Efficient approach for computing the discrimination ratio-based variant of information entropy for image processing

Abstract

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.

Entropy in Landscape Ecology: A Quantitative Textual Multivariate Review

“…For example, Leopold and Langbein [2] presented the "concept of entropy in landscape evolution", and proposed that landscapes evolve toward maximization of entropy, measured by the most probable condition of the landscape with regard to the distribution of matter and energy, and proposed a series of equations to measure and predict this in hydrological systems. This focus on landscape evolution and maximization of entropy has been rekindled in recent research on calculating Boltzmann configurational entropy of landscapes (e.g., [14,15,17,22]), but this new focus is best seen as the continuation of an older line of work on entropy in ecology, which formally focused on thermodynamic and structural aspects of ecosystems and landscapes.…”

“…Cushman [7] further demonstrated the generality of this method and its practical application to large landscapes with many patch types. This inspired a number of recent papers evaluating different measures of landscape configurational entropy [16][17][18][19][20][21][22].…”

“…Despite recent interest in landscape entropy (e.g., [7,[14][15][16][17][18][19][20][21][22][23]), including recent review papers (e.g., [13,18]) there has not yet been a comprehensive, quantitative review of a broad and representative sampling of the literature addressing entropy issues in ecology. Such a broad review using objective and quantitative methods would be very useful to understand the scope of work, its evolution and areas of focus and recent innovation.…”

Union of Class-Dependent Collaborative Representation Based on Maximum Margin Projection for Hyperspectral Imagery Classification

“…Specifically, band selection preserves the most discriminative bands while discarding some redundant and noisy bands to reduce the band number [26][27][28][29][30][31][32]. The classical methods such as maximum variance principal component analysis (MVPCA) [26], constrained band selection (CBS) [27], entropy-based [28][29][30], and evolution-based band selection [31] have been shown to be effective. Recently, a Boltzmann entropy-based band selection was developed, which can characterize both statistical information of HSI and spatial distribution of pixels [29].…”

“…Recently, a Boltzmann entropy-based band selection was developed, which can characterize both statistical information of HSI and spatial distribution of pixels [29]. Moreover, a band selection method based on a variant of entropy has also proved efficient [30]. As a limitation, the band subsets selected by most of these traditional band selection techniques are not enough to describe the discriminants for different types of classes to some extent [32].…”