7A-6-2 
are followed in section 3. In section 4, we give 
a simple conclusion. 
2. SOLUTION ROUTE OF THE 
METHOD 
The method is set out not only from 
application, but also from geometric space. 
Different geometric spaces have different 
geometric construction and characteristics. 
For example, a 3D Euclidean space, the 
commonly used geometric space, is 
constituted by three axes, which are 
orthogonal each other and extend to infinity; a 
3D affine space is constitute by three un 
coplanarity vectors; a 3D projective space is 
built by an enclosed tetrahedron and a unit 
point. Different ways to construct a geometric 
space bring different description and solution 
route to a same problem. And in a certain 
geometric space, the problem can be got its 
solution with more convenience. From this 
point, we select projective space to do the 
work of object positioning. 
The method can be divided into the following 
three steps: 
S, : Transforming Euclidean coordinates 
of image points into projective 
coordinates 
For digital camera is widely used in 
photography, pixel coordinate (i, j) of image 
point is easily got, which is in a 2D Euclidean 
coordinate system. The coordinate firstly is 
changed into its quasihomogeneous form of (i, 
j, c) by adding a nonzero instant number c at 
its behind. Then a transformation matrix is 
used to transform it into projective 
coordinates (u, v, w). The transformation 
matrix is formed from four image points' 
quasihomogeneous coordinates and these four 
points are constituted the 2D projective 
coordinate system on image plane. 
S 2 : Getting object points' 3D projective 
coordinates from image points' 2D 
projective coordinates 
There are 3 ways to get object point's 
projective coordinate, which are different with 
image number. These ways are closely 
connected with getting the projective 
invariants in computer vision [Hartley, 1994] 
[Quan,1995] [Xiong, 1995] and they have been 
adapted to fit our work. 
Based on 2 images: When two images are 
used, according to the coplanarity condition, 
we use 8 or more pair of homologous points to 
calculate the fundamental matrix, then 
decomposing the matrix as a product of a 
skewsymmetric matrix and a regular matrix, 
from which two camera matrices can be easily 
obtained. At last using the intersection to 
reconstruct the object model and get the object 
points' projective coordinates. 
Based on 3 images: From the projective 
coordinates of object and image point and the 
image forming equation in projective space, 
we can build another relationship between 
object and image points' coordinates. From 
one image, we can build one relationship 
between them, in which there are 3 
independent unknowns about object points' 
coordinates. When 3 images are used, it is 
enough to get the values of these unknowns. 
To get the final solution, certain approximate 
values of object point are required to be used 
as reference. 
Based on 4 images: The coefficient matrix of 
the linear equations, built from the 
relationship between the object and image 
points' projective coordinates with multiple 
images, has the rank of 4, even through 6 
unknowns are needed to be determined. So 
when 4 images are used, two series of basic