Guehring, Jens 
  
Thus, assuming ©, —2 and C -25 (which corresponds to a modulation of 50), 0%, =0.057 is obtained. Since 4 
projector lines are used for the range [0,27] (Figure 5), this transforms to 0.036 or 1/ 28 of the line width. 
Thus, from theoretical analysis, the accuracies which can be obtained by phase shifting are comparable to those in 
photogrammetry. 
One problem using phase shift measurements is that small errors in phase measurement near the changeover from 27 
to O can cause large measurement errors with a magnitude of about 1 period or 4 projector lines (Figure 6 (b)). 
  
  
  
  
  
  
  
  
  
A 
w no © + 
  
  
  
  
+ 
  
  
© 
  
(a) (b) (c) 
Figure 6. (a) Ideal combination of gray code and phase measurement. (b) Small errors in either phase or gray code 
measurement cause large peaks in the combination. (c) Oversampling allows for detection and even correction of gross 
measurement errors up to 1 line of magnitude. 
This problem can be solved by an oversampling technique. If the resolution of the projected gray code is half the length 
of a period, we can specify valid ranges for phase measurements, observed at a specific pixel position. This allows to 
detect and even correct for gross measurement errors (Figure 6 (c)). 
However, it has to be taken into account that non-uniform object surface properties, such as a sharp change from black 
to white result in systematic measurement errors. Also, since the camera pixels effectively integrate over a certain area 
of the stripe code, the above error estimation is only true with a camera resolution sufficiently higher than the projector 
resolution. 
Another problem arises if we want to combine measurements from different cameras using the same projector. The 
phase shift method yields for each camera pixel the corresponding projector stripe number with substripe accuracy. This 
means there is no direct link between image coordinates acquired by different cameras which might improve accuracy 
and reliability of the resulting surface points. 
3.3 Solutions to the Correspondence Problem - Line Shift Processing 
3.3.4 Requirement Analysis 
Based on the experience we made with our previous system, a detailed analysis of all requirements for the design of our 
new method has been performed. We identified the following requirements, all of which have not been met by a single 
system to date: 
e Abilitity for automation: The system should be able to adapt automatically to different objects without user 
interaction. 
e Efficiency: Dense surface measurements of some 100.000 surface points should be feasible within a couple of 
seconds. 
e Versatility: The method should extend over a wide range of sensor configurations, particularly the combination of 
multiple cameras with a calibrated or uncalibrated projector. 
e Insensitivity to reflectance properties of object surface: Changes in surface reflectance should not cause systematic 
errors in range measurement. 
e Accuracy information for 3-D coordinates: In addition to the object point coordinates, statistical measures for the 
quality of point determination should be available and used by further processing steps. 
e Consistency and reliability: The system should prefer consistent and reliable points over complete coverage of the 
object's surface, especially in the presence of unfavorable lighting conditions and reflective surfaces. 
  
332 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000.