for the angle 
or the so called any--time behavior.
The later one will be discussed in the following. The term
``any--time'' describes the possibility to get a result from
the algorithm at any--time;
the accuracy and quality of the result will increase over time. For real--time
tracking applications, this means, that one can switch dynamically
from tracking one object very accurately to synchronously tracking more
than one object with a reduced accuracy, and vice versa. The any--time
behavior guarantees, that for both task the same time is needed.
The representation of active rays allows for such an dynamically increasing
representation accuracy of the contour. After an initialization step
for each iteration we can get a more accurate contour. But we also
might stop because after the initialization step we already have
a representation of the contour. This representation increases in
accuracy for each iteration. If there is only a small amount of time,
for example for fast moving objects or the synchronously tracking of
several objects, we can stop the iterative procedure after a few
iteration steps. If there is more time we can increase the iteration
steps and get a more accurate contour representation. Finally, this
procedure might be steered by the distance of the contour elements to
neighboring contour elements.
If the distance between neighboring contour elements
corresponding to 
and 
is large, then is would be
useful to add one extra ray between the angles 
and 
to get a better approximation of the contour between the
angles 
and 
. The algorithm is summarized in
4.
Figure 4: Any--time algorithm for contour extraction