position estimate can be determined by computing 
the locale centroid. Figure 6 depicts a sequence of 
intersecting feasible regions resulting in a single 
locale for the target location. 
  
FIGURE 6 
SUCCESSIVE INTERSECTION OF FEASIBLE 
REGIONS TO OBTAIN THE LOCALE 
It has been seen that the locale pattern is very 
sensitive to small variations in the shape of the 
target. It would seem then, that the position decoding 
algorithm would be very sensitive to the deviations 
of the contour map model of the target from reality, 
either due to noise, distortion, or lack of accurate 
representation. This problem is alleviated by 
recording in the truth map the relative probability, 
for each level of the contour map, that the target was 
located there. A grey scale representation of this is 
depicted in figure 7. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
FIGURE 7 
USE OF PROBABILTIY DISTRIBUTION 
FOR FEASIBILITY REGIONS 
The probability used in the truth map might be 
exponential with repect to the magnitude of the 
difference between the observed pixel value and that 
of the contour levels. The truth map then represents a 
portion of the probability distribution for the spatial 
coordinates of the target given the pixel value. 
Successive pixels are appropriately combined by 
point-wise product of the probability distributions for 
their independent pixels. 
It is more practical to store the logarithm of the 
probability distribution, that is; the square magnitude 
difference between the observed pixel value and the 
contour level. In this case, the joining of the 
information from successive pixels is achieved by 
summing the corresponding log-probabilities. This 
results in a straightforward algorithm which 
iteratively updates a "truth map" of numbers. After 
all the pixels have been processed, the region within 
the truth map defined by all those cells with the 
highest value is taken to be the locale for the target. 
The possibilities for tuning and refining the 
algorithm are many fold. The selection of the list of 
pixels can be done so that the most useful ones 
appear first. For example, symmetrically opposed 
pixels can be processed in succession to take 
advantage of a symmetric target shape, or pixels 
occuring where the image has maximum gradient can 
be selected first since these generally contain better 
positional information. As the feasible regions are 
intersected, and the candidate area of the locale 
diminishes in size, processing can be terminated at a 
preselected tolerance, thereby avoiding the processing 
of unnecessary pixels. Pixels which yield no highly- 
likely cells in the truth map can be deemed defective 
and eliminated from the analyis. Various probability 
measures and pixel weights can be tailored. Occluded 
or missing pixels present no obstacle to the 
completion of the algorithm. 
The algorithm has been implemented with simulated 
target images and noise, without elaborate tuning, 
and its performance has been extremely robust and 
near-optimal. The ease with which good performance 
is achieved has been impressive. 
9. COMPUTATIONAL 
CONSIDERATIONS 
The truth table is the primary storage element of the 
position decoding algorithm. To economize on space 
and associated processing, the truth table is allocated 
only about 15 cells on a side, that is; the unit square 
representing the area of a pixel is divided into about 
225 cells. Since locales tend to be smaller than this 
cell size, a method is needed to ensure that at least 
one cell is selected by the intersection of feasible 
regions. This is accomplished by storing the log- 
probability in the truth table and selecting the cell(s) 
with the highest probability. Once the truth map has 
been evaluated for all the pixels, the process is 
reiterated with the resolution of the truth map 
increased and centered over the previously selected 
cells. At each iteration position decoding provides a 
better estimate of the shape and location of the 
locale. This process of incrementally increasing the 
resolution of the truth map is continued until either 
the cell size is less than .001 or the locale is clearly 
resolved (extends over about 1/3 of the truth map). 
Iterative refinement of the truth map not only saves 
storage space, it dramatically reduces the number of 
cells which must be evaluated and updated during the 
processing. A further reduction is achieved by 
processing only those cells which have a sufficiently 
high probability value. 
Associated with the processing of each cell of the 
truth table is an evalutation of the contour map 
representing the target. It is important that this 
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