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If the intensity | (x,y) is measured at each pixel for three different but known phase angles, the resulting 
equation system for the three unknowns H (x,y), M (x,y) and ¢ (x,y) can be solved. 
For very fast applications, there is no need for three-phase projection, if a colour sine wave is projected and 
recorded. Phase information can then be taken from the red, green and blue parts of the projected image 
/Sasse 1994/. This method, using colour projection, is technically complex, and is difficult and complicated to 
implement. 
3. CENTRAL PROJECTION AND BUNDLE TRIANGULATION 
Machine and computer vision implements CLA with the objective of calculating object coordinates quickly. In 
this case, accuracy is not the primary requirement. Therefore either distortion-free lenses or simple algorithms 
for the distortion correction are used. The mathematical projection model describes only the relationship 
between a plain of light in the object and image space. Consequently there are no object points which 
correspond directly to one image point. The mathematical ambiguity of the stripe projection can be eliminated, 
by the possibility of computer-controlled projection not only of the lines but also of the columns. Now every 
point in the object space corresponds texactly to one image point. In this way the LCD-projector can be used as 
a camera which does not receive but rather emits signals (active triangulation). The collinearity equations, 
which are usually used in photogrammetry, apply under these conditions for the mathematical description of the 
projection of the LCD-projector and the camera /Wester-Ebbinghaus 1986/. 
The object coordinates of the projected grid crosses can be calculated by object recording from different 
perspectives by using calibrated CCD sensors. Now the relation between object and image coordinates can be 
described by means of collinearity equations (Fig. 3). Corresponding to mathematical lens distortion algorithms 
used in photogrammetry, the radial-symmetric, radial-asymmetric and tangential distortion can be calculated 
precisely by means of bundle triangulation. 
Prose 
Camera 4 
Camera 1 E 20 Camera 3 
S Camera 2 / p d 
   
  
  
  
  
Fig. 3 Comprehensive photogrammetric system calibration by grid projection /Strutz 1993/ 
Bundle triangulation results in mean residuals of 1/40 pixel of the imaging CCD sensors (SONY XC77) of the 
projected grid crosses. The relative measurement accuracy in the image space of the projector is better than 
1: 10000. 
4. COMBINATION OF DIFFERENT PERSPECTIVES 
Each arrangement of a projector and CCD camera enables to recorded to object from one angle. This 
evaluation results in coordinates in a local coordinate system. The object recording from another angle again 
IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop "From Pixels to Sequences", Zurich, March 22-24 1995