Image Processing Reference
In-Depth Information
The utility of the frequency domain approach is apparent when we consider that the frequency
domain is partitioned into FFT bins and we have a very fast way of computing the metric, and
in many cases more convenient than by calculating the autocorrelation, or by traditional
periodogram (Schuster, 1898). If we did have the extra processing time, it may make sense to
calculate the entropy off the autocorrelation as that would definitely retain more of the
information measure, and thus not losing information due to the transformation process. In
practice, however, many times we want to know only relative entropy measures, so the loss in
precision is not as important as long as we maintain the relative ordering or rank.
As an intuitive interpretation of this measure consider that a value of S near 0 (if < f >
normalized to 1) indicates that the program is very specialized and is only trying to a few
things at once. As S approaches 1 it becomes a general purpose application that attempts to
control many different behaviours or responds to events of a more random nature. If S goes
much greater than 1, then the temporal complexity turns even more random, even
approaching fractal. It becomes progressively harder to test such systems because of the
diverging spread in time scales.
This turns into a useful metric since any sufficiently capable controller program or event-
driven system will try to accommodate as much real-world functionality as possible, and
since the real world tends to disorder and to maximize entropy, this will track an
increasingly complex scenario. So in practice, we will have fast cycles interspersed with
slower cycles corresponding perhaps to human events or sporadic signals.
Fig. 2. Variation of power spectrum with increasing disorder. (a) Ordered signal with
harmonics generates a low entropy signal. (b) Disordered signal generates a larger intropy.
In further practical terms, to apply the metric we need to run a simulation or collect data from
a real or prototype system to gather the statistics. It may be possible to evaluate a program
statically but that would require an introspective analysis of a program's structure, a task
much more involved than collecting the statistics during typical use or as a test scenario.
The possibility of using this approach on non-concurrent programs such as a single-tasking
event-driven program exists but these have less inherent complexity due to their sequential
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