Implicit, Nonparametric Shape Reconstruction from Unorganized Points Using A Variational Level Set Method (1998)
| Venue: | Computer Vision and Image Understanding |
| Citations: | 95 - 19 self |
BibTeX
@ARTICLE{Zhao98implicit,nonparametric,
author = {Hong-kai Zhao and Stanley Osher and Barry Merriman and Myungjoo Kang},
title = {Implicit, Nonparametric Shape Reconstruction from Unorganized Points Using A Variational Level Set Method},
journal = {Computer Vision and Image Understanding},
year = {1998},
volume = {80},
pages = {295--319}
}
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Abstract
In this paper we consider a fundamental visualization problem which arises in computer vision, computer graphics and numerical simulation. The problem is to find a curve in two dimensions, or a surface in three dimensions which can be regarded as the shape represented by a set of unorganized points, and/or curves, and/or surface patches. We do not assume any knowledge of the ordering, connectivity or topology of the data sets or of the true shape. Only the location of each point or general Hausdorff distance to the data set is known. The key idea in our approach is to find an implicit nonparametric representation of the curve or surface on a fixed rectangular grid. With this representation of surfaces we can easily (a) find the closest point and distance from any point to the surface (useful in illumination and many other applications), (b) find the intersection curve of two surfaces which is guaranteed to lie on both surfaces in our representation, and (c) perform any Boolean operatio...
