Abstract
The entropy of shortest distance (ESD) between geographic elements (“elliptical intrusions”, “lineaments”, “points”) on a map, or between "vugs", "fractures" and "pores" in the macro- or microscopic images of triple porosity naturally fractured vuggy carbonates provides a powerful new tool for the digital processing, analysis, classification and space/time distribution prognostic of mineral resources as well as the void space in carbonates, and in other rocks. The procedure is applicable at all scales, from outcrop photos, FMI, UBI, USI (geophysical imaging techniques) to micrographs, as we shall illustrate through some examples. Out of the possible applications of the ESD concept, we discuss in details the sliding window entropy filtering for nonlinear pore boundary enhancement, and propose this procedure as unbiased thresholding technique.
Highlights
In the early years of Information Theory, Good ([1,2], see [3,4]) introduced the influential “how to keep the forecaster honest” paradigm, that is how to design a payoff system which would force the forecaster to give an unbiased prediction
In the spirit of the "entropy of shortest distance" we expect that if the distances of the dots from the nearest lines are very randomly distributed, with large entropy, there is no valid relation between the two sets of objects
I 1 (the upper bound of entropy in Equation (5c) has a similar scaling) both our entropy of shortest distance (ESD) measures are scale free, as for example the entropy map in Figure 9 only depends on the image in Figure 8 and not on its scale
Summary
In the early years of Information Theory, Good ([1,2], see [3,4]) introduced the influential “how to keep the forecaster honest” paradigm, that is how to design a payoff system which would force the forecaster to give an unbiased prediction. Much later (in 1972 [5]) it was proved mathematically that the only way to do this is intimately connected with the concept of Shannon entropy
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
