id for 
s acquired 
s. Proc. 
on, San 
shading 
Artificial 
ol. 
r Inc. 
hod for 
tiple 
1, 
UNIFORM FULL-INFORMATION IMAGE MATCHING USING COMPLEX CONJUGATE WAVELET PYRAMIDS 
He-Ping Pan 
Cooperative Research Centre for Sensor Signal and Information Processing 
SPRI Building, Technology Park, Adelaide 
The Levels, SA 5095, Australia 
Email: heping@cssip.edu.au 
Commision Ill, Working Group 2 
KEY WORDS: Image Matching, Surface Reconstruction, Algorithms, Automation 
ABSTRACT 
Stereo image matching is reconsidered from the viewpoint of full-information exploitation via a uniform transformation of 
information through scale space. We consider the general stereo situation where both interior and relative orientation of two 
images are unknown. It is shown that wavelet multiresolution analysis provides an adequate transformation and representation 
of image signal information with desired properties such as good space-frequency locality and information preservation. In 
particular, complex conjugate wavelets are used for phase-based matching. Technically, this paper presents a basic procedure 
for top-down matching two stereo images using complex conjuage wavelet pyramids for the standard case where two images 
may have a lower bound of stereo overlapping of 60% and relative rotation around principal axis is small. A strategy of spiral 
parallax propagation is developed for tackling the unknown partial correspondence on the top level. A complete example on 
matching two real aerial images is shown. 
1 INTRODUCTION 
Image matching may be considered as the central and most 
difficult problem in photogrammetry and stereo vision for sur- 
face reconstruction from multiple images. It has received 
great attention from many photogrammetrists and computer 
vision specialists, as well as researchers from pattern recogni- 
tion and artificial intelligence over last three or more decades. 
The problem is extremely hard to solve perfectly, partly be- 
cause the problem domain of image matching in general is not 
a closed one, partly because of the lack of adequate funda- 
mental mathematical and informatic theories and tools for a 
thorough understanding of the information-processing mech- 
anism throughout the image matching process. 
Due to the length limit, this paper does not give a compre- 
hensive overview on the related literature of general image 
matching and wavelets. Briefly, existing approaches for stereo 
image matching may be classified into several clusters accord- 
ing to the choice of matching primitives, matching criterion 
and strategies as follows. 
Signal Correlation 
The most obvious approach to stereo image matching is to 
correlate two image functions over each pair of local areas. It 
is thus often called image correlation, or area-based matching, 
etc. This is perhaps the earliest approach, and obviously an 
engineering solution. (Heleva, 1976; Ackerman, 1984) 
Feature Matching 
Feature matching was introduced naturally to overcome 
the inabilities of area-based signal correlation by attempting 
matching only on information-rich points or more complicated 
primitives such as edges, regions, etc. It was inspired by the 
studies on biological vision (Grimson, 1981; Forstner, 1986) 
Global Matching 
Instead of matching local areas or features separately, the 
approach of global matching attempts to match all pairs of 
homologous image points or features within a simultaneous 
framework, typically via least-squares adjustment or other re- 
laxation procedures (Grün, 1985; Poggio et al, 1985; Rosen- 
holm, 1987; Rauhala, 1987; Barnard 1989; Zhang et al 1992). 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
Object-Space Image Matching 
Object-space image matching, so-called typically by pho- 
togrammetrists, assumes a coherent facet model of the scene 
surfaces a priori. This is largely true for the terrain viewed 
from a relatively high altitude in aerial photography (Ebner 
et al, 1987; Wrobel, 1987; Helava, 1988, Heipke, 1992). 
Image-Domain Approach Revisited 
The approach that we are proposing here, briefly called uni- 
form full-information image matching, may be considered as 
a natural development of the three image-domain approaches 
(signal correlation, feature matching, and global matching). 
We rely on exploiting the full information beared in the im- 
age signals. We require the representation of image signal 
information to be uniform through scale space. We do not 
distinguish explicit features such as points, edges/lines, re- 
gions, textures, shading, etc; instead, we use full-information 
representation which may be considered as implicit feature 
vectors. In particular, we use wavelet multiresolution analysis 
(wavelet pyramid) as information representation of image sig- 
nals for image matching. We also use general effective match- 
ing strategies inspired by biological vision. Large continuity 
and minor discontinuity of parallax field is also considered in 
practical algorithms. 
2 UNIFORM FULL-INFORMATION IMAGE 
MATCHING 
The notion of uniform full-information image matching may 
be best described briefly as follows. A digital image is a func- 
tion f(z,y) on a 2-dimensional support. For image matching 
or in general, pattern recognition, a representation of f(x, y) 
is to be chosen in such a way so that the constructs in the 
new representation may be related to salient information of 
the original signal function f(z,y). |n general, let us as- 
sume f(z,y) is to be represented by a vector of projections 
of f(z, y) onto n basis functions v;(z, y) 
f(z,y) — (a1,a2,...,an) (1) 
a; = «fins, v; v) 2:4 531,2,.. 5m (2)