Extraction of topologically simple isosurfaces from volume datasets

There are numerous algorithms in graphics and visualization whose performance is known to decay as the topological complexity of the input increases. On the other hand, the standard pipeline for 3D geometry acquisition often produces 3D models that are topologically more complex than their real forms. We present a simple and efficient algorithm that allows us to simplify the topology of an isosurface by alternating the values of some number of voxels. Its utility and performance are demonstrated on several examples, including signed distance functions from polygonal models and CT scans.

[1]  Brian Wyvill,et al.  Shrinkwrap : an adaptive algorithm for polygonizing an implicit surface , 1993 .

[2]  Herbert Edelsbrunner,et al.  Topological persistence and simplification , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[3]  Marc Levoy The Digital Michelangelo Project , 1999, Comput. Graph. Forum.

[4]  Touradj Ebrahimi,et al.  MESH: measuring errors between surfaces using the Hausdorff distance , 2002, Proceedings. IEEE International Conference on Multimedia and Expo.

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

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

[7]  Valerio Pascucci,et al.  Efficient computation of the topology of level sets , 2002, IEEE Visualization, 2002. VIS 2002..

[8]  Zoë J. Wood,et al.  Isosurface Topology Simplification , 2002 .

[9]  Joachim Giesen,et al.  Surface reconstruction based on a dynamical system † , 2002, Comput. Graph. Forum.

[10]  Pedro V. Sander,et al.  Texture mapping progressive meshes , 2001, SIGGRAPH.

[11]  Edward H. Adelson,et al.  The Laplacian Pyramid as a Compact Image Code , 1983, IEEE Trans. Commun..

[12]  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.

[13]  Jesse Freeman,et al.  in Morse theory, , 1999 .

[14]  Zoë J. Wood,et al.  Topological Noise Removal , 2001, Graphics Interface.

[15]  David P. Dobkin,et al.  MAPS: multiresolution adaptive parameterization of surfaces , 1998, SIGGRAPH.

[16]  J Jobson Daniel,et al.  Retinex Image Processing: Improved Fidelity to Direct Visual Observation , 1996 .

[17]  Valerio Pascucci,et al.  Contour trees and small seed sets for isosurface traversal , 1997, SCG '97.

[18]  Marc Levoy,et al.  A volumetric method for building complex models from range images , 1996, SIGGRAPH.

[19]  Renato Pajarola,et al.  Topology preserving and controlled topology simplifying multiresolution isosurface extraction , 2000 .

[20]  Joachim Giesen,et al.  The flow complex: a data structure for geometric modeling , 2003, SODA '03.

[21]  Peter Schröder,et al.  Normal meshes , 2000, SIGGRAPH.

[22]  Gilles Bertrand,et al.  A three-dimensional holes closing algorithm , 1996, Pattern Recognit. Lett..

[23]  Mikhail N. Vyalyi,et al.  Construction of contour trees in 3D in O(n log n) steps , 1998, SCG '98.

[24]  S. Osher,et al.  Geometric Level Set Methods in Imaging, Vision, and Graphics , 2011, Springer New York.

[25]  Jihad El-Sana,et al.  Controlled simplification of genus for polygonal models , 1997, Proceedings. Visualization '97 (Cat. No. 97CB36155).

[26]  Steven J. Gortler,et al.  Geometry images , 2002, SIGGRAPH.

[27]  Craig Gotsman,et al.  Triangle Mesh Compression , 1998, Graphics Interface.

[28]  Roger Crawfis,et al.  Isosurfacing in higher dimensions , 2000 .

[29]  C.W.A.M. van Overveld,et al.  How to shrinkwrap a critical point : an algorithm for the adaptive triangulation of iso-surfaces with arbitrary topology , 1996 .

[30]  Andrea Bottino,et al.  How to Shrinkwrap through a Critical Point : an Algorithm for the Adaptive Triangulation of Iso-Surfaces with Arbitrary Topology , 1996 .

[31]  Pere Brunet,et al.  Approximation of a Variable Density Cloud of Points by Shrinking a Discrete Membrane , 2005, Comput. Graph. Forum.

[32]  Marc Levoy,et al.  The digital Michelangelo project: 3D scanning of large statues , 2000, SIGGRAPH.

[33]  Jack Snoeyink,et al.  Computing contour trees in all dimensions , 2000, SODA '00.

[34]  J. A. Sethian,et al.  Fast Marching Methods , 1999, SIAM Rev..

[35]  Stefan Friedrich,et al.  Topology , 2019, Arch. Formal Proofs.

[36]  R. K. Shyamasundar,et al.  Introduction to algorithms , 1996 .

[37]  Zia-ur Rahman,et al.  Retinex Image Processing: Improved Fidelity To Direct Visual Observation , 1996, CIC.

[38]  Wolfgang Straßer,et al.  Real time compression of triangle mesh connectivity , 1998, SIGGRAPH.

[39]  Marshall M. Cohen A Course in Simple-Homotopy Theory , 1973 .

[40]  E. C. Zeeman,et al.  On the dunce hat , 1963 .

[41]  John Hart Morse Theory for Implicit Surface Modeling , 1997, VisMath.

[42]  Xiao Han,et al.  A topology preserving deformable model using level sets , 2001, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001.

[43]  Jarek Rossignac,et al.  Edgebreaker: a simple compression for surfaces with handles , 2002, SMA '02.

[44]  Pierre Alliez,et al.  Valence‐Driven Connectivity Encoding for 3D Meshes , 2001, Comput. Graph. Forum.