They are talking about Shannon's entropy. One way to view entropy is to relate it to the amount of uncertainty about an event associated with a given probability distribution. Entropy can serve as a measure of 'disorder'. As the level of disorder rises, the entropy rises and events become less predictable.
Back to the definition of entropy in the paper:
H(s_m) is the entropy of the random variable s_m. Here is the probability that outcome s_m happens. m are all the possible outcomes. The probability density p_n is calculated using the gray level histogram, that is the reason why the sum runs from 1 to 256. The bins represent possible states.
So what does this mean? In image processing entropy might be used to classify textures, a certain texture might have a certain entropy as certain patterns repeat themselves in approximately certain ways. In the context of the paper low entropy (H(s_m) means low disorder, low variance within the component m. A component with low entropy is more homogenous than a component with high entropy, which they use in combination with the smoothness criterion to classify the components.
Another way of looking at entropy is to view it as the measure of information content. A vector with relatively 'low' entropy is a vector with relatively low information content. It might be [0 1 0 1 1 1 0]. A vector with relatively 'high' entropy is a vector with relatively high information content. It might be [0 242 124 222 149 13].
It's a fascinating and complex subject which really can't be summarised in one post.
answered Nov 17 '16 at 16:39
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