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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
  
COE Von) 
a 52) 
= HY) d ue 
Dy euros uq] 
=v, 3 zl. 
= 20x, = Xt) ER 20m ES Yann) = 
= Am = Xan ) E 2(v,, van) 1 | 
  
  
m 
2 2 2 
Xuqoc. SY, JY 
” 
2 2 2 2 
Xo 7X3 tX —Y» 
2 
2 2 2 2 
Xs = Xa (n-1) " M m E. Yam-ı) 
? 
2 2 2 2 
Xp re Xon + Nin E Y 
  
  
where Xo, Vo = the coordinates of the centre of the circle 
dd 7 = l...m) — the coordinates of 777 points on 
the circle whose radius is Rı 
Xi V1; (i =1...n) = the coordinates of 77 points on 
the circle whose radius is R, 
A is a coefficient matrix whose size is (M X A )X4 
L is a constant matrix whose size is (M X A )X1 
X is a unknown number matrix whose size is 4 X 1 
After resolving the X , the coordinates of the fixed axis of the 
solid of rotation can be worked out obviously. At the same time 
the distance from the every space point projected on the surface 
of the solid of rotation to its fixed axis can be computed out by 
the formula (2). 
3. DATA AND EXPERIMANTAL RESULTS 
31 Design Data 
The size of the rotating platform is 60cm X 60cm. A planar grid 
is fixed upon it, which supplies the controlling points and the 
coordinates system. There are 185 18-324 controlling points in 
the planar grid. The interval of these points is the same and is 
30mm. Each point has its own serial number which is exclusive. 
By using the coordinates of these points, the digital camera and 
the slide projector can be calibrated correctly and the extrinsic 
parameters of both are also calculated out entirely. 
The size of the feature slide designed is 1024 pixels X 768 
pixels. Because the target solid of rotation in the experiment is 
a convenient cup that is relatively small, the texture feature is 
designed as a line which is better to show the edge of the solid 
of rotation. The line is located in the centre of the slide so that 
its equation is expressed as: 
X 2512 (5) 
where X,Y =the coordinates of the points on the line 
Y= 10...7671 pixel unit 
When the line is projected on the surface of the solid of rotation, 
the feature texture on it becomes a curve. This curve is sure to 
be corresponding to one section of the line in the slide. The 
homologous points can be gotten by the crossing between the 
homologous epipolar lines and the curve and the crossing 
between the homologous epipolar lines and the section of the 
line. 
3.2 Image Sequences 
When the positions of the camera and the projector are adjusted 
well and fixed relatively, both need to be focused respectively. 
The distance from the digital camera and the slide projector to 
the rotating platform is about 1.5 meters. Then a convenient cup 
is put on the centre of the rotating platform, which is the target 
solid of rotation. The slide projector projects the line in the 
slide onto the surface of the cup. It is ascertained that the 
projected line is through the whole body of the cup, which is 
very important and necessary. Then the camera is used to take 
sequential images of the convenient cup with the slide projector 
illuminating when the rotating platform rotates continually. In 
the experiment the camera takes images from 4 orientations and 
there are 4 images in total as the image data shown in the 
Figure 2. The size of each image is 1300pixels X 1030pixels. 
  
Figure 2. The sequential images with the feature