ROBUSTNESS TEST TO OBJECT POSITIONING IN PROJECTIVE SPACE 
Xingwen Wang Deren Li 
School of Information Engineering 
Wuhan Technical University of Surveying and Mapping 
Wuhan, P. R. China 
xwwang@rcgis.wtusm.edu.cn 
dli@dns.wtusm.edu.cn 
KEY WORDS: Robustness, Object Positioning, Projective Space, Real-Time Photogrammetry, 
Computer Vision, Fundamental Matrix, Camera Matrix 
abstract: 
The advantage and possibility of object positioning in projective space have been investigated in 
our previous work. The kernel of the method is to get object points' 3D projective coordinates 
from image points' 2D projective coordinates. We have introduced 3 ways, which are different 
with image number, to do this work. For taking the method into application in real-time 
photogrammetry, we tested its robustness with the three ways. In this paper we show some test 
results and give an explanation about why their robustness are different. 
1. INTRODUCTION 
With the widely use of uncalibrated camera in 
close range photogrammetry and the 
requirement of real-time processing, we 
introduced a new method about object 
positioning [Wang & Li, 1998]. Compared 
with other photogrammetry methods, it is 
carried out in projective space. In this 
geometric space, the images of uncalibrated 
camera can be directly taken into use without 
interior orientation. At the same time, the 
image forming equation is described as a 
linear equation, which brings great 
convenience in processing. So, this method 
gets the solution directly from the image 
points without any approximate values of 
interior and exterior orientation elements. It is 
applicable to convergent photography in close 
range photogrammetry and can realize real 
time solution. Moreover, compared with the 
DLT method, its requirement to control point 
is five. So it is also called five-point based 
direct solution. 
The kernel of the method is to get object 
points' 3D projective coordinates from image 
points' 2D projective coordinates. We have 
introduced 3 ways to do so, which are 
respectively based on two, three and four 
images. Apparently, the three ways are based 
on different image number. In calculation, 
they have different requirement to 
homologous points and certain approximate 
values of object points. From our analysis, we 
think multiple images, approximate values 
and homologous points compensate each other 
in many calculations. We will discuss this 
point in other paper. For taking this method 
into use, we tested its robustness using all the 
three ways with simulated values and pseudo 
stochastic noise. In this paper we show some 
test results and give an explanation about why 
their robustness are different. 
In the following we first simply review the 
solution route of the method in section 2, then 
some test results are listed and the explanation 
7A-6-1