2. Androx ICS-400 system with 2Mbyte video 
memory, an extensive library of C-callable graphics and 
digital signal processing functions. 
3. Two Panasonic WV-CD20 CCD cameras with a 
resolution of 560 by 482 (8.8 mm by 6.6 mm image field) 
pixels and changeable lenses. 
4. A NEC Multisync color monitor. 
3.3 General Procedure 
The experimental procedure can be summarized in the five 
following steps. 
1. For this experiment, the control/test model consists 
of ten precision machine blocks whose dimensions are 
known. The size of the model is approximately 6 by 6 by 4 
inches. The CCD cameras are positioned about 7 inches 
apart and about 26 inches above the model. Multiple 
images are taken with both cameras under various 
illumination conditions. 
2. Using the image displayed on the monitor for each 
camera, determine the image coordinates of the control 
points on the surface of the model whose object coordinates 
were previously determined. For the purpose of easy and 
accurate recognition, a set of well-distributed corners of 
the blocks were selected. A C-language program, which 
uses various digital signal processing functions of the 
Androx system with operator's interactive instructions, 
was developed for determining the coordinates of the 
chosen points. 
3. Using both cameras, images were taken of a surface 
of random dots which was superimposed upon the control 
model as shown in Fig. 3. The illumination should be 
carefully arranged so that both cameras receive 
approximately the same amount of exposure. For the 
purpose of noise reduction, more than one image is taken 
and averaged. 
4. The images containing the random dots were 
matched. The image coordinates of the dots resulting from 
the matching process were then placed into the same input 
data file which contains the image coordinates of the object 
control points. 
5. Thebundle adjustment program was executed on the 
input data files using different weight constraints on 
particular variables. As a result the object coordinates of 
the model points, as well as those of the dots on the surface 
of the specimen, were determined. 
3.4 Computational Procedures 
The chief computational procedures utilized during the 
experiment included the self-calibrating analytical 
photogrammetry bundle adjustment method and the image 
matching method which was used to determine the image 
coordinates of the random dots. 
3.4.1. Bundle Adjustment Method. This solution was 
patterned after Brown [10], [11]. Contributions to the 
     
  
   
   
  
   
   
   
   
   
   
   
    
   
  
  
  
  
   
   
  
   
    
   
    
  
   
   
   
  
   
  
   
   
   
   
  
  
   
   
  
  
   
   
  
  
  
  
  
  
program were made by Orrin Long, Marquess Lewis and 
Mark Nebrich. The software was modified by Weiyang 
Zhou for this application. 
The basis for the solution is the collinearity equations as 
follows: 
gu 10 Kueh ima SZ] 
Fx = Xs Xpp*! | mg) Rj Kio+maolY Vid +m33(Zj Zid 
Al (X;-Xic)+mo2(Y;-Yıc)+Mo3(Zj-Zie) ] 
Fy 7 Ys'Ypp*f | m5; (X X.) maa(Y- Yo) &mas(Z Zi) 
Where m is a function of camera orientation angles w, ¢, 
and x and Xjcs Yic and Zic provide the camera's position in 
object space. Xj, Y; and Zj are the coordinates of point j in 
the object coordinate system. Interior orientation 
parameters are represented by f, Xpp, and ypp. The image 
coordinates are xg and ys. 
Using a linearized version of these two equations for each 
image point a least squares solution provided all of the 
parameters and object coordinates after sufficient 
iterations. 
The project efforts are currently experimenting with the 
expansion of the self-calibration techniques through the 
incorporation of additional parameters which affect the 
image coordinates. 
3.4.2. Matching Method.  Image-matching 
methods fall into two groups. With the area-based 
methods, such as [2] and [6], two windows of pixels, one on 
each image of the pair, are judged to be a match or not 
according to the similarity between the intensities of the 
pixels within the two windows. The similarity is 
determined by calculating statistical values, making these 
methods statistical by nature. The second group of image 
matching methods is based on feature, usually edge, 
information of images [3] [5] [9]. The form and 
distribution of the features in images are used instead of 
absolute intensities of the pixels. 
It is now generally agreed that edge-based methods have 
advantages over the area-based methods because it is more 
reasonable to match images by the variation of pixel 
intensities than by absolute values of pixel intensities and it 
is usually more economical in terms of computing time, 
though there are some methods for improving the 
efficiency of area-based methods [8]. 
In mechanical experiments with paper, since there is 
usually not much texture on paper surfaces, it has been a 
common practice to place a random pattern onto the surface 
to enrich the texture. For example, dots with irregular size 
and shape are used in many experiments. Inthis work, these 
dots serve as targets for feature-based image matching. 
In order to measure the deformation, there are two types of 
matching. 1) The matching of two images taken by the 
same camera before and after the deformation of the