# Full text: Proceedings International Workshop on Mobile Mapping Technology

```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
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