TY - JOUR

T1 - A GPU-BASED ALGORITHM for APPROXIMATELY FINDING the LARGEST COMMON POINT SET in the PLANE under SIMILARITY TRANSFORMATION

AU - Aiger, Dror

AU - Kedem, Klara

N1 - Funding Information:
This work was partly supported by the MAGNET program of the Israel Ministry of Industry and Trade (IMG4 consortium).
Publisher Copyright:
© 2009 World Scientific Publishing Company.

PY - 2009/4/1

Y1 - 2009/4/1

N2 - 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.

AB - 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.

KW - Approximation algorithms

KW - GPU

KW - Hausdorff distance

KW - computational geometry

KW - geometric pattern matching

KW - randomized algorithms

UR - http://www.scopus.com/inward/record.url?scp=85073242183&partnerID=8YFLogxK

U2 - 10.1142/S0219467809003459

DO - 10.1142/S0219467809003459

M3 - Article

AN - SCOPUS:85073242183

VL - 9

SP - 287

EP - 298

JO - International Journal of Image and Graphics

JF - International Journal of Image and Graphics

SN - 0219-4678

IS - 2

ER -