A Microstructure-Based Approach to Calculate Boltzmann Entropy for Measuring the Information Content of Multispectral Remote Sensing Images

The spatial structure of multispectral remote sensing images (MRSI) constitutes a fundamental component of the geospatial data. Recently, Boltzmann entropy has been introduced into the measurement of spatial information of MRSI, which has proven effective in capturing the composition and configuration of MRSI. However, the existing Boltzmann entropy calculation approach does not account for information redundancy caused by image noise and spatial correlation. This results in the spatial information content of MRSI being imprecise and incomplete. Thus, a new approach to calculate Boltzmann entropy based on image texture features is proposed in this paper, which adds redundancy and noise-reduction mechanisms. Specifically, this novel approach extracts the texture features of the MRSI using the Local Binary Patterns (LBP) operator, and then the macrostate is defined as an abstract representation of the original microstructure, such as edges, corners, flat areas, spots, and noise. The microstates originate from the uncertainty of the grayscale value due to spectral mixing between neighboring units. Three experiments demonstrate that the proposed Boltzmann entropy calculation approach can effectively capture the disorder of the spatial structure of MRSI and satisfy the requirement for thermodynamic consistency. Furthermore, it can reduce the information redundancy caused by the spatial correlation of the image neighborhood and mitigate the effect of noise on the image information content. Consequently, this approach addresses a limitation of the existing Boltzmann entropy, providing a novel metric for the spatial information measurement of MRSI.