Another obvious way to find useful data in the samples might be to try a pattern-matching approach at a very low level; by simply dividing the sign into a fixed number of equally sized segments, find the average value of attributes such as the x, y and z positions, rotation value and finger positions over all the frames in that segment.
Mathematically, we can express this in the following way. For the
moment, consider only the average value of the x position. Let 
be
the x position in the ith segment, and let d be the number of
segments we want to divide the sign into. The the value of 
is given
by:
where n is the number of frames and
This segments a set of frames into d sets, and we take the average of x position over the range of values we accepted. Graphically, it is much easier to see what is happening.
Figure 5.6: Original data and time-division approximation. Note
the clarity of the time-division approximation -- it also manages to
reduce the effects of noise.
.
Effectively, what this does is reduce the data on the motion into a form more easily amenable to learning. It reduces the data to fixed size, and at the same time averages the data, resulting in smoothing.
Thus you end up with a rough approximation of the ``shape'' of the sign. In figure 5.6 we can see an example of this being applied to the x, y and z positions. In this case, we are using a 5-segment division. Also note how much ``cleaner'' the signal is -- how much more characteristic of the sign it is, and that it is relatively free of noise. We can of course, do similar things for the rest of the variables.
Note also that because a fixed number of intervals are taken, it is relatively invariant to how long it takes to make a sign, provided that the relative timing is similar.
This also remedies one of the problems discovered with the histogram technique, when observing the type of errors made using histograms. Because the information in the histogram was not connected at all with time, signs that had the same ``sub-gestures'' but in a different order would have similar histograms. Most significantly, there are a number of signs that are the ``reverse'' of each other which were frequently confused. For example, want and don't want -- want the flat palm pointing to the chest is moved down the chest, and in don't want it is moved up the chest. These two signs would have similar histograms. By using some information gathered in time, it becomes easy to distinguish these two.
Time division was applied to the x, y and z position as well as wrist roll and finger flexure.
The same issue arises as did with the histograms as far as optimisation is concerned: what is the most generally optimal size for the number of segments to make?
Again, this cannot be determined theoretically easily and is a balance of the factors of sufficient characterisation of the sign while balancing noise and resolution.