Stream Set

At times, it might be convenient to talk about a set of streams - for example, Table 2.1 lists several streams. For the sign language domain, there may be many sign samples that have been collected. However, it's important that these sets have streams that are of the same ``type''.

Let $\mathit{SS}$ be a set of streams of the same type. Having the same type can be defined as follows:

Let $S_a = [c_{a1}, c_{a2}, ..., c_{an}]$ and $S_b = [c_{b1}, c_{b2}, ..., c_{bn}]$. Then

$$\mathit{SameType}(S_a, S_b) \equiv c_{ai} = c_{bi}\ \mathrm{s.t.}\ \forall i : 1 \leq i \leq n$$

So the stream set $\mathit{SS}$ is one with the property that:

$$\forall S_i, S_j \in \ensuremath{\mathit{SS}}\ \ :\ \mathit{SameType}(S_i, S_j)$$

In other words, the range of each channel is the same for each element of $\mathit{SS}$. Note that the domain of the streams is not necessarily the same; in other words the streams may be of different lengths or ``duration'' - the above imposes limits on the types of the channels, but not on the number of frames.