Bardera2009

CREATED: 200906170311 Optimal thresholding = segmentation with maximum structure = maximum excess entropy

Adaptive thresholding method based on maximization of excess entropy

Use of uniformly distributed lines to overcome the main drawbacks of the excess entropy computation

Given a chain of random variables, the entropy of a block of L consecutive random variables \[H(X^L) = - \sum p(x^L) \lg p(x^L)\]

The entropy rate is \[h = \lim_{L \rightarrow \infty} H(X^L)/L = \lim_{L \rightarrow \infty} h(L)\] where \[h(L) = H(X^L) - H(X^{L-1})\]

The entropy rate <= Shannon entropy, equal when there is no correlation between consecutive symbols

The excess entropy [[Crutchfield1983]] is a measure of the structure of a system. \[E = \sum_{L=1}^{\infty} h(L) - h = \lim_{L \rightarrow \infty} H(X^L) - hL\] captures how h(L) converges to its asymptotic value h.