Gamal Seedahmed 
  
detected. Subpixel localization is required because the pixel size is most likely larger than the expected 
precision of the fiducial centers. Another objective is the requirement for a general, fast, accurate, 
reliable, and robust solution accommodating different types of fiducial marks. A system is general if it 
can cope with different problems as they may occur in the production environment. A third objective is 
the system should cope with image resolution where the fiducial centers have been lost; as long as the 
fiducial mark is still identifiable, the location may be determined from the features that describe the 
fiducial mark (Seedahmed and Schenk, 2000). 
2 MODEL-BASED RECOGNITION OF FIDUCIAL MARKS 
The object recognition problem in general, can be defined as a labeling problem based on models of 
known objects. Formally, given an image containing one or more objects of interest and a set of labels 
corresponding to a set of models known to the object recognition system, the system should assign 
correct labels to regions, or a set of regions, in the image. 
An object recognition system must have the following components to perform the task: Model- 
database, feature detector, hypothesizer, and hypothesis verifier (Theodoridis and Koutroumbas, 1999). 
The model database contains all the models known to the system. The information in the model 
database depends on the approach used for recognition. It can vary from a qualitative or functional 
description to precise geometric information. In this study the model database contains information 
about the CAD design of the fiducial mark, its optical projection factor onto the film, and the pixel size 
of the image. 
3 HOUGH TRANSFORM 
The basic idea behind any transform-based features is that an appropriately chosen transform can 
exploit and remove information redundancies, which usually exist in the set of samples obtained by any 
measurement techniques. If the transform is suitably chosen, transform domain features can exhibit 
information-packing properties compared with the original input samples (Theodoridis and 
Koutroumbas, 1999). 
The last few years have seen an increasing use of parameter estimation techniques that use a voting 
mechanism. One of the most popular voting methods is the Hough Transform (HT). The HT is 
considered as a parameter estimation strategy based on the statistical mode. More common strategies 
such as least- squares error fitting are based on the statistical mean. The HT has achieved engineering 
importance in several areas of image understanding (Brown, 1986), (Leavers, 1992). Since its early 
formulation, the Hough Transform (Hough, 1962) has undergone intense investigation, which have 
resulted in several generalizations and a variety of applications. The basic mechanism is a voting 
scheme in the parameter space. The parameters that receive a higher vote are declared winners, 
followed by a de-Houghing to find the required curve at the image space using the detected parameters. 
In order to gain a basic understanding of HT we will describe the straight-line algorithm. A straight- 
line in the sense of HT is a set of collinear points, see Fig. (2). The HT is a mapping 4 from R” into the 
function space defined by: 
  
  
  
h :(x, y) — p 7 xcosÓ * ysinO (1) 
1 
Y e 
t 1 Original 
coordinste 
plane 
p 2 Hough plane 
3 
© 
Lk 
X Ne, P 
  
Fig. 2: The polar representation of a line and its Hough space. 
  
International Archives of Photogrammetry and Remote Sensing. Vol, XXXIII, Part B3. Amsterdam 2000. 825