A GPU-BASED ALGORITHM for APPROXIMATELY FINDING the LARGEST COMMON POINT SET in the PLANE under SIMILARITY TRANSFORMATION

Dror Aiger, Klara Kedem

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the following geometric pattern matching problem: Given two sets of points in the plane, P and Q, and some (arbitrary) δ> 0, find the largest subset B-P and a similarity transformation T (translation, rotation and scale) such that h(T(B),Q) < Î, where h(.,.) is the directional Hausdorff distance. This problem stems from real world applications, where δis determined by the practical uncertainty in the position of the points (pixels). We reduce the problem to finding the depth (maximally covered point) of an arrangement of polytopes in transformation space. The depth is the cardinality of B, and the polytopes that cover the deepest point correspond to the points in B. We present an algorithm that approximates the maximum depth with high probability, thus getting a large enough common point set in P and Q. The algorithm is implemented in the GPU framework, thus it is very fast in practice. We present experimental results and compare their runtime with those of an algorithm running on the CPU.

Original languageEnglish
Pages (from-to)287-298
Number of pages12
JournalInternational Journal of Image and Graphics
Volume9
Issue number2
DOIs
StatePublished - 1 Apr 2009

Keywords

  • Approximation algorithms
  • GPU
  • Hausdorff distance
  • computational geometry
  • geometric pattern matching
  • randomized algorithms

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