OPTIMAL POSITION ESTIMATION IN DIGITAL IMAGE METROLOGY 
D.I. Havelock! and H. Ziemann2 
1 NRC Physics 2 Institute Für Navigation 
M-36 Montreal Rd. Keplerstr. 11 
Ottawa, Ontario Postfach 560 
Canada D-7000 Stuttgart 1 
K1A OR6 Germany 
HAVELOCK@NRCPHY .BITNET HDAA@DSORUS1I.EARN 
ABSTRACT 
Photogrammetric digital image metrology needs accurate sub-pixel positioning of targets. 
With high quality digital image acquisition, quantization effects are a significant source of 
position estimation errors. Analysis of the degeneracy in the information content due to 
quantization requires techniques which are different from those used for continuous or 
analog imagery. From the analytical approaches of digital image representation theory has 
come the unifying and general concept of the "locale", or "feasibility region", upon which 
optimal position estimation can be based. A locale is simply the region of target positions 
which result in the same observed digital image of the target. The approach treats digital 
imagery differently from conventional techniques and throws new light on the analysis of 
geometric precision. It has led to an easily determined bound on the possible geometric 
precision and a natural statement of the meaning of optimal precision. Futhermore, a 
theoretically optimal algorithm, referred to as "position decoding", has been developed 
using the concept of locales and the principles of signal decoding from communication 
theory. Simulation results have been promising and exciting. They have shown the 
algorithm to be robust and near optimal in the presence of noise. The algorithm is 
introduced and comparative performance reported. 
1. INTRODUCTION : ili ; 
Sub-pixel position estimation is necessitated by the 
insatiable need for improved accuracy and the 
  
Digital image processing will undoubtedly play a 
major role in the future of photogrammetry. The 
large field of digital image processing is composed of 
diverse applications, most of which are concerned 
with the context or texture of the image data. Few are 
concerned, as photogrammetry is, with the metrology 
and geometry of digital images. Relatively little of 
the literature is presently devoted to the problems of 
extracting geometric measurements from digital 
images and so there is little support outside of the 
photogrammetric community for important topics 
such as the metric quality of digital images or 
techniques for precise mensuration on digital images. 
This paper addresses these fundamental issues, briefly 
reviewing some aspects of digital image acquisition, 
reviewing the theory of locales and then introducing a 
new optimal position estimation algorithm. 
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unavoidable cost associated with large data volumes 
caused by small pixels. The objective is to use a 
manageable pixel size and extract all possible 
positioning information at that resolution. As a 
rough rule of thumb, a very good position estimation 
procedure in an application will achieve about 1/20th 
of a pixel positioning accuracy (often reported as one 
part in 10,000 with a 512 by 512 pixel image). 
There are many pragmatic reasons why better sub- 
pixel precision is seldom achieved; lighting 
problems, mechanical instability, scene 
unpredictability, electronic and sensor noise and 
algorithm sub-optimality. In some applications, 
particularily in high precision photogrammetry, 
many of these problems have been resolved. In these 
situations, the fundamental limitations of