(0 DD <A DON OO 0 
collected from image processing, i.e measured edges. 
These noisy measurement values are filtered according 
to the presently supposed set of state variables. It is 
distinguished between the rigid motion of the overall 
figure (inertial 3-D pose), its geometic properties (3-D 
shape), and the movement of the articulated body 
(multiple limb motion). Individual estimators are in 
operation simultanously for determining the best 
fitting state variables belonging to these three classes; 
all together maintain geometric coherence of the 
semi-independent partial volume models, and 
temporal coherence of motion and movement 
variables. So, in a deductive step expected edge 
roperties derived from an instantiated generic model 
having become a specific model for a time instant) are 
used to direct the image measurement process and to 
assess measurement quality. 
The essential information that the models are to 
deliver constists of the motion states in all joints (joint 
angles) in order to solve the pattern recognition task. 
The figure movement is regarded as fully recoverabic 
from theses state variables as psychological recognition 
experiments [Johansson 73] show that joint positions 
traced over time are sufficient for that purpose. 
To follow one exemplary estimation cycle in discrete 
time (see figure 8), one set of knee state varibles, 
flexion angle and angular velocity, is propagated from 
time instance k to k +1 through the following transition 
equation (prediction block in figure 8) 
6 cosor sinor/o | (0 (5) 
ô k+1  \ —osinwt COSwT Ö k 
where w is the cycle frequency and 7 the sample time. 
This transition matrix is well suited to predict cyclic 
changes. Accepting other state variables to be valid 
that influence the image features (here: shank skeleton 
0.5 
  
pelvis angle (in rad) 
  
  
  
  
time (in sec.) 
Fig. 9: Curves of estimated pelvis and knee angles 
    
    
    
   
    
   
     
   
    
   
    
    
       
    
   
    
line segment properties), an approximate perspective 
mapping equation for edge orientation for the shank, 
B = arctan [S sin(pr) ZEN (6) 
cos(0p --Ok) 
is applied, with Ky ,K; camera parameters, 9r, Op , Ok 
jaw angle of whole figure, flexion relativ angles in 
pelvis and knee joints, respectively. 
Figure orientation is expected to be greater than 0 deg. 
in this case (90 deg. is walking direction perpendicular 
to the viewer). When deviations to the real values 
increase considerably due to decrease of figure 
orientation from 90 deg. the knee angles are not 
observable any more and no innovation takes place. 
Provided that corresponding image features are found, 
mapped edes and measured edge are compared and 
the internal model is adjusted. After application of 
constraints which check whether the recent values are 
reasonable or not, ie. whether they are within the 
physiologically possible ranges or are consistent with 
movement semantics, the next estimation cycle begins. 
Figure 9 shows curves of estimated pelvis and knee 
flexion angies recovered from the same animation 
sequence (broken lines) against the reference values. 
The pelvis estimates Tippee the true values about 
one cycle in advance. The knee angles have not been 
limited to the 0°-level here. The estimation is robust 
also when invalid measurement values fail to up-date 
the state estimates, e.g. in the interval from 2.64 - 3.12 
sec. for the knee angle. All curves quickly converge 
towards their true values in the beginning. 
  
knee angle (in rad) 
  
  
  
-0.7 
time (in sec.)