extended) and also the maximum pixel 
value at 4.37 sec. mean that the knee is 
farthest in front of the head (the knee 
is most retracted). 
The pixel distance from its value at 4.33 
seconds to that at 4.37 seconds is large. 
The large displacement of the right knee 
means that its velocity, kinetic energy 
and impulsive force are all large. Carl 
has large impulsive force for subsequent 
movement in running, so he has great 
thrust(ground reaction force). 
It can also be said that the flexed leg 
links the moment of inertia to increase 
the angular velocity of the swinging 
thigh. Rapid leg retraction at the . knee 
appears to control the thigh movement, 
feedback and 
feedforward. These results which are 
which is based on 
obtained in this study are useful not 
only Sports dynamics but also for 
biomechanical analysis of human movement. 
4. Orientation 
Each image has not any control point 
except white straight line of the running 
course. Camera angle and focal length 
are always changing. To orient these 
images, it's necessary special idea. 
White track lines are very noisy for the 
image enhancement. In the case of 
orientation, however, these white lines 
give useful information. For example, 
Fig.9 1s an image at the goal. X and Y- 
coordinates can be estimated by crossing 
points of track line because of the width 
of each track line and each line section 
are given. Here, orientation becomes two- 
dimensional projective transformation as 
follows. 
b4x*bo5y*ba 
X= 
b7x+bgy+1 
(1) 
byx+bzY+bg 
Y= 
b7x*bgy*1 
        
      
        
      
    
    
    
      
      
      
      
      
      
     
   
   
     
    
     
    
    
  
   
  
  
   
    
      
   
    
   
    
   
   
   
   
   
   
   
   
  
  
   
  
  
   
    
  
  
  
  
Fig.9 Image of Neighborhood Goal 
Eight unknown parameters in Equ.(1) are 
estimated more than four control point by 
the least 
collinearity equation can be rewritten as 
square solution. The 
follows, 
X= [(a441(Z-Z9)*843X9)x*(a91(Z-Z9) * 
a23Xoly- (a341(2-293*a33X9 Ef] 
b oi gictidagy ia39f) 
(2) 
Y= [{a12(Z-Zg)+aj3Yo})x+{a22(Z-Zg)+ 
a33Yoy-7(a323(2-29) ta33Yo Mf ] 
Pin qat day age) 
In Equ.(2) ajj are elements of rotation 
matrix of coefficients with omega-phi- 
kappa. Xo » Yo » 2o are camera position and 
f 1s focal length. Focal length is 
Equ.(2) and 
approximate value of focal length is 
needed to solve the 
estimated by the relationship between the 
length of goal line on the image and 
actual length. Comparing the right-hand 
sides of Equ.(1) and. Equ.(2); exterior 
orientation parameters are calculated by 
using b4-bg. 
Considering that the video camera is 
fixed from start to end in spite of 
rotation angles always changing, camera 
position for all images can be determined 
from the above equation. Although there 
are four unknown parameters (omega phi 
kappa and focal length) for the each 
image. Focal length can be estimated by 
utilizing the width of track line. Except