An efficient and collision-free hole-filling algorithm for orthodontics

Hole filling of teeth and gums is an essential stage in orthodontics after segmentation. The patching mesh should keep the morphological features of generic teeth and gums while avoiding collision between two adjacent teeth. This paper presents an efficient hole-filling algorithm to reconstruct the missing part of teeth and gums. Our proposed method involves four necessary steps: boundary construction and projection, hole triangulation in 2D, back projection of vertices to 3D, and mesh fairing. By combining constrained Delaunay triangulation in 2D with back projection of vertices to 3D using mean value coordinates, we achieve high robustness of hole triangulation and a high-quality initial patching mesh. In addition, we propose an automatic method to control the deformation degree to avoid collision. Our experiments demonstrate that the proposed method can achieve satisfactory results, not only in morphology, but also in efficiency. The results are very similar to real teeth and gums and can meet the requirements of orthodontics in medicine.

[1]  M. Wang,et al.  An Automatic Hole-Filling Algorithm for Polygon Meshes , 2008 .

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

[3]  Jianhuang Wu,et al.  An Integrated Approach to Filling Holes in Meshes , 2010, 2010 International Conference on Artificial Intelligence and Computational Intelligence.

[4]  Jonathon Shlens,et al.  A Tutorial on Principal Component Analysis , 2014, ArXiv.

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

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

[7]  Tao Ju,et al.  Robust repair of polygonal models , 2004, ACM Trans. Graph..

[8]  Qing Yu,et al.  Single-Tooth Modeling for 3D Dental Model , 2010, Int. J. Biomed. Imaging.

[9]  Michael S. Floater,et al.  Mean value coordinates , 2003, Comput. Aided Geom. Des..

[10]  Daniel Cohen-Or,et al.  Least-squares meshes , 2004, Proceedings Shape Modeling Applications, 2004..

[11]  Marco Attene,et al.  A lightweight approach to repairing digitized polygon meshes , 2010, The Visual Computer.

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

[13]  Jonathan Richard Shewchuk,et al.  Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator , 1996, WACG.

[14]  Leif Kobbelt,et al.  An intuitive framework for real-time freeform modeling , 2004, ACM Trans. Graph..

[15]  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.

[16]  Neil A. Dodgson,et al.  Advances in Multiresolution for Geometric Modelling , 2005 .

[17]  Kai Hormann,et al.  Surface Parameterization: a Tutorial and Survey , 2005, Advances in Multiresolution for Geometric Modelling.

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

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

[20]  Paul-Louis George,et al.  The advancing-front mesh generation method revisited , 1994 .