Object matching using a locally affine invariant and linear programming techniques

Hongsheng Li, Xiaolei Huang, Lei He

Research output: Contribution to journalArticle

37 Scopus citations

Abstract

In this paper, we introduce a new matching method based on a novel locally affine-invariant geometric constraint and linear programming techniques. To model and solve the matching problem in a linear programming formulation, all geometric constraints should be able to be exactly or approximately reformulated into a linear form. This is a major difficulty for this kind of matching algorithm. We propose a novel locally affine-invariant constraint which can be exactly linearized and requires a lot fewer auxiliary variables than other linear programming-based methods do. The key idea behind it is that each point in the template point set can be exactly represented by an affine combination of its neighboring points, whose weights can be solved easily by least squares. Errors of reconstructing each matched point using such weights are used to penalize the disagreement of geometric relationships between the template points and the matched points. The resulting overall objective function can be solved efficiently by linear programming techniques. Our experimental results on both rigid and nonrigid object matching show the effectiveness of the proposed algorithm.

Original languageEnglish (US)
Article number6189359
Pages (from-to)411-424
Number of pages14
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Volume35
Issue number2
DOIs
StatePublished - Jan 7 2013

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Vision and Pattern Recognition
  • Computational Theory and Mathematics
  • Artificial Intelligence
  • Applied Mathematics

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