Elsevier

Computational Geometry

Volume 46, Issue 6, August 2013, Pages 591-603
Computational Geometry

Shape matching under rigid motion

https://doi.org/10.1016/j.comgeo.2013.01.002Get rights and content
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Abstract

We present improved algorithms to match two polygonal shapes P and Q to approximate their maximum overlap. Let n be their total number of vertices. Our first algorithm finds a translation that approximately maximizes the overlap area of P and Q under translation in O˜(n2ε3) time. The error is additive and it is at most εmin{area(P),area(Q)} with probability 1nO(1). We also obtain an algorithm that approximately maximizes the overlap of P and Q under rigid motion in O˜(n3ε4) time. The same error bound holds with probability 1nO(1). We also show how to improve the running time to O˜(n+ε3) for the translation case when one of the polygons is convex.

Keywords

Shape matching
Overlap
Random sampling
Arrangement

Cited by (0)

Research supported by the Research Grant Council, Hong Kong, China (project No. 611711).