(2a) 
(2b) 
(2c) 
T5). 
; Ts 
and 
Le. 
(c), 
(3a) 
(3b) 
(3c) 
(3d) 
(3e) 
  
  
  
  
Fig.6: Leg skeleton geometry 
SL = const (3f) 
Oo = const (3g) 
with 7,11, /2, d, sr, length of whole leg, thigh, shank, 
foot and step length, « angle between foot and the 
horizontal, and G9, ®o, Vo angles at the beginning of 
swing phase (see figure 6). 
The double support phase is modelled by extrapolation 
of the swing phase E KR in the direction of the 
negative time axis and linearly incrementing the anole 
between ground and toeing-off foot during double 
support time. By varying mechanical constants or 
modifying the boundary conditions - where applicable 
- different gait patterns can be produced. 
Although oh effort has gone into biomechanical 
analyses [Schmid-Schónbein 86, Baumann 86] and 
dynamic gait descriptions are applied widely in the 
field of computer animation [Bruderlin 89, Wilhelms 
87] and also in robotics, particularly in designing 
walking machines [Miura 84], fully kinetic modelling of 
figure movements continues to become rapidly 
complicated. Numerous material parameters, external 
and reactive forces constraining the possiblz 
movement range are to be assessed. In fact, the 
difficulty of movement definition is shifted to a wise 
choice of generalized forces the knowledge of which is 
sparse. 
Therefore, a second method, the procedural 
description of movements, is implemented mainly for 
waving arms in a simple manner. For upper limb 
animation, generator functions produce joint angle 
curves of sinusoidal and triangular shapes. In addition 
the leg movement of a cyclist riding a bike has been 
modelled employing inverse kinematics equations. The 
movements of this method appear less sophisticated 
but are realistic enough to serve their purposes. 
In order to unify all limb and body movements and to 
be able to switch smoothly between single movement 
patens a third approach utilizes fairly popular 
ey-frame interpolation technique together with 
cinematographic movement studies [Muybridge 55]. 
Here, a movement paitern is defined by designing a set 
of n body poses 
S(x) = [$o,51, ... ‚Sn-1} withx € [xo ‚xn]. (4a) 
Using the Hermite form of cubic parametric splines 
(as a piecewise approximation of cubic polynomial 
functions) 
Si(x) = ai + bilx-xi) + cxx) + di(x-—xi)®, (4b) 
an interpolation between joint angle control points is 
performed. For calcuiating ai, bi, ci, d; the control 
point position and either first or second derivatives at 
the two interval boundaries are utilized (from interval 
to interval continuity of theses values is provided). For 
joint movements of the model this means a direct 
definition of angular velocity or acceleraction which 
allows to account for physical boundary conditions in 
the context of movement definition. 
Subsequently, the movement description is factored 
into shape and motion; a separate manipulation of 
positional and time splines according to [Steketee 85] 
gives the user various possibilities to alter the 
movement appearance and to create complicated 
patterns. These also can be blended with partial 
movements generated by both methods described 
above. Figure 7 depicts a typical movement pass 
defined by 9 key-frames. 
3. ANALYSIS 
3.1. Image processing 
For extracting image information edges are the feature 
primitives. They are detected by differential operations 
erformed in limited search areas on a grey scale 
intensity image, alternatively with homogenous 
background or with distracting edges. As edge 
detector one mask out of a set of five individual 
gradient masks - 5x5-picture elements (ict) each - is 
applied in two orthogonal search directions. The 
search paths are a few 10 pixels long yielding several 
correlation extrema in the image area in question. 
As a human figure in motion exhibits a non-rigid shape 
a meaningful local connection of single measurement 
values (in a gestalt-sense of psychology) within a limb 
finder supplies orientation, position, length and 
variance FP a confidence s for straight line 
segment approximations of limb parts. Criteria for 
connecting single data values for a least squares fit are 
their absolute and relative sizes, their standard 
deviation estimated from a correlation function 
discussion, and the relationship with expected line 
properties assumed by the dynamic process model. 
Especially vertical lines as contour elements and 
double edges are searched for. The successful 
operation of the image analysis can be monitored by 
the reconstruction of a stick figure (see figure 7). 
Apart from the two vertical lines, short lines