The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B3b. Beijing 2008 
743 
According to the rotation matrix, the three rotation angles are 
respectively as follows: 
a v a, cos Q + b, sin 0 
tan cp | . = —— = — I 
sinco ; . = —b 3i = a 2 sinQ-b 3 cos0 
b u a, sin 0 - b, cos 0 
tan K, = —!— = —— : ! 
b 2i a 2 sin 0 — b 2 cos 0 
The direction cosines in Fomula(3) is that of the Z th image. 
While the position of the projector and CCD camera is fixed, 
the transformation matrix[7] between them can be calculated in 
the first place. Then the calibration parameters of the projector 
in every angle can be computed as the calibration parameters of 
CCD camera is known in every corresponding angle. Equation 
(4) indicates that the rotating matrix of the projector in every 
angle, where R p and R c are respectively the rotating 
matrix of the projector and CCD camera in the Z th angle, 
R c ' is a corresponding inverse of the rotating matrix R c of 
CCD camera in the first place, R p ^ is the rotating matrix of 
the projector in the first place. In the equation (5), 
Xs pi , Ys pj , Zs pi and Xs p i , Ys p j , Zs p j are respectively 
the three position elements of the projector in the Z th angle and 
in the first place, while Xs Ci , Ys Ci , Zs a 
and Xs ci , Ys cl , Zs cx are respectively the three position 
elements of CCD camera in the Z th angle and in the first place. 
^P; ~ K C , ' K Ci ' K/] 
(4) 
~Xs p j 
1 
Q 
1 
1 
G 
1 
G 
1 
Ys PI 
= 
+ R c •R c] 
Ys - Ys 
iò P \ 
_Zs„ _ 
_ Z S Ci _ 
7ç - 7v 
_ 1 ^ ò c\ _ 
While the calibration parameters of CCD camera are computed 
by space resection[8, 9] with iterative method after rotating an 
angle, simultaneously the calibration parameters of the projector 
are done in the corresponding position. Calculated the interior 
and exterior orientation elements of CCD camera and the 
projector in every angle, the point cloud of the model in every 
view is obtained by space intersection. Then all the point cloud 
is in the same reference frame and it provides perfect initial 
value to the next seamless registration. 
4. EXPERIMENTAL RESULTS 
Table 1 lists the results computed in origin angle, which are the 
interior orientation elements of the CCD camera and the digital 
projector 
parameter 
CCD Camera 
Digital Projector 
f 
3807.86904 pixel 
2819.00516 pixel 
xO 
650.77228 pixel 
510.07340 pixel 
yO 
498.95924 pixel 
381.77845 pixel 
Table 1 the interior orientation elements of CCD camera and the 
digital projector 
Based on the above depicted, it is calculated the calibration 
parameters of the CCD camera and the digital projector in every 
angle of view. And it is charted as shown in Fig.2 and Fig.3, 
which are distributed regularly. For it is circled by the plane of 
the rotating grid table, the change of the Zs value is almost 
invariable from Fig.2 and Fig.3, and the other five parameters 
distribute regularly in such as sinusoid, cosine, etc. And it is 
obtained the initial value owing to the calibration parameters of 
the CCD camera and the digital projector in every angle of view. 
Furthermore it can be also forecasted in every visual angle from 
them. And Fig.4 is shown the result of 3D model of sheetmetal 
part. 
»00 
«00 » 
400 - 
200 - 
0- 
*400 - 
-600 
-600 
— 
pM 
kappa 
2- 
To ’ ¡8 T Si T 5 ' a 5 10 IS 20 25 
Fig.2 the exterior orientation elements of CCD camera in every visual angle