This Article 
 Bibliographic References 
 Add to: 
Partitioning 3D Surface Meshes Using Watershed Segmentation
October-December 1999 (vol. 5 no. 4)
pp. 308-321

Abstract—This paper describes a method for partitioning 3D surface meshes into useful segments. The proposed method generalizes morphological watersheds, an image segmentation technique, to 3D surfaces. This surface segmentation uses the total curvature of the surface as an indication of region boundaries. The surface is segmented into patches, where each patch has a relatively consistent curvature throughout, and is bounded by areas of higher, or drastically different, curvature. This algorithm has applications for a variety of important problems in visualization and geometrical modeling including 3D feature extraction, mesh reduction, texture mapping 3D surfaces, and computer aided design.

[1] J.P. Serra, Image Analysis and Mathematical Morphology. London: Academic Press, 1982.
[2] H. Hoppe, “Progressive Meshes,” Proc. SIGGRAPH '96, pp. 99-108, 1996.
[3] A. Varshney, P. Agarwal, and F.P.B. Jr, “Automatic Generation of Multiresolution Hierarchies for Polygonal Models,” Proc. First Workshop Simulation and Interaction in Virtual Environments, pp. 25-28, 1995.
[4] A.W.F. Lee, W. Sweldens, P. Schröder, L. Cowsar, and D. Dobkin, “MAPS: Multiresolution Adaptive Parameterization of Surfaces,” Computer Graphics (SIGGRAPH '98 Proc.), M. Cohen, ed., vol. 32, pp. 95-104, July 1998.
[5] C.L. Bajaj and T. Dey, "Convex Decomposition of Polyhedra and Robustness," SIAM J. Computing, vol. 21, pp. 339-364, 1992.
[6] B. Chazelle and L. Palios, “Triangulating a Nonconvex Polytope,” Discrete and Computational Geometry, vol. 5, pp. 505-526, 1990.
[7] B. Chazelle, D.P. Dobkin, N. Shouraboura, and A. Tal, “Strategies for Polyhedral Surface Decomposition: An Experimental Study,” Proc. 11th Ann. ACM Symp. Computational Geometry, pp. 297-305, June 1995.
[8] J. Koënderink and A. van Doorn, “The Structure of Two-Dimensional Scalar Fields with Applications to Vision,” Biological Cybernetics, vol. 33, pp. 151-158, 1979.
[9] D. Eberly, Ridges in Image and Data Analysis. Dordrecht: Kluwer Academic, 1996.
[10] R.B. Fisher, A.W. Fitzgibbon, and D. Eggert, “Extracting Surface Patches from Complete Range Descriptions,” Proc. Int'l Conf. Recent Advances in 3-D Digital Imaging and Modeling, pp. 148-154, Ottawa, Canada, May 1997.
[11] D. Faugeras and M. Hebert, “A 3-D Recognition and Positioning Algorithm Using Geometric Matching between Primitive Surfaces,” Proc. Eighth Int'l Joint Conf. Artificial Intelligence, pp. 996-1,002, 1983.
[12] P.J. Besl, Surfaces in Range Image Understanding. New York: Springer-Verlag 1988.
[13] E. Trucco and R.B. Fisher, "Experiments in Curvature-Based Segmentation of Range Data," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, no. 2, pp. 177-181, Feb. 1995.
[14] M. Baccar, “Surface Characterization Using a Gaussian Weighted Least Squares Technique towards Segmentation of Range Images,” master's thesis, Univ. Tennessee, K noxville, May 1994.
[15] A.C.F. Colchester, “Network Representation of 2D and 3D Images,” 3D Imaging in Medicine, K.H. Höhne, H. Fuchs, and S. Pizer, eds., pp. 45-62, Springer-Verlag, 1990.
[16] L.D. Griffin, A.C.F. Colchester, and G.P. Robinson, “Scale and Segmentation of Gray-Level Images Using Maximum Gradient Paths,” Image and Vision Computing, vol. 10, pp. 389-402, 1992.
[17] L.R. Nackerman, “Two-Dimensional Critical Point Configuration Graphs,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 6, no. 4, pp. 442-450, 1984.
[18] J. Koënderink and A. van Doorn, “Local Features of Smooth Shapes: Ridges and Courses,” SPIE Proc. Geometric Methods in Computer Vision II, vol. 2031, pp. 2-13, 1993.
[19] W.E. Lorensen and H.E. Cline, “Marching Cubes: A High Resolution 3D Surface Construction Algorithm,” Computer Graphics (SIGGRAPH '87 Proc.), vol. 21, pp. 163-169, 1987.
[20] J. Koënderink, Solid Shape. Cambridge, Mass.: MIT Press, 1991.
[21] J. Sethian, Level Set Methods: Evolving Interfaces in Geometry, Fluid Mechanics, Computer Vision and Materials Science. New York: Cambridge Univ. Press, 1996.
[22] R.T. Whitaker, “A Level-Set Approach to 3D Reconstruction From Range Data,” Int'l J. Computer Vision, vol. 29, pp. 203-231, Oct. 1998.
[23] C. Gourley, “Pattern Vector Based Reduction of Large Multimodal Data Sets for Fixed Rate Interactivity during Visualization of Mutliresolution Models,” PhD thesis, Univ. of Tennessee, K noxville, 1998.
[24] C. Gourley, C. Dumont, and M.A. Abidi, “Fixed-Rate Interactivity for Visualization of Photo-Realistic Multiresolution Models,” Am. Nuclear Soc.: Eighth Topical Meeting on Robotics and Remote Systems, Apr. 1999.

Index Terms:
Surfaces, surface segmentation, watershed algorithm, curvature-based methods.
Alan P. Mangan, Ross T. Whitaker, "Partitioning 3D Surface Meshes Using Watershed Segmentation," IEEE Transactions on Visualization and Computer Graphics, vol. 5, no. 4, pp. 308-321, Oct.-Dec. 1999, doi:10.1109/2945.817348
Usage of this product signifies your acceptance of the Terms of Use.