Harmonic maps and their applications in surface matching

Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149) Pub Date : 1999-06-23 DOI:10.1109/CVPR.1999.784731

D. Zhang, M. Hebert

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引用次数: 208

Abstract

The surface-matching problem is investigated in this paper using a mathematical tool called harmonic maps. The theory of harmonic maps studies the mapping between different metric manifolds from the energy-minimization point of view. With the application of harmonic maps, a surface representation called harmonic shape images is generated to represent and match 3D freeform surfaces. The basic idea of harmonic shape images is to map a 3D surface patch with disc topology to a 2D domain and encode the shape information of the surface patch into the 2D image. This simplifies the surface-matching problem to a 2D image-matching problem. Due to the application of harmonic maps in generating harmonic shape images, harmonic shape images have the following advantages: they have sound mathematical background; they preserve both the shape and continuity of the underlying surfaces; and they are robust to occlusion and independent of any specific surface sampling scheme. The performance of surface matching using harmonic maps is evaluated using real data. Preliminary results are presented in the paper.

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谐波映射及其在曲面匹配中的应用

本文利用谐波映射这一数学工具研究了曲面匹配问题。调和映射理论是从能量最小化的角度研究不同度量流形之间的映射。通过谐波映射的应用，生成了一种称为谐波形状图像的曲面表示形式，用于表示和匹配三维自由曲面。谐波形状图像的基本思想是将具有圆盘拓扑结构的三维曲面斑块映射到二维域，并将曲面斑块的形状信息编码到二维图像中。这将表面匹配问题简化为二维图像匹配问题。由于谐波映射在谐波形状图像生成中的应用，使得谐波形状图像具有以下优点:具有良好的数学背景;它们保持了下垫面的形状和连续性;它们对遮挡具有鲁棒性，且不依赖于任何特定的表面采样方案。用实际数据对谐波映射曲面匹配的性能进行了评价。本文给出了初步结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149)

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