742
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B3b. Beijing 2008
merge all model data.
3) Reference frame of the object
Reference frame of the object takes the object as reference
object. In spite of the change concerning other reference frame
to the object, its point coordinates are still fixedness.
4 ) Reference frame of the CCD camera
Reference frame of the CCD camera is the reference frame
which is considered the observer as the center.
5) Reference frame of the projector
Reference frame of the projector is the reference frame which
is considered the observer as the center, which is different from
that of CCD camera. So they are respectively two disparate
coordinates. To avoid coordinate transformation for the
complicated metrical data and complete the data
integration[ 1,2,3] of multi-view, it is operated only in one
reference frame. It always takes the rotating grid table as a
reference object, that is to say it is fixed. Considering coherence
of reference frame among arbitrary position of the rotating grid
table, CCD camera and projector are running. Then working out
their exterior orientation elements and calculating every model
point in every angle of view by space intersection. Thereafter all
the point cloud unified to one reference frame, which doesn’t
need to coordinate transformation and provides good initial
value to data integration for every point cloud of the model[4,5].
3. ACQUIRING INITIAL VALUE
3.1 Calibration of CCD Camera and Projector in Origin
Position
The purpose of camera and projector calibration is to find the
relations between 3-D space and 2-D planes(camera image
plane and projector slide plane). This calibration step is very
important since the coordinate computation depends on the
accuracy of calibration.
Furthermore, the values of the lens distortion existing in the
commercial projector are simultaneously calculated.
3.2 Initial Value Acquisition in Every Angle of View
If not depended on the rotating grid table, to acquire initial
value in every profile of the object to be measure is to calibrate
the CCD camera and projector in every different position. So it
is to remove them and repeat the operation in the origin position,
which need human intervene and reduce the degree of
automation. According to the turning angle by the rotating grid
table, the special point coordinates of the crosses relative to
those in origin position is calculated. And the correspondence
coordinates of the images are got by the interior and exterior
orientation elements of the CCD camera and the projector in
origin position, which is considered as the initial coordinates of
the images. It is completed the corresponding problem between
the special point and the image point for the angle change. Then
taking the rotating grid table as reference frame, where the
special points are fixed all the time, the CCD camera is
calibrated in every different position since the special point
coordinate and the corresponding image coordinate are known.
The camera and the projector in the original orientation is
calibrated by using the approach of 2D-DLT(two dimensional
direct linear transformation) and collinearity equation. Take the
original orientation of the rotating table as the reference frame,
while the table is rotating, the exterior orientation element Z s ,
of CCD camera in every angle is never variable and X s , Y s
is changed by the angle. Known the exterior orientation
elements of CCD camera in the original orientation, its exterior
orientation elements in every orientation are reckoned by its
angle, as shown in Formula(l), (2)and( 3). Then extracted
precisely the center of the cross, its exterior orientation elements
in every orientation are calculated accurately by resection as
known its interior orientation elements, the space point
coordinate of the center in the cross and the corresponding mage
coordinate.
As the rotating grid table is firstly designed to be able to get the
coordinates of the points of the grid, and the image of the planar
grid captured from camera is acquired, the camera is calibrated
by using the relation of 2D-DLT and collinearity equation. A
light stripe projected from the projector is usually called as a
virtual image. The light stripe captured by the CCD camera is
the intersection of the light stripe plane and the object surface.
Before the calibration of the digital projector, the rotating grid
table should be covered by a white paper or other things, which
make the primary planar grid seems to be a white plane. The
calibration of the projector is used structured light with light
stripe pattern as the pattern has its characteristic. For the
calibration of the digital projector, the camera is required to
have been calibrated already or its intrinsic parameters are
known in advance. A target grid slide is designed first so that
the coordinates of its grid points can be got as the known datum
for the projector. The camera is used to take an image of the
planar grid table while the positions of the camera and the
projector are always fixed. The coordinates of the grid points in
the image projected on the planar grid table, which are
considered as the space 3-D coordinates of the grid points, are
worked out by using the image processing method. As the space
3-D coordinates of the grid points projected have been got by
the process, and the image coordinates of these points in the
target grid slide are known as is designed in advance, the
calibration parameters of the slide projector can be computed by
using the relation of 2D-DLT and collinearity equation[6].
Assumed that capturing the i — l(/>2)th image, the grid
table contrarotates 6 by Z axes, then the orientation of the
CCD camera corresponding to the 1 th image is:
K)
r cos 0
sin 0
0^
(x s )
Y s ,
=
- sin 0
sin 0
0
Y s
°i-1
7
V S/ )
V 0
0
K
7
V 5 -. J
The corresponding rotation matrix is:
4 =
coô siiô 0
-sirô sir0 0
f coô sirô 0^1
-siiô sirô 0
° 0 \
<2, coô+è; sirô
-o, sirô+^ COÔ —tf sirô+^ coô
»V.
<h <h <h
k \ b,
V 0 0 U5 ^
Cf COÔ+^ sirô Cf COô+^ siiô ^
-Cf sirô+^ coô
<3 ;
(2)
