Efficient Approach for Computing the Discrimination Ratio-Based Variant of Information Entropy for Image Processing

Information content is an important criterion for many image processing algorithms such as band selection and image fusion. Usually, information content is quantified by using information entropy (i.e., Shannon entropy); however, this is not a suitable measure because information entropy is independent of the spatial distribution of image pixels. Thus, improved information entropies and variants of information entropy have been developed. Among all the entropic measures, the discrimination ratio-based variant of information entropy (hereinafter DVIE) has recently been demonstrated to be the most effective. On the other hand, DVIE is the most inefficient measure in terms of computation time, which severely restricts its applications. To solve this problem, we present a three-strategy approach to efficiently compute the DVIE of an image. The first strategy is to use a simplified equation for DVIE. The second strategy is to selectively compute the two computationally intensive components of DVIE - intra-distance and extra-distance - based on the computational complexity. Only one distance was computed, and the other distance was derived based on the lookup table of average distances. The third strategy was to efficiently construct the lookup table based on geometric symmetry. We performed both validation and evaluation experiments to demonstrate that the proposed approach was not only valid for accurately computing DVIE, but it was also highly efficient. Our proposed approach saved more than 99% of the time taken for the original approach, without compromising the accuracy; therefore, DVIE was made applicable for processing images.