A triangulation-based hole patching method using differential evolution

In this work, a new hole patching method (namely as, HPDE) is proposed to repair the damaged or ill-scanned three dimensional objects in real engineering applications. Our method differentiates from other related algorithms mainly on the following three aspects. Firstly, our algorithm sufficiently utilizes the point information around the considered hole for each prediction by constructing point correspondences on both sides of the boundary curve of the hole; secondly, the missing points in the hole region are predicted by the algorithm of differential evolution (DE), which is used to obtain the topological and geometrical structures of the mesh in the hole region; thirdly, operations of mesh optimization are adopted for improving the quality of the obtained triangulation mesh. Numerical results on kinds of holes with complex shape and large curvature, and a comparison with two recently proposed algorithms verify the effectiveness of the algorithm, further experiments on the noisy data points illustrate the robustness of the algorithm against noise.

[1]  Peter Liepa,et al.  Filling Holes in Meshes , 2003, Symposium on Geometry Processing.

[2]  F. Prieto,et al.  MÉTODO DE LLENADO DE HUECOS EN MALLAS TRIANGULARES EMPLEANDO FUNCIONES DE BASE RADIAL , 2007 .

[3]  S. Osher,et al.  Fast surface reconstruction using the level set method , 2001, Proceedings IEEE Workshop on Variational and Level Set Methods in Computer Vision.

[4]  Michel Couprie,et al.  Hole filling in 3D volumetric objects , 2010, Pattern Recognit..

[5]  Prosenjit Bose,et al.  Filling holes in triangular meshes by curve unfolding , 2009, 2009 IEEE International Conference on Shape Modeling and Applications.

[6]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[7]  P Cignoni,et al.  DeWall: A fast divide and conquer Delaunay triangulation algorithm in Ed , 1998, Comput. Aided Des..

[8]  Greg Turk,et al.  Simplification and Repair of Polygonal Models Using Volumetric Techniques , 2003, IEEE Trans. Vis. Comput. Graph..

[9]  Steve Marschner,et al.  Filling holes in complex surfaces using volumetric diffusion , 2002, Proceedings. First International Symposium on 3D Data Processing Visualization and Transmission.

[10]  Kazuhiro Nakahashi,et al.  Robust generation of high‐quality unstructured meshes on realistic biomedical geometry , 2006 .

[11]  Marshall W. Bern,et al.  A new Voronoi-based surface reconstruction algorithm , 1998, SIGGRAPH.

[12]  Gabriel Taubin,et al.  A signal processing approach to fair surface design , 1995, SIGGRAPH.

[13]  Yen-Chu Hung,et al.  Hole filling of triangular mesh segments using systematic grey prediction , 2012, Comput. Aided Des..

[14]  Wei-Cheng Xie,et al.  Iteration and optimization scheme for the reconstruction of 3D surfaces based on non-uniform rational B-splines , 2012, Comput. Aided Des..

[15]  William E. Lorensen,et al.  Marching cubes: A high resolution 3D surface construction algorithm , 1987, SIGGRAPH.

[16]  Tony DeRose,et al.  Surface reconstruction from unorganized points , 1992, SIGGRAPH.

[17]  R. Storn,et al.  Differential Evolution - A simple and efficient adaptive scheme for global optimization over continuous spaces , 2004 .

[18]  Yongtae Jun,et al.  A piecewise hole filling algorithm in reverse engineering , 2005, Comput. Aided Des..

[19]  Micha Sharir,et al.  Filling gaps in the boundary of a polyhedron , 1995, Comput. Aided Geom. Des..

[20]  Anath Fischer,et al.  Reconstruction of Freeform Objects with Arbitrary Topology Using Neural Networks and Subdivision Techniques , 2003 .

[21]  Flavio Prieto,et al.  A Hole-Filling Algorithm for Triangular Meshes Using Local Radial Basis Function , 2006, IMR.

[22]  Wei Zhao,et al.  A robust hole-filling algorithm for triangular mesh , 2007, 2007 10th IEEE International Conference on Computer-Aided Design and Computer Graphics.

[23]  Hans-Peter Seidel,et al.  A General Framework for Mesh Decimation , 1998, Graphics Interface.

[24]  Alan M. Shih,et al.  A novel hole patching algorithm for discrete geometry using non-uniform rational B-spline , 2011 .

[25]  Wei Yu,et al.  Diversity-maintained differential evolution embedded with gradient-based local search , 2013, Soft Comput..

[26]  Alan M. Shih,et al.  Hybrid Approach for Repair of Geometry with Complex Topology , 2011, IMR.

[27]  Marco Attene,et al.  ReMESH: An Interactive Environment to Edit and Repair Triangle Meshes , 2006, IEEE International Conference on Shape Modeling and Applications 2006 (SMI'06).

[28]  Tony DeRose,et al.  Mesh optimization , 1993, SIGGRAPH.

[29]  P. N. Suganthan,et al.  Differential Evolution: A Survey of the State-of-the-Art , 2011, IEEE Transactions on Evolutionary Computation.