Band selection for hyperspectral images helps improve the efficiency of data processing and even the accuracy of classification. It is to reduce the dimensionality of a hyperspectral image by selecting representative bands. In such a process, the quantification of band similarity is the fundamental issue, and it is usually achieved by using an information-theoretic measure, such as mutual information or relative entropy. However, these measures are incapable of quantifying similarity in terms of both composition and configuration. To solve this problem, the Boltzmann entropy (BE), which captures both configurational and compositional information, is employed in this letter. More precisely, the difference in BE between two bands is used for such quantification. The corresponding search strategy is designed for band selection. Experimental evaluation was carried out using remote sensing images for classification. The results clearly demonstrate the superiority of the proposed band selection method over traditional information-theoretic methods: an increase of up to 27% in classification accuracy was observed when using the difference in relative BE with 20 selected bands. In addition, another comparison with some state-of-the-art methods was conducted. The results show that the proposed method is still very competitive; it outperformed all the others when the number of selected bands ranges from 18 to 23. This letter, the first of its kind, reveals that the BE may form a new base for information-theoretic approaches to image processing and even for spatial information science in a broad sense.

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.