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
