Polyhedral surface decomposition with applications

Abstract This paper addresses the problem of decomposing a polyhedral surface into “meaningful” patches. We describe two decomposition algorithms—flooding convex decomposition and watershed decomposition, and show experimental results. Moreover, we discuss three applications which can highly benefit from surface decomposition. These applications include content-based retrieval of three-dimensional models, metamorphosis of three-dimensional models and simplification.

[1]  Bernard Chazelle,et al.  Triangulating a non-convex polytype , 1989, SCG '89.

[2]  Marc Rioux,et al.  A content-based search engine for VRML databases , 1998, Proceedings. 1998 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No.98CB36231).

[3]  William E. Lorensen,et al.  Decimation of triangle meshes , 1992, SIGGRAPH.

[4]  Ayellet Tal,et al.  Polyhedron realization for shape transformation , 1998, The Visual Computer.

[5]  Raimund Seidel,et al.  On the difficulty of triangulating three-dimensional Nonconvex Polyhedra , 1992, Discret. Comput. Geom..

[6]  Paul J. Besl.  Triangles as a Primary Representation , 1994, Object Representation in Computer Vision.

[7]  Edward E. Smith,et al.  An Invitation to cognitive science , 1997 .

[8]  Wayne E. Carlson,et al.  Shape transformation for polyhedral objects , 1992, SIGGRAPH.

[9]  Marc Alexa,et al.  Merging polyhedral shapes with scattered features , 1999, Proceedings Shape Modeling International '99. International Conference on Shape Modeling and Applications.

[10]  Marshall W. Bern,et al.  Compatible tetrahedralizations , 1993, SCG '93.

[11]  Jean Serra,et al.  Image Analysis and Mathematical Morphology , 1983 .

[12]  Micha Sharir,et al.  Piecewise-Linear Interpolation between Polygonal Slices , 1996, Comput. Vis. Image Underst..

[13]  Gill Barequet,et al.  Multilevel sensitive reconstruction of polyhedral surfaces from parallel slices , 2000, The Visual Computer.

[14]  Ross T. Whitaker,et al.  Partitioning 3D Surface Meshes Using Watershed Segmentation , 1999, IEEE Trans. Vis. Comput. Graph..

[15]  Marc Alexa.  Merging polyhedral shapes with scattered features , 2000, The Visual Computer.

[16]  Michael Elad,et al.  Content based retrieval of VRML objects: an iterative and interactive approach , 2002 .

[17]  Bernard Chazelle,et al.  Matching 3D models with shape distributions , 2001, Proceedings International Conference on Shape Modeling and Applications.

[18]  Bernard Chazelle,et al.  Convex Partitions of Polyhedra: A Lower Bound and Worst-Case Optimal Algorithm , 1984, SIAM J. Comput..

[19]  Bernard Chazelle,et al.  Triangulating a nonconvex polytope , 1990, Discret. Comput. Geom..

[20]  Micha Sharir,et al.  Castles in the air revisited , 1994, Discret. Comput. Geom..

[21]  Bernard Chazelle,et al.  Strategies for Polyhedral Surface Decomposition: an Experimental Study , 1997, Comput. Geom..

[22]  C. Bajaj.  Algebraic Geometry and its Applications , 1994 .

[23]  Bernard Chazelle,et al.  Decomposition Algorithms in Geometry , 1994 .

[24]  Chandrajit L. Bajaj,et al.  Convex Decomposition of Polyhedra and Robustness , 1992, SIAM J. Comput..

[25]  Romain Raffin,et al.  Curvilinear displacement of free-form-based deformation , 2000, The Visual Computer.

[26]  Irving Biederman,et al.  Visual object recognition , 1993 .

[27]  Uwe Schöning.  Graph Isomorphism is in the Low Hierarchy , 1988, J. Comput. Syst. Sci..

[28]  David P. Luebke,et al.  A Developer's Survey of Polygonal Simplification Algorithms , 2001, IEEE Computer Graphics and Applications.

[29]  Hiromasa Suzuki,et al.  3D geometric metamorphosis based on harmonic map , 1997, Proceedings The Fifth Pacific Conference on Computer Graphics and Applications.

[30]  Michael S. Floater,et al.  Parametrization and smooth approximation of surface triangulations , 1997, Comput. Aided Geom. Des..