Thermodynamics-Based Evaluation of Various Improved Shannon Entropies for Configurational Information of Gray-Level Images

Abstract

Abstract:The quality of an image affects its utility and image quality assessment has been a hot research topic for many years. One widely used measure for image quality assessment is Shannon entropy, which has a well-established information-theoretic basis. The value of this entropy can be interpreted as the amount of information. However, Shannon entropy is badly adapted to information measurement in images, because it captures only the compositional information of an image and ignores the configurational aspect. To fix this problem, improved Shannon entropies have been actively proposed in the last few decades, but a thorough evaluation of their performance is still lacking. This study presents such an evaluation, involving twenty-three improved Shannon entropies based on various tools such as gray-level co-occurrence matrices and local binary patterns. For the evaluation, we proposed: (a) a strategy to generate testing (gray-level) images by simulating the mixing of ideal gases in thermodynamics; (b) three criteria consisting of validity, reliability, and ability to capture configurational disorder; and (c) three measures to assess the fulfillment of each criterion. The evaluation results show only the improved entropies based on local binary patterns are invalid for use in quantifying the configurational information of images, and the best variant of Shannon entropy in terms of reliability and ability is the one based on the average distance between same/different-value pixels. These conclusions are theoretically important in setting a direction for the future research on improving entropy and are practically useful in selecting an effective entropy for various image processing applications.

Spatial Heterogeneity Analysis: Introducing a New Form of Spatial Entropy

“…However, as [ 3 ] pointed out, there is an array of landscape indices proposed to measure the configurational characteristics of landscape patterns. Fortunately, several literatures (for instance, [ 33 , 34 ]) have presented a critical view of the effectiveness of these configurational metrics. According to the results of these recent studies, we choose two other similar entropy-related metrics (spatial entropy, referred to as H sc , proposed by Claramunt [ 21 ]; interspersion and juxtaposition index, referred to as IJI, as proposed by McGarigal and Marks [ 35 ]) for a comparative purpose.…”

“…The fundamental idea behind the simulation strategy is to create a series of increasingly configurational disordered patterns, and then to examine whether these metrics capture the increasing disorder or not [ 25 ]. In order to obtain a sequence of such landscapes, we followed the discussion by [ 3 , 34 ], the mixtures of ideal gases in thermodynamics revisited (see Figure 2 ). The salient characteristic of gaseous mixtures is that, as [ 37 ] noted, during the mixing process, the disorder of the system increases logarithmically until the system reaches its thermodynamics equilibrium, i.e., the maximum degree of disorder.…”

“…Similar to the process of gaseous mixtures, a set of increasingly configurational disordered patterns can be generated (see [ 34 ], and the simulation strategy is presented in Appendix B ). Figure 3 shows twenty-four different landscape configurations at a dimensionality of 6 × 6 cells with three classes and the same proportion of each class.…”

“…Furthermore, a statistical test (regression analysis) is applied to evaluate the validation of all three metrics, that is to say, whether their values of these different landscape configurations present a valid logarithmic trend [ 37 ]. In this study, the coefficient of determination ( ) values of the regression model are used to verify the goodness of fit, and if is greater than a half, then the regression model can usually be regarded as a good fit [ 34 , 38 ].…”

Calculating the Wasserstein Metric-Based Boltzmann Entropy of a Landscape Mosaic

“…To the best of our knowledge, there are two solutions to this limitation of Shannon entropy. The first is to improve Shannon entropy, and many improved forms of Shannon entropy have been proposed in the last few decades, e.g., [29][30][31]; see a recent review published by this journal [32]. Although most of the improved forms of Shannon entropy are valid means of quantifying configurational information, there is no definite correlation between Shannon entropy and thermodynamics [33][34][35].…”