CSIOR: Circle-Surface Intersection Ordered Resampling

Abstract Triangular mesh is one of the most popular 3D modalities, which usage spans a wide variety of applications in computer vision, computer graphics and multimedia. Raw mesh surfaces generated by 3D scanning devices often suffer from mesh irregularity and also lack the implicit ordered structure that characterizes 2D images. Therefore, they are not suitable to be processed as such, especially for applications requiring fine surface analysis tasks. In this paper, we propose CSIOR, a novel mesh regularization technique exhibiting novel capabilities including (a) quasi-equilateral triangle and ordered tessellation that can accommodate non-convex shaped surfaces, (b) implicit generation of iso-geodesic contours, and (c) preservation of the object geometric properties, such as shape and surface corrugations (relief patterns). We evidence the superiority of our technique over current methods through a series of experiments performed on a variety of surfaces with relief patterns.

[1]  G. Kunert.  Toward anisotropic mesh construction and error estimation in the finite element method , 2002 .

[2]  Qiang Du,et al.  Centroidal Voronoi Tessellations: Applications and Algorithms , 1999, SIAM Rev..

[3]  Andrea Giachetti,et al.  Recognition of Geometric Patterns Over 3D Models , 2018, 3DOR@Eurographics.

[4]  Shi-Min Hu,et al.  Preserving detailed features in digital bas-relief making , 2011, Comput. Aided Geom. Des..

[5]  J. Macgregor,et al.  Image texture analysis: methods and comparisons , 2004 .

[6]  L. Cohen,et al.  Surface segmentation using geodesic centroidal tesselation , 2004 .

[7]  Cheng Wang,et al.  Point cloud resampling using centroidal Voronoi tessellation methods , 2018, Comput. Aided Des..

[8]  Bruno Lévy,et al.  Mesh parameterization: theory and practice , 2007, SIGGRAPH Courses.

[9]  Alberto Del Bimbo,et al.  Representing 3D texture on mesh manifolds for retrieval and recognition applications , 2015, 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[10]  Michael M. Kazhdan,et al.  Screened poisson surface reconstruction , 2013, TOGS.

[11]  Andrea Giachetti,et al.  Retrieval of Surfaces with Similar Relief Patterns , 2017, 3DOR@Eurographics.

[12]  Qiang Du,et al.  Constrained Centroidal Voronoi Tessellations for Surfaces , 2002, SIAM J. Sci. Comput..

[13]  Andrea Giachetti,et al.  Shrec'17 Track: Retrieval of surfaces with similar relief patterns , 2017 .

[14]  Dong-Ming Yan,et al.  Isotropic Remeshing with Fast and Exact Computation of Restricted Voronoi Diagram , 2009, Comput. Graph. Forum.

[15]  Iasonas Kokkinos,et al.  Intrinsic shape context descriptors for deformable shapes , 2012, 2012 IEEE Conference on Computer Vision and Pattern Recognition.

[16]  Washington Mio,et al.  Correlations Between the Morphology of Sonic Hedgehog Expression Domains and Embryonic Craniofacial Shape , 2015, Evolutionary Biology.

[17]  Stefano Berretti,et al.  Boosting 3D LBP-based face recognition by fusing shape and texture descriptors on the mesh , 2015, 2015 IEEE International Conference on Image Processing (ICIP).

[18]  Akshay K. Singh,et al.  Deformable models in medical image analysis , 1996, Proceedings of the Workshop on Mathematical Methods in Biomedical Image Analysis.

[19]  Laurent D. Cohen,et al.  Geodesic Remeshing Using Front Propagation , 2003, International Journal of Computer Vision.

[20]  Naoufel Werghi,et al.  An ordered topological representation of 3D triangular mesh facial surface: concept and applications , 2012, EURASIP J. Adv. Signal Process..

[21]  Hervé Delingette,et al.  General Object Reconstruction Based on Simplex Meshes , 1999, International Journal of Computer Vision.

[22]  Alexander M. Bronstein,et al.  Expression-Invariant Representations of Faces , 2007, IEEE Transactions on Image Processing.

[23]  Paolo Cignoni,et al.  Almost Isometric Mesh Parameterization through Abstract Domains , 2010, IEEE Transactions on Visualization and Computer Graphics.

[24]  Leif Kobbelt,et al.  Teaching meshes, subdivision and multiresolution techniques , 2004, Comput. Aided Des..

[25]  Pierre Alliez,et al.  Isotropic Remeshing of Surfaces: A Local Parameterization Approach , 2003, IMR.