Can we quantify the relationship between multispectral remote sensing images and land use and land cover maps? An explicit information transfer model based on Boltzmann entropy

Multispectral remote sensing images (MRSI) contain rich information about geographical objects and phenomena, such as land use and land cover. To extract such information, classification is normally carried out to yield land use and land cover maps (LULCM). A lot of techniques have been developed for classification, yet such a fundamental problem has not been solved as mathematical models for predicting the upper and lower limits of land cover classification accuracy with a given MRSI. This study aims to tackle this key problem by considering classification as an explicit information transfer process from images to maps and then build a mathematical model (Boltzmann-entropy-based) for the process with Shannon’s information theory and Crooks’ Thermodynamic Fluctuation as theoretical foundation. The model is designed to predict both upper and lower limits of classification accuracy instead of a definite value and is expressed in terms of Boltzmann entropies of MRSI and LULCM, total number of classes, and two basic parameters defined by prior knowledge. Verification experiments are carried out with 1091 images and three well-established classifiers (support vector machine, random forests, and K-nearest neighbors). The results demonstrate that (i) the values of information in MRSI and LULCM are strongly correlated, and (ii) the Boltzmann-entropy-based model can predict both upper and lower limits of classification accuracy. This study provides a novel perspective for understanding land cover classification and opens the door for the establishment of new theories in remote sensing.