a Multiscale Skeleton Hierarchy,” Image Analysis and Processing, A. Del Bimbo, ed., pp. 369-376, Lecture Notes on Computer Science, vol. 1310, Berlin: Springer, 1997.
[23] G. Borgefors, G. Ramella, G. Sanniti di Baja, and S. Svensson, “On the Multiscale Representation of 2D and 3D Shapes,” Graphical Models and Image Processing, vol. 61, pp. 44-62, 1999.
[24] G. Borgefors, G. Ramella, and G. Sanniti di Baja, “Multiscale Skeletons from Binary Pyramids,” Advances in Visual Form Analysis, C. Arcelli, L.P. Cordella, and G. Sanniti di Baja, eds., pp. 31-42, Singapore: World Scientific, 1997.
[25] G. Sanniti di Baja and E. Thiel, “Skeletonization Algorithm Running on Path-Based Distance Maps,” Image and Vision Computing, vol. 14, pp. 47-57, 1996.
[26] G. Borgefors, “Distance Transforms in Digital Images,” Computer Vision, Graphics, and Image Processing, vol. 34, pp. 344-371, 1986.
[27] S. Yokoi, J.I. Toriwaki, and T. Fukumura, “An Analysis of Topological Properties of Digitized Binary Pictures Using Local Features,” Computer Graphics and Image Processing, vol. 4, pp. 63-73, 1975.
[28] C. Arcelli and G. Sanniti di Baja, “Euclidean Skeleton via Center-of-Maximal-Disc Extraction,” Image and Vision Computing, vol. 11, pp. 163-173, 1993.

Index Terms:
Skeleton, decomposition, multiresolution, binary pyramid.
Citation:
Gunilla Borgefors, Giuliana Ramella, Gabriella Sanniti di Baja, "Hierarchical Decomposition of Multiscale Skeletons," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 23, no. 11, pp. 1296-1312, Nov. 2001, doi:10.1109/34.969119
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