ISPRS Commission III, Vol.34, Part 3A „Photogrammetric Computer Vision“, Graz, 2002 
  
cameras are ignored as unreliable. In planar or smooth object 
surface patches, the correct combinations of all points are 
usually found. The 3-D coordinates can then be reliably 
computed using intersection. For each 3-D point, a quality index 
is also obtained which indicates how well the corresponding 
projection rays intersected in space. This can be used to filter 
the data before any further processing in a suitable 3-D 
modelling program. 
  
Figure 2. 16 light spots projected on an object. 
The measured area can be programmed in advance using the 
movable light projector and the rotating measurement table. The 
number of measured points and the desired density of points can 
be freely chosen. Actual measurements from different rotation 
table positions are transformed to the same base coordinate 
system automatically by using special target points placed in the 
table. 
For different materials, a different light source can be chosen. 
For most metals, plastics and soft materials, white light is 
suitable. For translucent plastics and glass, laser light is 
preferred. 
3. CALIBRATION 
The Mapvision 4D system requires careful system calibration to 
get it to measure in a correctly scaled, orthogonal 3-D 
coordinate system. The calibration is performed using a 
standard free-network bundle adjustment, which determines the 
relative positions and orientations of the cameras, as well as the 
unknown interior orientations and various additional lens 
distortion parameters of each camera. The absolute scale of the 
coordinate system is fixed by observing the end-points of a 
known scale bar, and by using the distance as a constraint in the 
adjustment. The distance should be observed in sufficiently 
many (say, 50-100) different orientations and positions, well 
distributed in the whole measuring volume, in order to get the 
best calibration results. It is better to use arbitrary rather than 
regular orientations and positions for the calibration distances. 
The observations are averaged over several repeated 
measurements, which improve the quality of the observations 
and makes the calibration more robust. The original calibration 
method is described in article (Haggrén and Heikkilä, 1989). 
Approximate values for the calibration can be obtained by using 
at least six known 3-D points and the well-known DLT-method, 
or the all-from-scratch method described in (Niini, 2000), or 
simply by using the values from a previous calibration. The last 
method is especially suitable when recovering an accidentally 
broken calibration. Either a complete recalibration, or a quick 
determination of only the external orientations is possible. 
When planar circular targets are used, the centre of the original 
circle is not projected on the actually measured centre of the 
image of the circle. This image is usually an ellipse, except 
when the image plane and the plane containing the original 
circle are parallel and the image is also a circle (Heikkilä, 
1997). Using a triangle-shaped, three-target calibration tool, this 
effect can be taken into account (Figure 3). 
  
Figure 3. Calibration tool. 
The third, ring target is used to recognize and order the targets 
correctly, and the three points together determine the orientation 
of the triangle with respect to the image planes, so that a 
projective correction to the image observations can be made 
iteratively during the adjustment. The projective corrections 
could also be avoided by using spherical targets. 
It is possible that using an insufficient number of distances in 
the calibration may leave the final 3-D coordinate system 
locally slightly curved. This probably comes from the combined 
effect of the higher order radial distortion coefficients and the 
sparsity of the observed distances. There may exist quadratic 
saddle surfaces where the observed distances are correct, but the 
coordinate system is not homogeneously straight. 
The orthogonality of the 3-D coordinate system can be further 
strengthened by measuring points (using the light scanner) 
along a known plane whose flatness is a magnitude better than 
the desired accuracy of the system. The plane can be observed 
in several different positions and orientations to remove any 
possible local curvature of the coordinate system. The image 
observations of these points enter the adjustment, and the 
corresponding 3-D points are constrained to lie on the same 
plane. Each different plane orientation adds four new 
parameters in the adjustment. The equation AX+BY+CZ+D=0 
can be used, which simply states that the 3-D point with 
coordinates X, Y, Z lies on the plane determined by parameters 
A, B, C, and D. Because only three of these parameters are 
independent, a normalizing constraint equation is also needed: 
A°+B+C+D"=1. 
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