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Object Matching Using a Locally Affine Invariant and Linear Programming Techniques
Feb. 2013 (vol. 35 no. 2)
pp. 411-424
Hongsheng Li, Comput. Sci. Dept., Southwestern Univ. of Finance & Econ., Chengdu, China
Xiaolei Huang, Dept. of Comput. Sci. & Eng., Lehigh Univ., Bethlehem, PA, USA
Lei He, Digital Conversion Service, Libr. of Congress, Potomac, MD, USA
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.
Index Terms:
linear programming,computational geometry,image matching,least squares approximations,matched point reconstruction errors,object matching,locally affine-invariant geometric constraint,linear programming techniques,linear programming formulation,auxiliary variables,template point set,least squares,Linear programming,Mathematical model,Pattern matching,Least squares approximation,Probabilistic logic,Vectors,USA Councils,linear programming,Feature matching,object matching,locally affine invariant
Citation:
Hongsheng Li, Xiaolei Huang, Lei He, "Object Matching Using a Locally Affine Invariant and Linear Programming Techniques," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 35, no. 2, pp. 411-424, Feb. 2013, doi:10.1109/TPAMI.2012.99
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