layer on a glass plate (Maas, 1991a); as opposed to 
film-based patterns this way a perfectly binary trans- 
parency characteristics was achieved. In order to 
avoid the cumbersome calibration of a projector the 
information of the projected pattern was not used 
actively (Regensburger, 1990), but only passively. 
Image coordinates on the pattern slide and projector 
orientation- and calibration data need not to be 
known. 
This way the surface gets marked with a large number 
of dots, which are of elliptical shape in the general 
case. The marked surface can be recorded simulta- 
neously with two or more CCD cameras or (non- 
simultaneously) with one camera from two or more 
positions. If good approximate values of the surface 
are given, two cameras resp. two camera positions are 
sufficient; if good approximate values are missing or 
if the surface shows strong modulations or discontinu- 
ities, three or four cameras may become necessary. À 
configuration with one projector and four cameras is 
shown in Figure 1. 
PTT 
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Figure 1: Four camera configuration 
The data processing from the raw digitized images to 
the surface description can be divided into the major 
steps: 
* image preprocessing 
image analysis and image coordinate determina- 
tion 
establishment of correspondences between images 
using epipolar line information 
* 3D coordinate computation 
» interpolation and surface description 
The whole procedure can be set up to work 
completely automatically for single surface measure- 
ments or for sequences of surface measurements e.g. 
in deformation analysis processes. For a detailed 
  
   
   
   
   
   
   
  
  
   
  
  
  
  
  
  
  
  
  
  
  
   
  
  
  
  
  
  
  
   
  
  
  
  
  
  
  
  
  
  
  
   
   
  
   
   
   
   
   
   
   
   
   
     
description see (Maas, 1991a). 
The same procedure has basically been installed and 
analysed thoroughly for the determination of 3D- 
coordinates of particles visualizing turbulent flows 
(Maas, 1991b, Maas, 1992a). Unlike the recording of 
moving particles in water the targets are situated on a 
mostly continuous and relatively static surface here, 
by which some of the problems occuring there are 
discarded and the targets can be called relatively well- 
behaved. Their image coordinates can be determined 
at an accuracy of 1/20 of a pixel or better by simple 
thresholding and computation of the centre of gravity. 
The problem of ambiguities in the establishment of 
stereoscopic correspondences, extensively discussed 
in (Maas, 1992b), has to be solved here as well. Only 
if the surface is relatively plane and if good approxi- 
mate values are available, or when the number of 
projected dots is small, the correspondence problem 
can be solved reliably with a system based on only 
two camera positions. in practical applications with 
problematic surface properties like reflecting or dull 
black regions, non-perfect projection and image 
quality (e.g. depth of focus in projection and 
imaging), occlusions, strong modulations or surface 
discontinuities three or four cameras (resp. camera 
positions) will be necessary to solve ambiguities and 
obtain unambiguous correspondences by the method 
of intersection of epipolar lines or similar methods 
(Maas, 1992b). Having established consistent triplets 
(resp. quadruplets) of corresponding image points in 
the image coordinate datasets the spatial coordinates 
can be computed by spatial intersection or together 
with the camera calibration data in a one-step bundle 
solution. The resulting object coordinates can be 
interpolated to a regular grid or rendered to derive 
CAD structures. 
The method is a truly simultaneous technique, but the 
number of projectable points is limited to about 1/50 
of the number of image pixels due to the projection of 
discrete dots, which have to cover at least 2 x 2 pixels 
in the digitized image to allow for a coordinate deter- 
mination with subpixel accuracy. To increase the 
spatial resolution several exposures can be made from 
every camera station with the projected pattern phase- 
shifted by fractions of the dot raster width; however, 
the method cannot be called a strictly simultaneous 
method then. 
The camera orientation and calibration is a crucial 
step as deficiencies in the calibration will make the 
epipolar lines miss the correctly matching points; thus 
large errors in the calibration will not only influence 
the accuracy but may make the whole method fail if