Abstract
Skeletons can be viewed as a compact shape representation in that each shape can be completely reconstructed from its skeleton. However, the usefulness of a skeletal representation is strongly limited by its instability. Skeletons suffer from contour noise in that small contour deformation may lead to large structural changes in the skeleton. A large number of skeleton computation and skeleton pruning approaches has been proposed to address this issue. Our approach differs fundamentally in the fact that we cast skeleton pruning as a trade-off between skeleton simplicity and shape reconstruction error. An ideal skeleton of a given shape should be the skeleton with a simplest possible structure that provides a best possible reconstruction of a given shape. To quantify this trade-off, we propose that the skeleton simplicity corresponds to model simplicity in the Bayesian framework, and the shape reconstruction accuracy is expressed as goodness of fit to the data. We also provide a simple algorithm to approximate the maximum of the Bayesian posterior probability which defines an order for iteratively removing the end branches to obtain the pruned skeleton. Presented experimental results obtained without any parameter tuning clearly demonstrate that the resulting skeletons are stable to boundary deformations and intra class shape variability.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Siddiqi K, Pizer S. Medial Representations: Mathematics, Algorithms and Applications. Berlin: Springer, 2008
Blum H. Biological shape and visual science (part I). J Theor Biol, 1973, 38: 205–287
August J, Siddiqi K, Zucker S. Ligature instabilities and the perceptual organization of shape. Comput Vis Image Und, 1999, 76: 231–243
Dimitrov P, Phillips C, Siddiqi K. Robust and efficient skeletal graphs. In: CVPR. Hilton Head Island: IEEE, 2000. 417–423
Siddiqi K, Bouix S, Tannenbaum A, et al. Hamilton-Jacobi skeletons. Int J Comput Vision, 2002, 48: 215–231
Aslan C, Tari S. An axis-based representation for recognition. In: ICCV. Beijing: IEEE, 2005. 1339–1346
Torsello A, Hancock E. Correcting curvature-density effects in the Hamilton-Jacobi skeleton. IEEE Trans Image Process, 2006, 15: 887–891
Borgefors G, Ramella G, di Baja G S. Hierarchical decomposition of multiscale skeleton. IEEE Trans Pattern Anal, 2001, 13: 1296–1312
Katz R, Pizer S. Untangling the blum medial axis transform. Int J Comput Vision, 2003, 55: 139–153
Bai X, Latecki L, Liu W Y. Skeleton pruning by contour partitioning with discrete curve evolution. IEEE Trans Pattern Anal, 2007, 29: 449–462
Bai X, Latecki L. Discrete skeleton evolution. In: EMMCVPR. Ezhou: Springer, 2007. 362–374
Eede M, Macrini D, Telea A, et al. Canonical skeletons for shape matching. In: ICPR. Hong Kong: IEEE, 2006. 64–69
Ward A, Hamarneh G. Gmat: the Groupwise Medial Axis Transform for Fuzzy Skeletonization and Intelligent Pruning. Technical Report. School of Computing Science, Simon Fraser University, 2008
Ward A, Hamarneh G. The groupwise medial axis transform for fuzzy skeletonization and pruning. IEEE Trans Pattern Anal, 2010, 32: 1084–1096
Aslan C, Erdem A, Erdem E, et al. Disconnected skeleton: shape at its absolute scale. IEEE Trans Pattern Anal, 2008, 30: 2188–2203
Bai X, Latecki L. Path similarity skeleton graph matching. IEEE Trans Pattern Anal, 2008, 30: 1282–1292
Macrini D, Siddiqi K, Dickinson S. From skeletons to bone graphs: medial abstraction for object recognition. In: CVPR. Anchorage: IEEE, 2008. 1–8
Bai X, Wang X G, Latecki L, et al. Active skeleton for non-rigid object detection. In: ICCV. Kyoto: IEEE, 2009. 575–582
Levinshtein A, Sminchisescu C, Dickinson S. Multiscale symmetric part detection and grouping. In: ICCV. Kyoto: IEEE, 2009. 2162–2169
Adluru N, Latecki L J, Lakaemper R, et al. Contour grouping based on local symmetry. In: ICCV. Rio de Janeiro: IEEE, 2007. 1–8
Latecki L, Lakeamper R, Eckhardt U. Shape descriptors for non-rigid shapes with a single closed contour. In: CVPR. Hilton Head Island: IEEE, 2000. 424–429
Arcelli C, di Baja G S. A width-independent fast thinning algorithm. IEEE Trans Pattern Anal, 1985, 7: 463–474
Pudney C. Distance-ordered homotopic thinning: a skeletonization algorithm for 3d digital images. Comput Vis Image Und, 1998, 72: 404–413
Leymarie F, Levine M. Simulating the grassfire transaction form using an active contour model. IEEE Trans Pattern Anal, 1992, 14: 56–75
Golland P, Grimson E. Fixed topology skeletons. In: CVPR. Hilton Head Island: IEEE, 2000. 10–17
Tang Y, You X. Skeletonization of ribbon-like shapes based on a new wavelet function. IEEE Trans Pattern Anal, 2003, 25: 1118–1133
Brandt J, Algazi V. Continuous skeleton computation by voronoi diagram. CVGIP: Image Und, 1992, 55: 329–338
Ogniewicz R, Kübler O. Hierarchic voronoi skeletons. Pattern Recogn, 1995, 28: 343–359
Mayya N, Rajan V. Voronoi diagrams of polygons: a framework for shape representation. In: CVPR. Seattle: IEEE, 1994. 638–643
Arcelli C, di Baja G S. Euclidean skeleton via center-of-maximal-disc extraction. Image Vision Comput, 1993, 11: 163–173
Malandain G, Fernandez-Vidal S. Euclidean skeletons. Image Vision Comput, 1998, 16: 317–327
Choi W P, Lam K M, Siu W C. Extraction of the euclidean skeleton based on a connectivity criterion. Pattern Recogn, 2003, 36: 721–729
Kimmel R, Shaked D, Kiryati N, et al. Skeletonization via distance maps and level sets. Comput Vis Image Und, 1995, 3: 382–391
Ge Y, Fitzpatrick J. On the generation of skeletons from discrete euclidean distance maps. IEEE Trans Pattern Anal, 1996, 18: 1055–1066
Meyer F. Skeletons and perceptual graphs. Signal Process, 1989, 16: 335–363
Maragos P, Schafer R W. Morphological skeleton representation and coding of binary images. IEEE Trans Acoust Speech Signal Proc, 1986, 34: 1228–1244
Goutsias J, Schonfeld D. Morphological representation of discrete and binary images. IEEE Trans Pattern Anal, 1991, 39: 1369–1379
Kresch R, Malah D. Morphological reduction of skeleton redundancy. Signal Process, 1994, 38: 143–151
Zhu S, Yuille A. Forms: a flexible object recognition and modeling system. Int J Comput Vision, 1996, 20: 187–212
Sebastian T, Klein P, Kimia B. Recognition of shapes by editing their shock graphs. IEEE Trans Pattern Anal, 2004, 26: 550–571
Liu T, Geiger D, Kohn R. Representation and self-similarity of shapes. In: ICCV. Bombay: IEEE, 1998. 1129–1135
Siddiqi K, Shokoufandeh A, Dickinson S, et al. Shock graphs and shape matching. Int J Comput Vis, 1999, 35: 13–32
Shaked D, Bruckstein A. Pruning medial axes. Comput Vis Image Und, 1998, 69: 156–169
Mokhtarian F, Mackworth A. A theory of multiscale, curvature-based shape representation for planar curves. IEEE Trans Pattern Anal, 1992, 14: 789–805
Gold C, Thibault D, Liu Z. Map generalization by skeleton retraction. In: ICA Workshop on Map Generalization. Ottawa: ICA, 1999
Jiang H B, Liu W P, Wang D, et al. Case: connectivity-based skeleton extraction in wireless sensor network. In: INFOCOM. Rio de Janeiro: IEEE, 2009. 2916–2920
Krinidis S, Chatzis V. A skeleton family generator via physics-based deformable models. IEEE Trans Image Process, 2009, 18: 1–11
Choi H, Choi S, Moon H. Mathematical theory of medial axis transform. Pac J Math, 1997, 181: 57–88
Feldman J, Singh M. Bayesian estimation of the shape skeleton. Proc Natl Acad Sci U. S. A., 2006, 103: 18,014–18,019
Belongie S, Malik J, Puzicha J. Shape matching and object recognition using shape contexts. IEEE Trans Pattern Anal, 2002, 24: 509–522
Shen W, Bai X, Hu R, et al. Skeleton growing and pruning with bending potential ratio. Pattern Recogn, 2011, 44: 196–209
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Shen, W., Bai, X., Yang, X. et al. Skeleton pruning as trade-off between skeleton simplicity and reconstruction error. Sci. China Inf. Sci. 56, 1–14 (2013). https://doi.org/10.1007/s11432-012-4715-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11432-012-4715-3