ACCURACY IMPROVEMENT IN AUTOMATED SURFACE MEASUREMENT
Mushairry Mustaffar
Postgraduate Student *
Deptartment of Civil Engineering and Surveying
University of Newcastle, NSW 2305
AUSTRALIA
Commission IIl, Working Group III/2
KEY WORDS : digital image matching, surface measurement, object reconstruction, accuracy, surface model
ABSTRACT
Area-based matching has been acknowledged as being more precise than feature-based matching at finding
corresponding points on digital images. This paper investigates a method of further improving the accuracy of the area-
based technique by modifying the functional model describing the relationship between the windows. The method
replaces the approximations made using an affine transformation. It makes use of a surface model and the collinearity
conditions in determining the transformation needed. Since there is greater fidelity involved in the transformation, it is
hypothesised that the improved functional model will allow the use of larger windows for matching and hence improve
accuracy. The derivation of the theory and some experimental results will be presented. Initial experimental results show
that the proposed method is capable of attaining absolute accuracy mildly superior to conventional area-based
matching.
1.0 INTRODUCTION
Techniques in digital image matching, or ^ image
correlation, have been developed within various
disciplines over the last few decades and a vast number
of approaches exists. These techiques can be classified
into two main groups, viz, feature-based and area-based
matching. Stereo image matching techniques make use
of a selected area or features within the image or the
combination of both for matching (Li 1991). However, it is
well accepted that area-based matching (ABM) method is
more precise than feature-based matching for finding
corresponding points on digital images. Methods in area-
based matching have been developed by Foerstner
(1982) and Gruen (1985). Some examples of the
applications and experiments done on ABM in various
fields have been reported by Ackermann (1984), Pertl
(1985), Rosenholm (1987b), Crippa et. al. (1993), Hahn &
Brenner (1995). Further extensions of area-based
matching were proposed by Gruen & Baltsavias (1987)
whereby methods of constraining the matching with
model coordinates (X,Y,Z) through the collinearity
conditions were proposed. Their methods, known as
geometrically constrained area-based matching, use a
unified (combined) least squares solution in which
corrections to the affine parameters and model
coordinates (X,Y,Z) were solved iteratively. Rosenholm
(1987a) proposed the method of multi-point area-based
matching technique in evaluating three-dimensional
models. Area-based method is further extended by
Baltsavias (1991) through the use of images from several
viewpoints (multi-image). Recent development of the
area-based method is proposed by Wrobel (1991),
Heipke (1992) whereby matching is done on a global
approach by integrating multi-image matching and object
surface reconstruction.
* Currently on study leave from :
The Faculty of Civil Engineering
Universiti Teknologi Malaysia
80990 Johor Bahru, MALAYSIA.
555
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
This paper investigates a method of improving the
accuracy of the traditional area-based technique by
modifying the functional model through the use of a
surface model to describe the relationship between the
windows. The method replaces the assumptions made
using an affine transformation. It also serves as a
compromise to the more complex global area-based
matching method. The method proposed here makes use
of a surface model and the collinearity conditions in
determining the transformation needed. It solves, through
an iterative least squares solution, directly the corrections
to image coordinates (x,y) of the search window. In
addition, two ‘new’ unknowns, the gradients in X and Y
directions on the surface at the point on the surface which
corresponds to the centre of the search window and their
second derivatives are introduced. Since the
transformation used is more rigorous than the affine, it is
hypothesised that the improved functional model will
allow the use of larger windows for matching and hence
improve accuracy. It is also hypothesised that the use of
a better functional model will converge more quickly to
give a solution.
2.0 AREA-BASED IMAGE MATCHING USING A
SURFACE MODEL
The basic area-based observation equation, which gives
a relationship between the radiometric values of
corresponding pixels in the left and right image windows,
can be written as follows :-
IL(xL.yL)* n(xy) 2 IR(XR.YR) (D
where,
IL, IR are the intensities of the left and right pixels
respectively
XL, yL are the image coordinates of the left pixel
XR, yRare the corresponding image coordinates on
the right image
n(x,y) is the difference caused by noise at the point
(x,y) on the left image
