Image Processing Reference
In-Depth Information
3.2 Comparison to single-scale metric
The same inputs as that for the Context-Switching Metric described earlier result in the
following Figure 6 . Note that in this case as well, the sample entropy is always higher for the
disordered signal than for the ordered signal. The reference 1/f noise level is shown on the
plot to indicate the asymptotic maximum entropy level achievable.
Multiscale Entropy
disordered
ordered
2
1.8
1/f noise
level
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
5
10
15
20
Scale Factor
Fig. 6. For the same pair of inputs we used on the context-switching metric, the multiscale
entropy appears as the following graph. It shows greater variety than the context-switching
metric over the time scales because the metric compares at different levels of resolution.
In practice, the multi-scale algorithm requires only a basic periodogram method invoked
over different time scales. The output is one value per temporal scale factor so the results are
best displayed as a graph, via a spreadsheet or bar-charting software for example. The
calculation is somewhat more brute force compared to the FFT, with complexity o(n 2 ) versus
o(n*ln(n)). The context-switching metric operates over a narrower time scale so gets rolled
into a single value, simplifying the presentation into a classical scalar metric.
4. Discussion
Interacting concurrent activities can produce behaviour that is difficult to anticipate. The
combinatorial capacities of just the ordering of parallel thread execution will exhaust any
brute force attempt at testing the possible permutations. Moreover, the possibilities of rare
anomalies attributed to corner cases of executions may take non-determinant times to
reveal, or worse, are not easily repeatable. The sporadic defect that occurs rarely in the lab
usually has a real origin and should never be ignored (Kuhn, et al, 2004).
The figure below shows a representative timeline trace of the interacting subsystems on a
typical automated ground vehicle. The task interactions are interleaved and pipelined.
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