International Archives of Photogrammetry and Remote Sensing. Vol. XXXII, Part 5. Hakodate 1998 
A Study on Real-Time Photogrammetry 
for Three-Dimensional Token Tracking 
Yongsheng ZHANG 
Institute of Remote Sensing &. Photogrammetric Engineering 
Zhengzhou Institute of Surveying &. Mapping 
E-mail ;yszhang @public2. zz. ha. cn 
P. R. China 
Commission V ,Working Group ICV / II 
KEYWORDS:real —time photogrammetry ,three —dimension ,token tracking » 
stereo vision ,motion vision 
ABSTRACT 
This paper presents a study on real-time photogrammetry for token tracking in three dimensions. 
We have a sequence of stereo frames from which we will compute ,using the algorithms of stereo 
vision, a sequence of three-dimensional frames. To be concrete,these three-dimensional frames 
will consist of sets of three-dimensional line segments. By tracking we mean the ability to follow 
the motion of a given segment and to estimate its kinenatecs. Since much more information is 
available than in the two-dimensional, we may expect to be able to solve much more difficult 
problems. Indeed ,we will directly estimate the three-dimensional kinematics of the line segments 
and will be able to cope with the problem of multiple-boject motion. We choose the state and 
determine the plant and the measurement equations. 
|. A BIT OF KINEMATICS 
We know from elementery kinematics that the 
motions of the points of a moving rigid body 
are conveniently described by a six-dimensio- 
nal entity called a screw, which is defind at 
every point p of space and noted S(P)= 
(Q,V (P)). Q is called the angular velocity, 
and V (P) is the velocity of the point of the 
solid in motion coinciding with P. The 
kinematic screw at one point entirely describes 
the motion of the solid since, at every point 
M, the velocity of the point of the solid 
coinciding with M is given by 
V(M)=V(P) +9 A PM (1) 
Letting P be at the origin O of our coordinate 
system ,we write V(P)=V ,0M=M,V (M)= 
M and rewrite equation (1) as 
M=V—9NM (2) 
If we assume that V and © are known 
functions of time ,then equation (2) appears as 
a first-order linear differential equation in M. 
No closed form solution ,in general ,exists for 
this equation ,except when © is not a function 
of time (motion with constant angular 
velocity), in which case the solution is given 
by 
M (t) =e“ WM (ty) + [ e®-98V (s)d s (3) 
% 
where © is the antisymmetric matrix 
representing the cross-product with Q(Qz-9 
  
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