Frame

Consider once again Figure 2.1. A channel is a ``horizontal'' cut through the data; and a stream is the name for whole object, but at times it is useful to talk of a vertical cut through the data; in essence to talk about the data on all channels at a particular point in time. For example, one might talk about time $t=29$ and ask what are the values of each of the channels at that time. This is exactly what a frame is. For a given stream $S = [c_1, c_2, ..., c_n]$, the function $\mathit{fr}$ is defined as:

$$\mathit{fr}: \mathrm{domain}(c_1) \rightarrow \mathrm{range}(c_1) \times \mathrm{range}(c_2) \times ... \times \mathrm{range}(c_n)$$

$$\mathit{fr}(t) = \langle c_1(t), c_2(t), ..., c_n(t) \rangle$$

Intuitively, a frame represents a ``slice'' of each of the channels at a given point in time. It represents the values of each of a channel for a given time $t$.

Note that in the above, the domain of $c_1$ is used, but any other $c_i$ would do.

The connection between channels, frames and streams is illustrated in Figure 2.2. In this diagram, we have three channels $\alpha$, $\beta$ and $\gamma$, with the range of the first two being the real numbers, and the range of the last being $\{r,g,b\}$. The stream consists of these three channels together. The ``length'' of the stream is 24 time-slices; in other words it consists of 24 frames. Each frame has three channels, and the domain of the function $\mathit{fr}$ in this case is $[0..23]$.