A Graph–Based Approach to Surface Reconstruction

A new approach to the reconstruction of a surface from an unorganized set of points in space is presented. The point set may for example be obtained with a laser scanner or a manual digitizing tool, and is the only source of information about the shape of the acquired object. The basic idea is to calculate the Euclidean minimum spanning tree (EMST) of the given points. The EMST is then augmented to the so‐called surface description graph (SDG). Finally the wire frame defined by the SDG are filled with triangles. The advantage of our approach is that also highly non‐convex and even disconnected surfaces are reconstructed quite reliably. This is demonstrated for a variety of data sets.

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

[2]  S. Rippa,et al.  Data Dependent Triangulations for Piecewise Linear Interpolation , 1990 .

[3]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

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

[5]  Robert Sedgewick,et al.  Algorithms in C , 1990 .

[6]  Nira Dyn,et al.  Algorithms for the construction of data dependent triangulations , 1990 .

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

[8]  Otto Nurmi,et al.  Algorithms for computational geometry , 1987 .

[9]  Tomás Feder,et al.  Optimal algorithms for approximate clustering , 1988, STOC '88.

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

[11]  Jeffrey L. Brown,et al.  Vertex based data dependent triangulations , 1991, Comput. Aided Geom. Des..

[12]  H. Edelsbrunner,et al.  Efficient algorithms for agglomerative hierarchical clustering methods , 1984 .

[13]  Larry L. Schumaker,et al.  Computing optimal triangulations using simulated annealing , 1993, Comput. Aided Geom. Des..

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

[15]  Tony DeRose,et al.  Mesh optimization , 1993, SIGGRAPH.

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