Principle

One simple application of the data calculated above is to sum the above. This would give us a measure of the total distance covered by the sign. This makes sense as a feature, since clearly some signs cover greater distances than others. For example the sign for all, a sign made by moving the palm face down in a large circle in front of the body, covers more distance than a sign like you, which is a short pointing gesture.

Thus we define the feature distance as:

where n is the number of frames in the sample.

Similarly some signs turn out to be more energetic than others, even though the distance covered may be similar. For example, something like all and go have a similar distance covered. However, in go, it's a quick flick of the wrist, and a momentarily faster motion than all -- thus it has more energy.

We cannot get an exact measure of the energy required to make a sign, because there are so many variables involved. Thus we make an approximation, based several assumptions:

• The packets come at equal time intervals. Thus the time between two consecutive frames is constant. This proved to be an empirically reasonable assumption.

• Most of the energy comes from the positional motion. This means that quick finger flicks, and wrist rotation are not included in the energy feature we calculate, although in some signs they can dominate, such as in maybe and flashlight.

• That the ``effective mass'' of the hand is some constant and the energy required to move the hand in all directions is approximately equal.

Using these assumptions, we can derive a measure of the energy. The textbook definition of energy is:

and a discrete approximation of this equation is given by:

Since F = ma and m is a constant, and converting to the naming we have used then we can say:

But and we have assumed that is a constant. Also is synonymous with then we have that:

This energy features, while approximate, should still prove to be useful.

Finally, one feature that is obvious is the number of frames that were taken to make the sign. This is perhaps a very weak attribute, since it is dependant on the way a person started the sign, and observation of the samplers while they were doing a sign indicated wide intra-sign variation. However, it is sometimes a useful attribute for gross differentiation between signs.