Robust and Adaptive Surface Reconstruction using Partition of Unity Implicits

Implicit surface reconstruction from unorganized point sets has been recently approached with methods based on multi-level partition of unity. We improve this approach by addressing local approximation robustness and iso-surface extraction issues. Our method relies on the J1 A triangulation to perform both the spatial subdivision and the iso-surface extraction. We also make use of orthogonal polynomials to provide adaptive local approximations in which the degree of the polynomial can be adjusted to accurately reconstruct the surface locally. Finally, we compare our results with previous work to demonstrate the robustness of our method.

[1]  Luiz Velho,et al.  Physically-based methods for polygonization of implicit surfaces , 1992 .

[2]  Mario Botsch,et al.  Feature sensitive surface extraction from volume data , 2001, SIGGRAPH.

[3]  Michael M. Kazhdan,et al.  Poisson surface reconstruction , 2006, SGP '06.

[4]  Marc Alexa,et al.  Approximating and Intersecting Surfaces from Points , 2003, Symposium on Geometry Processing.

[5]  Afonso Paiva,et al.  Robust adaptive meshes for implicit surfaces , 2006, 2006 19th Brazilian Symposium on Computer Graphics and Image Processing.

[6]  Ravi Krishna Kolluri,et al.  Provably good moving least squares , 2005, SIGGRAPH Courses.

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

[8]  Cláudio T. Silva,et al.  High-Quality Extraction of Isosurfaces from Regular and Irregular Grids , 2006, IEEE Transactions on Visualization and Computer Graphics.

[9]  Richard H. Bartels,et al.  Least-squares fitting using orthogonal multinomials , 1985, TOMS.

[10]  Hélio Lopes,et al.  Improved Partition of Unity Implicit Surface Reconstruction , 2006 .

[11]  Hans-Peter Seidel,et al.  3D scattered data interpolation and approximation with multilevel compactly supported RBFs , 2005, Graph. Model..

[12]  Richard H. Bartels,et al.  Algorithm 634: CONSTR and EVAL: routines for fitting multinomials in a least-squares sense , 1985, TOMS.

[13]  Richard K. Beatson,et al.  Reconstruction and representation of 3D objects with radial basis functions , 2001, SIGGRAPH.

[14]  H. Seidel,et al.  Multi-level partition of unity implicits , 2003 .

[15]  Mark Hall,et al.  Adaptive polygonalization of implicitly defined surfaces , 1990, IEEE Computer Graphics and Applications.

[16]  E Chernyaev,et al.  Marching cubes 33 : construction of topologically correct isosurfaces , 1995 .

[17]  Arthur W. Toga,et al.  Surface mapping brain function on 3D models , 1990, IEEE Computer Graphics and Applications.

[18]  Rosane Minghim,et al.  The Jal triangulation: An adaptive triangulation in any dimension , 2006, Comput. Graph..

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

[20]  Andrew H. Gee,et al.  Regularised marching tetrahedra: improved iso-surface extraction , 1999, Comput. Graph..

[21]  Enrico O. Purisima,et al.  A new tetrahedral tesselation scheme for isosurface generation , 1998, Comput. Graph..

[22]  Jules Bloomenthal,et al.  An Implicit Surface Polygonizer , 1994, Graphics Gems.

[23]  Roberto Scopigno,et al.  A modified look-up table for implicit disambiguation of Marching Cubes , 1994, The Visual Computer.

[24]  Nina Amenta,et al.  The Domain of a Point Set Surface , 2004, PBG.

[25]  Afonso Paiva,et al.  Vector field reconstruction from sparse samples with applications , 2006, 2006 19th Brazilian Symposium on Computer Graphics and Image Processing.