Graph-based surface reconstruction using structures in scattered point sets

The authors present an algorithm for the reconstruction of a surface from an unorganized set of points in space. The point data may be obtained from a laser range scanner or any other digitizing tool to describe the shape of the object(s). The basic idea of the algorithm is to construct some kind of wire frame for the surface, the so-called surface description graph. This is performed by applying several steps. In the final part of the algorithm this wire frame is then filled with triangles. Each step uses rules for the reconstruction which are based on human knowledge in geometric structures. These rules are designed to allow the reconstruction of artificial objects as well as natural objects and are extendable in many aspects for ongoing research. As a result of this approach, the algorithm is able to reconstruct surfaces in data sites with changing point density as well as high curvature of the surface. In addition, it automatically recognizes the number of objects covered in the point set. Several examples are given to demonstrate its features.

[1]  Charles T. Zahn,et al.  Graph-Theoretical Methods for Detecting and Describing Gestalt Clusters , 1971, IEEE Transactions on Computers.

[2]  Andreas Baader,et al.  Ein Umwelterfassungssystem für multisensorielle Montageroboter , 1995 .

[3]  Heinrich Müller,et al.  Interpolation and Approximation of Surfaces from Three-Dimensional Scattered Data Points , 1997, Scientific Visualization Conference (dagstuhl '97).

[4]  Dominique Attali,et al.  r-regular shape reconstruction from unorganized points , 1997, SCG '97.

[5]  Francis Schmitt,et al.  Surface Reconstruction from Unstructured 3D Data , 1996, Comput. Graph. Forum.

[6]  Chandrajit L. Bajaj,et al.  Sampling and reconstructing manifolds using alpha-shapes , 1997, CCCG.

[7]  Chandrajit L. Bajaj,et al.  Reconstructing Surfaces and Functions on Surfaces from Unorganized Three-Dimensional Data , 1997, Algorithmica.

[8]  Baining Guo,et al.  Surface reconstruction: from points to splines , 1997, Comput. Aided Des..

[9]  Matthias Eck,et al.  Automatic reconstruction of B-spline surfaces of arbitrary topological type , 1996, SIGGRAPH.

[10]  H. Edelsbrunner,et al.  Tetrahedrizing Point Sets in Three Dimensions , 1988, ISSAC.

[11]  Gerhard Roth,et al.  An Efficient Volumetric Method for Building Closed Triangular Meshes from 3-D Image and Point Data , 1997, Graphics Interface.

[12]  Remco C. Veltkamp,et al.  Closed Object Boundaries from Scattered Points , 1994, Lecture Notes in Computer Science.

[13]  Roderick Urquhart,et al.  Graph theoretical clustering based on limited neighbourhood sets , 1982, Pattern Recognit..

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

[15]  G. Hirzinger,et al.  Three-dimensional surface reconstruction based on a self-organizing feature map , 1993 .

[16]  Remco C. Veltkamp.  Boundaries through Scattered Points of Unknown Density , 1995, CVGIP Graph. Model. Image Process..

[17]  Robert M. O'Bara,et al.  Geometrically deformed models: a method for extracting closed geometric models form volume data , 1991, SIGGRAPH.

[18]  Gerd Hirzinger,et al.  A self-organizing algorithm for multisensory surface reconstruction , 1994, Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS'94).

[19]  Baba C. Vemuri,et al.  Geometric Methods in Computer Vision , 1991 .

[20]  Pascal Fua,et al.  Reconstructing Surfaces from Unstructured 3D Points , 1992, ECCV 1992.

[21]  John D. Radke,et al.  On the Shape of a Set of Points , 1988 .

[22]  Marie-Paule Cani,et al.  Automatic Reconstruction of Unstructured 3D Data: Combining a Medial Axis and Implicit Surfaces , 1995, Comput. Graph. Forum.

[23]  Guido Brunnett,et al.  Polyhedral Reconstruction of 3D Objects by Tetrahedra Removal , 1997 .

[24]  Robert Mencl,et al.  A Graph–Based Approach to Surface Reconstruction , 1995, Comput. Graph. Forum.

[25]  Jean-Daniel Boissonnat,et al.  Geometric structures for three-dimensional shape representation , 1984, TOGS.

[27]  Demetri Terzopoulos,et al.  Constraints on Deformable Models: Recovering 3D Shape and Nonrigid Motion , 1988, Artif. Intell..

[28]  Herbert Edelsbrunner,et al.  Weighted alpha shapes , 1992 .

[29]  Pascal Fua,et al.  From points to surfaces , 1991, Optics & Photonics.

[30]  Narendra Ahuja,et al.  Extraction of early perceptual structure in dot patterns: Integrating region, boundary, and component gestalt , 1989, Comput. Vis. Graph. Image Process..

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

[32]  Pascal Fua,et al.  Segmenting Unstructured 3D Points into Surfaces , 1992, ECCV.

[33]  Dimitris N. Metaxas,et al.  Dynamic 3D models with local and global deformations: deformable superquadrics , 1990, [1990] Proceedings Third International Conference on Computer Vision.

[34]  Jindong Chen,et al.  Automatic Reconstruction of 3D CAD Models from Digital Scans , 1999, Int. J. Comput. Geom. Appl..

[35]  Chandrajit L. Bajaj,et al.  Automatic reconstruction of surfaces and scalar fields from 3D scans , 1995, SIGGRAPH.

[36]  Herbert Edelsbrunner,et al.  Three-dimensional alpha shapes , 1992, VVS.

[37]  Richard Szeliski,et al.  Surface modeling with oriented particle systems , 1992, SIGGRAPH.

[38]  Robert Mencl,et al.  Nearest neighbour search for visualization using arbitrary triangulations , 1996 .