Adaptive subpixel cross-correlation in a point correspondence problem

Precise points matching on the images of a stereopair is one of central problems in the area of machine vision and digital photogrammetry. A lot of publications is devoted to investigations of this problem. Among well-known classical approaches the conventional normalized cross-correlation method occupies first place due to its fundamental importance and vast utilizing in practice during several decades. However, revealing drawbacks of the method connected with non-adaptive geometric properties have brought the creating of new more powerful methods, for example, adaptive least squares correlation [1]. The goal of this article is to provide consequential extension of classical normal cross-correlation that it could gain subpixel accuracy and adaptive geometric properties. It is shown that consecutive normalized cross-correlation application results in problem of a finding a vector of the amendments of six-parameter affine transformation as a generalized eigenvector problem. The theoretical decision of this problem in view of specific structure of matrixes obtained by linearization is offered. Effective algorithm of the numerical solution based on a triangular Cholecky decomposition is proposed. The main result obtained in the present paper is the proof of equivalence of least-square correlation and an adaptive extension of cross-correlation.