generally does not respect the number of pixels per 
line transmitted by the camera. The frame.grab 
simply resamples the line by interpolation. These 
problems have been discussed quite thoroughly in 
assessments of the use of CCD imagers for 
photogrammetric purposes, as in [15,3,2]. 
There are two basic approaches to overcoming the 
loss of geometric fidelity imposed by commercial 
digital image acquisition systems; signal analysis and 
specialized electronic circuitry. It has been shown for 
example, that by clever Fourier analysis of the image 
signal, the horizontal jitter introduced by the 
digitizer's resampling can be determined, hence 
corrected for [14]. Small targets can thus be 
positioned to an accuracy of about 1/60th of a pixel. 
With special electronics, one might expect to do 
better still. 
3. SUB-PIXEL IMAGE PROCESSING 
Empirical investigations into attainable sub-pixel 
position estimation in digitally reconstructed 
imagery, such as [18], have indicated that sub-pixel 
measurement is realizable, but the level of 
performance which can be attained is still a debatable 
issue. 
A difficulty with empirical results is that they are 
only strictly true for the particular system 
configuration used for the experiment and they are 
rarely assured of being optimal in any sense. 
Theoretical investigations on the other hand, tend to 
be idealized and optimistic. Neither empirical nor 
theoretical investigations have given a good 
framework of knowledge about sub-pixel position 
estimation which can be assimilated by the 
practitioners of the art. While there have been some 
important advances in terms of theory and practice, 
([5,4,12,17], to mention a few) there is a lack of 
cohesion or common basis on which they can be 
purviewed. The "locales theory" introduced in [11] 
may provide some of the required common ground for 
the important problem of sub-pixel position 
estimation. The locales theory introduces a bound for 
geometric precision against which other analysis and 
methodologies may be collectively compared. 
It is worth emphasizing perhaps, that the issue of 
sub-pixel position estimation can generally be 
isolated to just two components of the overall image 
processing task, namely the acquisition of the digital 
image and the sub-pixel position estimation 
algorithm itself. There are many other steps, as 
figure 1 indicates, which do not directly involve sub- 
pixel considerations. The position of a target may in 
fact be estimated twice, once in the course of 
detection or recognition, wherein an approximate 
pixel location is determined, and again during precise 
sub-pixel position estimation based on the raw gray 
scale image data. In this context, it is important that 
sub-pixel position estimation be clearly distinguished 
from the tasks of detection and recognition. It will be 
assumed throughout this paper that target position is 
known to approximately one pixel; it is the task of 
sub-pixel position estimation to improve upon the 
rough estimate. 
  
IMAGE ACQUISITION 
STORAGE 
  
  
  
ENHANCEMENT 
SEGMENTATION 
EXTRACTION 
  
  
  
  
   
NN ELITE, 
tot tata Eee 
OBJECT COORDINATES 
  
  
  
FIGURE 1. 
IMAGE PROCESSING STEPS FOR 
POSITION EXTIMATION 
(AFTER EL-HAKIM [9]) 
4. LOCALES 
This section will begin with a brief discussion of the 
history and terminology of locales. The concept of 
"locales" was developed in [11] for arbitrary targets 
and at about the same time for the more restricted 
case of binary line segments encoded by chain codes 
[6]. The idea is simple and useful: a locale is a region 
within which the object (target) may be moved 
without causing any change to its digital 
representation. The term "domain" used by Dorst and 
Smeulders [6] refers to a region in a transformation 
space of object position, but the principle is the 
same as for locales. The term "feasibility region", as 
adopted by Berenstein et. al. [1] for the object- 
position equivalent of the "domain", is the same as 
locale. Feasibility regions will be introduced in 
section 8 in the context of locale construction, 
whereby the former are intersected to generate the 
latter. 
Interest in locales arises from the fact that the locale 
size determines the position uncertainty due to 
quantization and the locale center is the optimal 
position estimate in terms of minimizing 
quantization errors. 
Just what is a "locale"? Consider the following 
example. A small dot might appear in a digital image 
as a sampled and quantized Gaussian function Q(i,j), 
56