Curve matching in the framework of Riemannian geometry

Yong Li; Robert L. Stevenson; Jiading Gai

doi:10.1117/12.805392

19 January 2009 Curve matching in the framework of Riemannian geometry

Yong Li, Robert L. Stevenson, Jiading Gai

Proceedings Volume 7257, Visual Communications and Image Processing 2009; 725716 (2009) https://doi.org/10.1117/12.805392
Event: IS&T/SPIE Electronic Imaging, 2009, San Jose, California, United States

Abstract

This paper addresses a fundamental problem in computer vision, curve matching. Curve matching and comparison play a key role in various applications. High-level vision problems usually require comparing curves, and the quality of tackling these problems relies much on the underlying curve matching techniques. Our goal is to define a distance on the space of plane (space) curves. The space of curves is taken as a manifold (topological space), and we consider Riemannian metrics on the manifold. The distance induced by a Riemannian metric is a metric, which, if not trivial, can be used as a similarity metric. This work also deals with the problem of partial curve matching given their starting points are known. Dynamic programming is used to implement partial matching, giving an efficient computational method. Experiments are conducted to test the distance invariant to translation and scaling.

Citation Download Citation

Yong Li, Robert L. Stevenson, and Jiading Gai "Curve matching in the framework of Riemannian geometry", Proc. SPIE 7257, Visual Communications and Image Processing 2009, 725716 (19 January 2009); https://doi.org/10.1117/12.805392

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