This Article 
 Bibliographic References 
 Add to: 
On the Generation of Skeletons from Discrete Euclidean Distance Maps
November 1996 (vol. 18 no. 11)
pp. 1055-1066

Abstract—The skeleton is an important representation for shape analysis. A common approach for generating discrete skeletons takes three steps: 1) computing the distance map, 2) detecting maximal disks from the distance map, and 3) linking the centers of maximal disks (CMDs) into a connected skeleton. Algorithms using approximate distance metrics are abundant and their theory has been well established. However, the resulting skeletons may be inaccurate and sensitive to rotation. In this paper, we study methods for generating skeletons based on the exact Euclidean metric. We first show that no previous algorithms identifies the exact set of discrete maximal disks under the Euclidean metric. We then propose new algorithms and show that they are correct. To link CMDs into connected skeletons, we examine two prevalent approaches: connected thinning and steepest ascent. We point out that the connected thinning approach does not work properly for Euclidean distance maps. Only the steepest ascent algorithm produces skeletons that are truly medially placed. The resulting skeletons have all the desirable properties: they have the same simple connectivity as the figure, they are well-centered, they are insensitive to rotation, and they allow exact reconstruction. The effectiveness of our algorithms is demonstrated with numerous examples.

[1] C. Arcelli and G. Sanniti Di Baja, "A Width-Independent Fast Thinning Algorithm," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 7, no. 4, pp. 463-474, July 1985.
[2] C. Arcelli and G. Sanniti di Baja, “Finding Local Maxima in a Pseudo-Euclidean Distance Transform,” Computer Vision, Graphics, and Image Processing, vol. 43, pp. 361-367, 1988.
[3] C. Arcelli and G. Sanniti Di Baja, "Euclidean Skeleton vis Centre-of-Maximal-Disc Extraction," Image and Vision Computing, vol. 11, no. 3, pp. 163-173, Apr. 1993.
[4] C. Arcelli and G. Sanniti di Baja, "Ridge Points in Euclidean Distance Maps," Pattern Recognition Letters, vol. 13, pp. 237-243, 1992.
[5] H. Blum, "A Transformation for Extracting New Descriptors of Shape," Models for the Perception of Speech and Visual Form, W. Walthen-Dunn, ed., 1967.
[6] H. Blum, "Biological Shape and Visual Science: Part I," J. Theoretical Biology, vol. 38, pp. 205-287, 1973.
[7] H. Blum and R.N. Nagel, "Shape Description Using Weighted Symmetric Axis Features," Pattern Recognition, vol. 10, pp. 167-180, 1978.
[8] G. Borgefors, “Distance Transforms in Digital Images,” Computer Vision, Graphics, and Image Processing, vol. 34, pp. 344-371, 1986.
[9] G. Borgefors, I. Ragnemalm, and G. Sanniti Di Baja, "Feature Extraction on the Euclidean Distance Transform," Proc. Sixth Int'l Conf. Image Analysis and Processing: Progress in Image Analysis and Processing II, pp. 115-122, 1991.
[10] M. Brady and H. Asada, "Smoothed Local Symmetries and Their Implementation," Int'l J. Robotics Research, vol. 3, no. 3, pp. 36-61, 1984.
[11] J.W. Brandt and V.R. Algazi, “Continuous Skeleton Computation by Voronoi Diagram,” CVGIP: Image Understanding, vol. 55, no. 3, pp. 329-338, 1992.
[12] P.-E. Danielsson, "Euclidean Distance Mapping," Computer Vision, Graphics, and Image Understanding, vol. 14, pp. 227-248, 1980.
[13] E.R. Davies and A.P.N. Plummer, "Thinning Algorithms: A Critique and a New Methodology," Pattern Recognition, vol. 14, no. 1, pp. 53-53, 1981.
[14] 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.
[15] Y. Ge, "Cortical Surface Maps and Euclidean Skeletons for Intersubject Registration of Brain Images," PhD dissertation, Dept. of Computer Science, Vanderbilt Univ., 1995.
[16] F. Klein and O. Kübler,“Euclidean distance transformation and model-guided image interpretation,” Pattern Recognition Letters, vol. 5, pp. 19-29, 1987.
[17] F. Leymarie and M.D. Levine, “Simulating the Grassfire Transform Using an Active Contour Model,” IEEE Trans. Pattern Analysis and Machine Intellingence, vol. 14, no. 1, pp. 56-75, Jan. 1992.
[18] M. Leyton, "Symmetry-Curvature Duality," Computer Vision, Graphics, and Image Processing, vol. 38, pp. 327-341, 1987.
[19] M. Leyton, "A Process-Grammar for Shape," Artificial Intelligence, vol. 34, pp. 213-247, 1988.
[20] F. Meyer, "Skeletons and Perceptual Graphs," Signal Processing, vol. 16, pp. 335-363, 1989.
[21] F. Meyer, "Digital Euclidean Skeletons," Proc. SPIE Visual Comm. and Image Processing, vol. 1,360, pp. 251-262, 1990.
[22] 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, pp. 420-437, 1992.
[23] I. Ragnemalm,“Neighborhoods for distance transformations using ordered propagation,” Computer Vision, Graphics, and Image Processing: Image Understanding, vol. 56, pp. 399-409, 1992.
[24] S.M. Pizer, C.A. Burbeck, J.J. Coggins, D.S. Fritsch, and B.S. Morse, "Object Shape Before Boundary Shape: Scale Space Medial Axes," Technical Report TR92-025, Dept. of Computer Science, Univ. of North Carolina at Chapel Hill, 1992.
[25] 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.
[26] S. Riazanoff, B. Cervelle, and J. Chorowicz, "Parametrisable Skeletonization of Binary and Multilevel Images," Pattern Recognition Letters, vol. 11, pp. 25-33, 1990.
[27] H. Rom and G. Medioni, "Hierarchical Decomposition and Axial Representation of Shape," Proc. SPIE Geometric Methods in Computer Vision, vol. 1,570, pp. 262-273, 1991.
[28] A. Rosenfeld and A.C. Kak,Digital Picture Processing. Academic Press, 2nd ed., 1982
[29] A. Rosenfeld and J. Pfaltz,“Sequential operations in digital picture processing,” J. ACM, vol. 13, pp. 471-494, 1966.
[30] H. Talbot and L. Vincent, "Euclidean Skeletons and Conditional Bisectors," Proc. SPIE Visual Comm. and Image Processing '92, vol. 1,818, pp. 862-876, 1992.
[31] L. Vincent, “Exact Euclidean Distance Function by Chain Propagations,” Proc. IEEE Int'l Conf. Acoustics Speech Signal Processing, pp. 520-525, 1991.
[32] M.W. Wright and F. Fallside, "Skeletonisation as Model-Based Feature Detection," IEE Proc..-I, vol. 140, no. 1, pp. 7-11, Feb. 1993.

Index Terms:
Euclidean, skeleton, shape analysis, medial axis transform, axis of symmetry, distance transform, Euclidean distance transform.
Yaorong Ge, J. Michael Fitzpatrick, "On the Generation of Skeletons from Discrete Euclidean Distance Maps," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 18, no. 11, pp. 1055-1066, Nov. 1996, doi:10.1109/34.544075
Usage of this product signifies your acceptance of the Terms of Use.