CSDL Home IEEE Transactions on Pattern Analysis & Machine Intelligence 2011 vol.33 Issue No.04 - April

Subscribe

Issue No.04 - April (2011 vol.33)

pp: 709-720

Carlo Arcelli , Institute of Cybernetics "E.Caianiello," CNR, Naples

Gabriella Sanniti di Baja , Institute of Cybernetics "E.Caianiello," CNR, Naples

Luca Serino , Institute of Cybernetics "E.Caianiello," CNR, Naples

ABSTRACT

A distance-driven method to compute the surface and curve skeletons of 3D objects in voxel images is described. The method is based on the use of the <3,4,5> weighted distance transform, on the detection of anchor points, and on the application of topology preserving removal operations. The obtained surface and curve skeletons are centered within the object, have the same topology as the object, and have unit thickness. The object can be almost completely recovered from the surface skeleton since this includes almost all of the centers of maximal balls of the object. Hence, the surface skeleton is a faithful representation. In turn, though only partial recovery is possible from the curve skeleton, this still provides an appealing representation of the object.

INDEX TERMS

Voxel image, surface skeleton, curve skeleton, distance transform, symmetry point, topology preservation.

CITATION

Carlo Arcelli, Gabriella Sanniti di Baja, Luca Serino, "Distance-Driven Skeletonization in Voxel Images",

*IEEE Transactions on Pattern Analysis & Machine Intelligence*, vol.33, no. 4, pp. 709-720, April 2011, doi:10.1109/TPAMI.2010.140REFERENCES

- [1]
Medial Representations, K. Siddiqi and S.M. Pizer, eds. Springer, 2008.- [2] G. Sanniti di Baja and S. Svensson, "Surface Skeletons Detected on the ${\rm D}^6$ Distance Transform,"
Advances in Pattern Recognition, F.J. Ferri et al., eds., pp. 387-396, Springer, 2000.- [3] K. Palágyi, "A 3-Subiteration 3D Thinning Algorithm for Extracting Medial Surfaces,"
Pattern Recognition Letters, vol. 23, no. 6, pp. 663-675, 2002.- [4] C. Arcelli, G. Sanniti di Baja, and L. Serino, "New Removal Operators for Surface Skeletonization,"
Discrete Geometry for Computer Imagery, A. Kuba et al., eds., pp. 555-566, Springer, 2006.- [5] M. Couprie, D. Coeurjolly, and R. Zrour, "Discrete Bisector Function and Euclidean Skeleton in 2D and 3D,"
Image and Vision Computing, vol. 25, no. 10, pp. 1543-1556, 2007.- [6] T. Ju, M.L. Baker, and W. Chiu, "Computing a Family of Skeletons of Volumetric Models for Shape Description,"
Computer-Aided Design, vol. 39, no. 5, pp. 352-360, 2007.- [7] C. Arcelli, G. Sanniti di Baja, and L. Serino, "An Iterative Algorithm to Skeletonize the Distance Transform of 3D Objects,"
Image and Vision Computing, vol. 27, pp. 666-672, 2009.- [8] C.M. Ma and M. Sonka, "A Fully Parallel 3D Thinning Algorithm and Its Applications,"
Computer Vision and Image Understanding, vol. 64, no. 3, pp. 420-433, 1996.- [9] Y. Zhou, A. Kaufman, and A.W. Toga, "Three-Dimensional Skeleton and Centerline Generation Based on an Approximate Minimum Distance Field,"
The Visual Computer, vol. 14, pp. 303-314, 1998.- [10] J. Chuang, C. Tsai, and M.-C. Ko, "Skeletonization of Three-Dimensional Object Using Generalized Potential Field,"
IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 22, no. 11, pp. 1241-1251, Nov. 2000.- [11] I. Bitter, A.E. Kaufman, and M. Sato, "Penalized-Distance Volumetric Skeleton Algorithm,"
IEEE Trans. Visualization and Computer Graphics, vol. 7, no. 3, pp. 195-206, July-Sept. 2001.- [12] S. Svensson, I. Nyström, and G. Sanniti di Baja, "Curve Skeletonization of Surface-Like Objects in 3D Images Guided by Voxel Classification,"
Pattern Recognition Letters, vol. 23, no. 12, pp. 1419-1426, 2002.- [13] W. Xie, R.P. Thompson, and R. Perucchio, "A Topology-Preserving Parallel 3D Thinning Algorithm for Extracting the Curve Skeleton,"
Pattern Recognition, vol. 36, no. 7, pp. 1529-1544, 2003.- [14] S. Bouix, K. Siddiqi, and A. Tannenbaum, "Flux Driven Automatic Centerline Extraction,"
Medical Image Analysis, vol. 9, pp. 209-221, 2005.- [15] T. Wang and A. Basu, "A Note on a Fully Parallel Thinning Algorithms and Its Applications,"
Pattern Recognition Letters, vol. 28, no. 4, pp. 501-506, 2007.- [16] C. Arcelli, G. Sanniti di Baja, and L. Serino, "From 3D Discrete Surface Skeletons to Curve Skeletons,"
Proc. Int'l Conf. Image Analysis and Recognition, A. Campilho and M. Kamel, eds., pp. 507-516, 2008.- [17] C. Pudney, "Distance-Ordered Homotopic Thinning: A Skeletonization Algorithm for 3D Digital Images,"
Computer Vision and Image Understanding, vol. 72, no. 3, pp. 404-413, 1998.- [18] C.M. Ma and S.Y. Wan, "Parallel Thinning Algorithms on 3D(18, 6) Binary Images,"
Computer Vision and Image Understanding, vol. 80, no. 3, pp. 364-378, 2000.- [19] G. Sanniti di Baja and I. Nyström, "Skeletonization in 3D Discrete Binary Images,"
Handbook of Pattern Recognition and Computer Vision, C.H. Chen and P.P.S. Wang, eds., pp. 137-156, World Scientific, 2005.- [20] C. Lohou and G. Bertrand, "Two Symmetrical Thinning Algorithms for 3D Binary Images, Based on P-Simple Points,"
Pattern Recognition, vol. 40, no. 8, pp. 2301-2314, 2007.- [21] D. Thibault and C.M. Gold, "Terrain Reconstruction from Contours by Skeleton Generation,"
Geo Informatica, vol. 4, no. 4, pp. 349-373, 2000.- [22] N. Gagvani and D. Silver, "Animating Volumetric Models,"
Graphical Models, vol. 63, no. 6, pp. 443-458, 2001.- [23] T. He, L. Hong, D. Chen, and Z. Liang, "Reliable Path for Virtual Endoscopy: Ensuring Complete Examination of Human Organs,"
IEEE Trans. Visualization and Computer Graphics, vol. 7, no. 4, pp. 333-342, Oct.-Dec. 2001.- [24] E. Sorantin et al., "Spiral-CT-Based Assessment of Tracheal Stenoses Using 3-D Skeletonization,"
IEEE Trans. Medical Imaging, vol. 21, no. 3, pp. 263-273, Mar. 2002.- [25] L. Wade and R.E. Parent, "Automated Generation of Control Skeletons for Use in Animation,"
The Visual Computer, vol. 18, no. 2, pp. 97-110, 2002.- [26] A. Brennecke and T. Isenberg, "3D Shape Matching Using Skeleton Graphs,"
Proc. Conf. Simulation and Visualization, pp. 299-310, 2004.- [27] Y. Fridman, S.M. Pizer, S. Aylward, and E. Bullitt, "Extracting Branching Tubular Object Geometry via Cores,"
Medical Image Analysis, vol. 8, no. 3, pp. 169-176, 2004.- [28] A. Chaturvedi and Z. Lee, "Three-Dimensional Segmentation and Skeletonization to Build an Airway Tree Data Structure for Small Animals,"
Physics in Medicine and Biology, vol. 50, no. 7, pp. 1405-1419, 2005.- [29] R.J.T. Sadleir and P.F. Whelan, "Fast Colon Centerline Calculation Using Optimized 3D Topological Thinning,"
Computerized Medical Imaging and Graphics, vol. 29, no. 4, pp. 251-258, 2005.- [30] N.D. Cornea and D. Silver, "Curve-Skeleton Properties, Applications, and Algorithms,"
IEEE Trans. Visualization and Computer Graphics, vol. 13, no. 3, pp. 530-548, May/June 2007.- [31] H. Blum, "A Transformation for Extracting New Descriptors of Shape,"
Models for the Perception of Speech and Visual Form, W. Wathen-Dunn, ed., pp. 362-380, MIT Press, 1967.- [32] J.L. Pfaltz and A. Rosenfeld, "Computer Representation of Planar Regions by Their Skeletons,"
Comm. ACM, vol. 10, no. 2, pp. 119-125, 1967.- [33] P.K. Saha and B.B. Chaudhuri, "Detection of 3D Simple Points for Topology Preserving Transformations with Application to Thinning,"
IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 16, no. 10, pp. 1028-1032, Oct. 1994.- [34] G. Bertrand and G. Malandain, "A New Characterization of Three-Dimensional Simple Points,"
Pattern Recognition Letters, vol. 15, no. 2, pp. 169-175, 1994.- [35] T.Y. Kong and A. Rosenfeld, "Digital Topology: Introduction and Survey,"
Computer Vision, Graphics, and Image Processing, vol. 48, pp. 357-393, 1989.- [36] A. Rosenfeld and A.C. Kak,
Digital Picture Processing, second ed. Academic Press, 1982.- [37] G. Borgefors and G. Sanniti di Baja, "Analyzing Nonconvex 2D and 3D Patterns,"
Computer Vision and Image Understanding, vol. 63, no. 1, pp. 145-157, 1996.- [38] M. Yamashita and T. Ibaraki, "Distances Defined by Neighborhood Sequences,"
Pattern Recognition, vol. 19, no. 3, pp. 237-246, 1986.- [39] P.P. Das, P.P. Chakrabarti, and B.N. Chatterji, "Distance Functions in Digital Geometry,"
Information Sciences, vol. 42, pp. 113-136, 1987.- [40] G. Borgefors, "On Digital Distance Transforms in Three Dimensions,"
Computer Vision and Image Understanding, vol. 64, no. 3, pp. 368-376, 1996.- [41] B. Verwer, "Local Distances for Distance Transformations in Two and Three Dimensions,"
Pattern Recognition Letters, vol. 12, no. 11, pp. 671-682, 1991.- [42] J. Piper and E. Granum, "Computing Distance Transformations in Convex and Non-Convex Domains,"
Pattern Recognition, vol. 20, no. 6, pp. 599-615, 1987.- [43] I. Nyström and G. Borgefors, "Synthesising Objects and Scenes Using the Reverse Distance Transformation in 2D and 3D,"
Image Analysis and Processing, C. Braccini et al., eds., pp. 441-446, Springer, 1995.- [44] S. Svensson and G. Sanniti di Baja, "Using Distance Transforms to Decompose 3D Discrete Objects,"
Image and Vision Computing, vol. 20, pp. 529-540, 2002.- [45] G. Borgefors, I. Nyström, G. Sanniti di Baja, and S. Svensson, "Simplification of 3D Skeletons Using Distance Information,"
Vision Geometry IX, L.J. Latecki et al., eds., pp. 300-309, SPIE, 2000.- [46] D. Shaked and A.M. Bruckstein, "Pruning Medial Axes,"
Computer Vision and Image Understanding, vol. 69, no. 2, pp. 156-169, 1998.- [47] Z. Chen and S. Molloi, "Automatic 3D Vascular Tree Construction in CT Angiography,"
Computerized Medical Imaging and Graphics, vol. 27, no. 6, pp. 469-479, 2003.- [48] S. Svensson and G. Sanniti di Baja, "Simplifying Curve Skeletons in Volume Images,"
Computer Vision and Image Understanding, vol. 90, no. 3, pp. 242-257, 2003.- [49] X. Bai and L.J. Latecki, "Skeleton Pruning by Contour Partitioning with Discrete Curve Evolution,"
IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 29, no. 3, pp. 449-462, Mar. 2007.- [50] AIM@SHAPE Shape Repository, http://shapes.aimatshape.netviewmodels.php , 2010.
- [51] P. Shilane, P. Min, M. Kazhdan, and T. Funkhouser, "The Princeton Shape Benchmark,"
Proc. Conf. Shape Modeling Int'l, June 2004.- [52] H. Breu, J. Gil, D. Kirkpatrick, and M. Werman, "Linear Time Euclidean Distance Algorithms,"
IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, no. 5, pp. 529-533, May, 1995.- [53] J.A. Sethian, "A Marching Level Set Method for Monotonically Advancing Fronts,"
Proc. Nat'l Academy of Sciences, vol. 93, no. 4, pp. 1591-1595, 1996.- [54] G. Borgefors, I. Ragnemalm, and G. Sanniti di Baja, "The Euclidean Distance Transform: Finding the Local Maxima and Reconstructing the Shape,"
Proc. Scandinavian Conf. Image Analysis, vol. 2, pp. 974-981, 1991.- [55] E. Remy and E. Thiel, "Look-Up Tables for Medial Axis on Squared Euclidean Distance Transform,"
Discrete Geometry for Computer Imagery, I. Nyström et al., eds., pp. 224-235, Springer, 2003. |