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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