where: 
N° - [Zo Anf 
f*iz, I- X,nf. «(Z,m,- Y, nfl 
U- "Ite Xon) * L(Z,m,- Ysnj| 
(Z,* Anf 
  
FlAo) - yi 
A, is an approximate value for the parameter A; 
NS 
Il 
The X, Y, Z, coordinates of point P, can be computed 
using equations (2) and the adjusted A. 
4. CALIBRATION OF THE PROJECTED BUNDLE 
The system calibration involves the determination of the 
camera inner orientation parameters and the parametric 
equations of all projected straight lines. This concept is 
depicted in figure 1. 
4 Z Camera Projector 
   
  
Xo,Yo,Zo 
  
» Projected points 
^ Control points 
  
  
  
  
Fig. 1 Reference system and the geometric concept 
of the calibration method. 
Although the simultaneous estimation of those 
parameters would be desirable, experiments 
demonstrated unreliable results and high computational 
costs. Considering this experience, a sequential solution 
was derived. It involves five steps, which are 
summarised in figure 2. 
The concept of the calibration method is similar to the 
AZ method, used in triangulation by independent models. 
Several images of the projected bundle are acquired on 
the parallel reference planes which have targets to be 
.— cameracalibrtion — | 
I 
  
  
  
  
  
  
  
: 
| control points measurements | RE I 
projected points measurements o: 
the ith plane 
3 A 
estimation of the space resection 
parameters 
(x, 6, €, Xc, Yc, Zc) 
  
  
P 3 
computation of the projected points 
coordinates in the camera reference 
system 
next image 
of the 
(i+1)th plane 
      
    
  
s 
  
estimation of the projector perspective center 
coordinates and straight lines parameters 
  
  
Fig. 2 Computation of the straight lines parameters 
used as control points. Different image coordinates of 
one point in several planes will correspond to the same 
straight line in the object space. Control points are used 
to compute the plane position and orientation with 
respect to the camera reference system. Therefore, the 
coordinates of the projected points over the plane can be 
computed. 
In the sequential approach the camera is firstly calibrated 
using self calibrating bundle adjustment with convergent 
cameras. The same structure of the range system can be 
used in this task. Previous experiments with real data 
have presented suitable results with four images and 20 
control points. 
The second step involves the features extraction of each 
image collected for the projection planes. The 
coordinates of the control and projected points are 
computed using the methods of feature extraction 
described in section 2. 
Position and orientation parameters of the camera with 
respect to the control points are computed in the third 
step using Space Resection. 
The fourth step attempts to compute the coordinates of 
the projected points in the camera reference system, 
using the position and orientation parameters previously 
computed. 
Once the reference plane is moved, another image is 
grabbed and steps 2, 3 and 4 are repeated, until, at 
least, three planes are available. 
Coordinates of the projector perspective center and 
straight lines parameters are estimated in the fifth step. 
These parameters are computed in a simultaneous least 
370 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B2. Vienna 1996