Efficient computation of isometry-invariant distances between surfaces

被引:139
作者
Bronstein, Alexander M. [1 ]
Bronstein, Michael M. [1 ]
Kimmel, Ron [1 ]
机构
[1] Technion Israel Inst Technol, Dept Comp Sci, IL-32000 Haifa, Israel
关键词
generalized multidimensional scaling; isometric embedding; Gromov-Hausdorff distance; intrinsic geometry; isometry-invariant surface matching; iterative optimization; multiresolution methods;
D O I
10.1137/050639296
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We present an efficient computational framework for isometry-invariant comparison of smooth surfaces. We formulate the Gromov-Hausdorff distance as a multidimensional scaling like continuous optimization problem. In order to construct an efficient optimization scheme, we develop a numerical tool for interpolating geodesic distances on a sampled surface from precomputed geodesic distances between the samples. For isometry-invariant comparison of surfaces in the case of partially missing data, we present the partial embedding distance, which is computed using a similar scheme. The main idea is finding a minimum-distortion mapping from one surface to another, while considering only relevant geodesic distances. We discuss numerical implementation issues and present experimental results that demonstrate its accuracy and efficiency.
引用
收藏
页码:1812 / 1836
页数:25
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