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International Archives of Photogrammetry and Remote Sensing. Vol. XXXII, Part 5. Hakodate 1998
ADAPTIVE SUBPIXEL CORRELATION BASED ON PRELIMINARY SEGMENTATION
S.Yu. ZHELTOV, Deputy Director
A.V. SIBIRYAKOV, Researcher,
State Research Institute of Aviation Systems,
Moscow, Russia
e-mail: zhl@fenix.niias.msk.su
Commission V, Working Group 1
KEY WORDS: Subpixel Cross-Correlation, Morphological Correlation, Subpixel Image Matching
ABSTRACT
This work deals with the subpixel point correspondence problem. Subpixel matching methods such as Least-Squares
Correlation [2] or Adaptive Subpixel Cross-Correlation [1] use six-parameter geometric transformation and two-
parameter radiometric transformation of the whole image patches to achieve subpixel matching accuracy. However
different regions inside image patch may have different distortion parameters. The method developed in this paper uses
the images preliminary segmented into regions. Each region possesses its own unknown distortion parameter set that
can be found by solving the correlation coefficient maximization problem. Two different kinds of correlation: widely used
normalized cross-correlation and morphological correlation are to be considered. In both cases the consecutive
correlation application results in problem of a finding a vector of the amendments of the parameters as a generalized
eigenvector problem. The theoretical decision of this problem in view of specific structure of matrices obtained by
linearization is offered.
1. INTRODUCTION
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 utilising 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 [2]. One of this article goals is to provide
consequential extension of classical normal cross-
correlation that it could gain subpixel accuracy and
adaptive geometric properties.
À subject of the given work is a situation, when the rough
decision of a correspondence problem is already received
and it is required to reach extreme possible accuracy of
matching. It can be achieved by using information about
preliminary image segmentation.
2. ADAPTIVE SUBPIXEL CROSS-CORRELATION
The adaptive subpixel cross-correlation method in a point
correspondence problem was first described in [1]. The
method uses normalized cross-correlation function as a
similarity measure of two image patches.
Let us denote f(x, y) - intensity distribution on left image
patch (also called template). Futher for the simplicity
195
assume that the average intensity of the template is equal
to zero: f=0. For this purpose we subtract template
average intensity from each intensity value
f(x,y) ^ foy) - f (1)
Let place an origin of a rectangular coordinate system
(x,y) in the middle of central pixel of the template. Denote
g(x1,y1) - intensity distribution on the right image patch
which corresponds to the template. The shape of this
patch differs from the shape of the template for the
reason of perspective distortions. An origin of coordinate
system (x1,y1) will be placed in the center of the right
image patch. Coordinate systems (x,y) and (x1,y1) are
connected by an unknown transformation (2), where p -
transformation parameters vector
X, = X, (x, y,p) (2)
Ji - y 05 y, p)
It is necessary to find a vector of parameters p by
maximizing of a normalized: cross-correlation of the
patches
2.10.80) ©
CY ^ YO sx y) = Ng?)
(x.y) (x.y)
k(p) =
