g(x,y) = d,* t(A* (X-Xg, Y-Yo)) + Bo 
with: 
g (x,y) = density at x,y (the image) 
t (x,y) =template 
d, gg = radiometric scale and offset 
A = affine transformation (2 x 2) matrix 
Xo yo = position of the template 
An affine transformation is chosen to model the 
geometric transformation because this is a good 
local approximation of the projective 
transformation from object to photo. This holds for 
a target on a flat surface. 
For the radiometric part of the model, as in the 
reaseaucross matching a linear model is chosen. 
For target images with a diameter of 40 pixels or 
more (circular matching window) the estimated 
precision of the position is around 1% of a pixel 
(0.1 um) standard deviation.This corresponds to a 
photoscale of about 1:100 for the large sized targets 
( 40 mm diameter of the ring). For smaller target 
images the estimated standard deviation is in the 
order of 296 of a pixel. The formal variance drops 
linear with an increase in diameter of the image 
size, because the number of gradient pixels 
increases linearly with the diameter. The estimated 
emulsion noise varies between 2.4% and 4.1% of 
the average density. Again correlation between 
density measurements have not been taken into 
account. 
  
figure 5: sample residual image (enhanced 
radiometric scale) 
In figure 5 a density residual image is depicted. The 
circular patterns show the imperfection of the 
227 
template model used. 
In principle the result of the autocorrelation and the 
matching method can be expected to be the same. 
Comparison between the two is hindered by the 
difference in correlation/matching window size 
(and shape). However, the estimated positions 
correspond to the level of the estimated standard 
deviations, i.e. below 3% of a pixel difference for 
good quality images. The estimated density noise is 
somewhat higher than the known photographic 
noise for both methods, indicating model errors of 
rather the same size. Still the least squares 
matching method should be preferred for the final 
position estimation because it is more robust. The 
template makes the algorithm insensitive to 
mishaps in the images as long as they do not 
interfere with the target edges in the image. An 
other advantage of the least squares matching is the 
fact that the affine deformation of the target image 
is determined. This is needed for the automatic 
identification of the target. 
6. Reading the target identification 
To automate the identification of a target, each 
target has, next to its number printed in the upper 
right corner a circular binary code containing the 
same number. The binary code consists of 10 bits 
allowing for 1024 different numbers. If a part of the 
code is obscured, reading it is not possible. But if 
the code can be read in one of the images we have 
identified the target in the other images as well if 
the relative orientation of the images is known. The 
relative orientation of the images can be 
determined with a minimum set of targets 
identified. 
Reading the cirular binary code consists of 3 steps: 
- sampling the code; 
- determining the start point of the code; 
- reading the code. 
Using the previously solved affine deformation of 
the target image 200 samples of the binary code are 
taken from the image using bilinear interpolation 
for resampling. The sampling is done at regular 
angular distances, 10 samples per bit along the 
centre of the bar code ring. An example of a 
sampled code is depicted in figure 6 . The location 
of the least significant bit is determined by