t of non-contact 
ured object for 
ce, the projector 
calibration of a 
The planar grid 
:d or its intrinsic 
] to calibrate the 
'€ coordinates of 
the intrinsic and 
ic and extrinsic 
n parameters are 
t forward in this 
The camera has 
ters are known 
ound to provide 
rrespondence of 
isformation, the 
ked out. By this 
| the. expensive 
posed technique 
ted by the space 
sing in future of 
> feasibility and 
inique proposed 
ita. 
It can be used to 
ts as the same 
ly the points of 
are lack of the 
of the measured 
insic parameters 
the calculation 
UTHM 
inar grid are the 
the projector, a 
target grid slide is designed first so that the coordinates of its 
grid points can be acquired as the known data. The camera 
requires to have been calibrated already or its intrinsic 
parameters are known in advance. The planar grid is also 
designed first to be able to obtain the coordinates of the points 
of the grid. 
First, the positions of the projector and the camera are adjusted 
to two appropriate places. The camera is focused to take clear 
photos of the planar grid and the projector is also focused to 
project clearly a target grid slide onto the plane. Second, the 
camera is used to take an image of the planar grid. Then the 
planar grid is covered by a white paper (or other things), which 
makes the planar grid seem to be a plane. The projector 
illuminates the target grid slide onto the plane. The camera is 
used again to take the images of the grid illuminated. In this 
process of taking the image of the illuminated grid, it is 
important that the positions of the camera and the planar grid 
are both never changed. Using the image processing method, 
the coordinates of the grid points of the image of planar grid are 
extracted. Because the space coordinates of the planar grid 
points are known as design, the extrinsic parameters of the 
camera can be calculated by the space resection method. So that 
the intrinsic and extrinsic parameters of the camera have been 
gotten at present. Using the image processing method again, the 
coordinates of the points of the image of the projected grid are 
extracted, too. By the collinear equations, the space coordinates 
of the projected points of the image are calculated in reverse, 
because the Z value of the space coordinates of these points is 
zero always. For the projector, the space coordinates of the grid 
points projected have been acquired by the process above, and 
the image coordinates of these points are known as design in 
advance. Using the correspondence of 2D-DLT and collinear 
equation, the decomposition of initial values of the projector 
intrinsic and extrinsic parameters is deduced. Third, the 
positions and orientations of the projector and the camera are 
changed to take another two images as the second step. At least 
all images need to be taken from two different positions and 
orientations. Then at least two sets of the initial values of the 
projector parameters can be computed out. Finally, the intrinsic 
parameters of the projector can be worked out by the whole 
adjustment based on these initial values above. So the ordinary 
projector has been calibrated entirely by this way. 
2.2 Algorithm 
The collinear equations are: 
  
X—x =-f a (X X, )+6,(Y-Y)+ce, (Z-Z,) 
s a x )50.(Y 27 Yee lZ-7) 2i 
aX - X, )* b,(Y - Y.)«c,(Z - Z.) 
aX - X,)«5,(Y - Y,)« e, (Z - Z,) 
  
y-y.m-f 
where f, xo, yg — the intrinsic parameters of the projector 
Xs» Ys, Zs = the coordinates of the projector centre 
X, Y, Z = the space coordinates of points 
x, y = the image coordinates of the relative points 
R (aj bj c; i71,2,3) 7 the rotated matrix made up of 
rotated angles 9, Q,K 
Z=0 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004 
2D-DLT is expressed as: 
ho X c h.Y oh, 
ho Xon Y] 
EX UY C. 
Abel 
x = 
  
  
where H;(i=1,2...8) = parameter 
X, Y = the space coordinates of the points projected 
x, y = the image coordinates of the relative points 
When the number of points observed in an image is more than 4 
the parameter H; can be calculated out. 
3 
According to the formula (2), formula (1) can be transferred 
into formula (3): 
a d Ds b ir I T 
" (/ a -Sx je i Ba) s - aX, LA ) 
= 3 
Lx ya 3) 
A A 
Math Th Led +6, 
( Bey ore Ha o ax, +b sez) 
“Bx fy 
A 
  
y = 
  
Compared formula (2) and (3), then: 
  
a, d, 
n ER 
(4) 
ho 
hf 
AA 
h, - fy 
Aoi Ao (5) 
| +0, by 4 
fs = [=k 
$ 
  
h =x, Ar +bY +¢,Z.) 
^ (6) 
fa = Vo za, t b,Y, - c,Z,) 
a, 
hkE-— 
; n 
h,--—