Research on the Fundamental Principles and Characteristics of Correspondence Function

Abstract EN

The correspondence function (CF) is a conceptrecently introduced to reject the mismatches from given putativecorrespondences.

The fundamental idea of the CF isthat the relationship of some corresponding points between twoimages to be registered can be described by a pair of vector-valuedfunctions, estimated by a nonparametric regressionmethod with more flexibility than the normal parametric model,for example, homography matrix, similarity transformation, andprojective transformations.

Mismatches are rejected bychecking their consistency with the CF.

This paper proposes avisual scheme to investigate the fundamental principles of theCF and studies its characteristics by experimentally comparingit with the widely used parametric model epipolar geometry(EG).

It is shown that the CF describes the mapping from thepoints in one image to their corresponding points in anotherimage, which enables a direct estimation of the positions of thecorresponding points.

In contrast, the EG acts by reducing thesearch space for corresponding points from a two-dimensionalspace to a line, which is a problem in one-dimensional space.

Asa result, the undetected mismatches of the CF are usually nearthe correct corresponding points, but many of the undetectedmismatches of the EG are far from the correct point.