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Mathematical Problems in Engineering
Volume 2015, Article ID 721842, 15 pages
Research Article

Research on the Fundamental Principles and Characteristics of Correspondence Function

1Department of Electrical and Computer Engineering, University of Windsor, Windsor, ON, Canada N9B 3P4
2School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
3Department of Electrical Engineering & Computer Science, University of Kansas, Lawrence, KS 66045, USA

Received 17 April 2015; Revised 19 August 2015; Accepted 20 August 2015

Academic Editor: Erik Cuevas

Copyright © 2015 Xiangru Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The correspondence function (CF) is a concept recently introduced to reject the mismatches from given putative correspondences. The fundamental idea of the CF is that the relationship of some corresponding points between two images to be registered can be described by a pair of vector-valued functions, estimated by a nonparametric regression method with more flexibility than the normal parametric model, for example, homography matrix, similarity transformation, and projective transformations. Mismatches are rejected by checking their consistency with the CF. This paper proposes a visual scheme to investigate the fundamental principles of the CF and studies its characteristics by experimentally comparing it with the widely used parametric model epipolar geometry (EG). It is shown that the CF describes the mapping from the points in one image to their corresponding points in another image, which enables a direct estimation of the positions of the corresponding points. In contrast, the EG acts by reducing the search space for corresponding points from a two-dimensional space to a line, which is a problem in one-dimensional space. As a result, the undetected mismatches of the CF are usually near the correct corresponding points, but many of the undetected mismatches of the EG are far from the correct point.