MULTIPLE IMAGE MATCHING 
Peggy Agouris 
Toni Schenk 
Department of Geodetic Science and Surveying 
The Ohio State University, Columbus, Ohio 43210-1247 
USA 
Commission III 
ABSTRACT 
Digital photogrammetry is concerned with the development of algorithms to automate photogrammetric tasks. 
The majority of efforts though are focused on single stereopairs. This paper addresses the task of simultaneously 
matching conjugate windows from multiple overlapping images. After establishing a theoretical understanding 
of the problem, we introduce several approaches and present the associated mathematical principles. We report 
on the advantages and disadvantages of each one, discuss various implementation issues and in conclusion, we 
examine potential applications in photogrammetric procedure. 
1. INTRODUCTION 
Digital photogrammetry has recently emerged as one of the 
most promising and multi-faceted photogrammetric subfields. 
A solid body of research work and a wide array of topics have 
laid the foundation for the evolution of the photogrammetric 
procedure. Among the research topics, automatic matching 
is one of the most challenging. 
Digital image matching attempts to identify sets of conju- 
gate entities from two or more overlapping images. From 
the diverse set of matching techniques [Lemmens, 1988], 
least squares matching is a popular choice [Ackerman, 1984]. 
Even though there already exists substantial work on this 
subject, most efforts have been focused on the stereomatch- 
ing case, which involves a single pair of images. This paper 
deals with simultaneously matching windows from multiple 
overlapping images using least squares techniques. The sig- 
nificance of this issue lies in the impracticality of handling 
single models at the time when processing large blocks is 
common practice in the photogrammetric industry. Success- 
ful and efficient completion of multiple image matching is 
expected to contribute significantly in the transition of digi- 
tal photogrammetry from an experimental to a production- 
oriented status. 
Significant research in the area of multiple image matching 
can be found in [Grün & Baltsavias, 1988],[Heipke, 1992] 
and [Helava, 1988]. In this paper, we present alternative ap- 
proaches to the subject by introducing geometric constraints 
and performing matching in the object space. The general 
least squares matching procedure is discussed in detail and 
is subsequently expanded to accommodate multiple image 
windows. We explore the theoretical issues of the proposed 
approaches and establish the corresponding mathematical 
principles. Then, we report on their advantages and disad- 
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vantages from a photogrammetric point of view and address 
several implementation issues. 
2. LEAST SQUARES MATCHING 
Least squares matching techniques attempt to match win- 
dows of pixels by establishing a correspondence between 
them which minimizes the differences of their gray values. 
Assuming gr(zr, yr) to be a window of n, x n; pixels in the 
left image, and g%(x%,Y%) an equal size approximation to its 
conjugate position in the right image, the objective is to es- 
timate a new location of the right image window gn(*n, yn) 
such that the gray value differences 
gi (2r, VL) = gn(2n, yn) — e(z, y) (1) 
are minimized. The estimation is performed by the trans- 
formation of the coordinates (2%,y%) and resampling of the 
corresponding gray values. The coordinates of the two win- 
dows are related through a perspective transformation to 
a common surface patch in the object space. Taking into 
account the very small size of the windows to be matched, 
their coordinates are assumed to be related to each other by 
a 6-parameter affine transformation 
TR = a1 + az + azyg, (2) 
and 
Yr = by + baxz + bayz (3) 
With linearization, the equations 
gi(21, yr) — e(z,y) = gR(=R, YR) (4) 
become 
gi(n, yr) — e(z,y) — gn(z5, yn) - gn.dvn -- gn,dyn (5) 
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