Reconstructing Curves and Surfaces from Samples

Tamal K. Dey
Indian Institute of Technology Kharagpur

Monday, December 7th, 1998, 12:00pm
Library/CATT Building, Room LC102, Brooklyn Campus

Abstract:

Reconstructing curves and surfaces from their samples is a problem of interset in many areas such as computer vision, geometric modeling, computer graphics and visualization. Given a set of sample points, a combinatorial reconstruction connecting the points is sought without any prior knowledge about the original curve or surface. In curve reconstructions a number of methods were known when the points are known to be uniformly sampled with certain density. We look at the problem when this is not necessarily the case. In surface reconstruction, the input may be an organized set of contours on parallel slices as obtained from CT and MRI scanning in medical applications, or a cloud of sample points as in CAD models. We present a Delaunay based method for the first case, which eliminates the costly step of a three dimensional Delaunay triangulation computation and improves the automatic detection of branchings in the surface. A simple algorithm is proposed for the case of unorganized samples which is empirically shown to be effective. Several outputs from the implementation of all these algorithms are presented to show their practical usability.

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