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Abstract. Images with large volumes are generated daily with the advent of advanced sensors and platforms (e.g., satellite, unmanned autonomous vehicle) of data acquisition. This incurs issues on the storage, processing, and transmission of images. To address such issues, image compression is essential and can be achieved by lossy and/or lossless approaches. With lossy compression, a high compression ratio can usually be achieved but the original data can never be completely recovered. On the other hand, with lossless compression, the original information is well reserved. Lossless compression is very desirable in many applications such as remote sensing, geological surveying. Shannon's source coding theorem has defined the theoretical limits of compression ratio. However, some researchers have discovered that some compression techniques have achieved a compression ratio that is higher than the theoretical limits. Then, two questions naturally arise, i.e., “When this happens?” and “Why this happens?”. This study is dedicated to giving answers to these two questions. Six algorithms are used to compress 1650 images with different complexities. The experimental results show that the generally acknowledged Shannon’s coding theorem is still good enough for predicting compression ratio by the algorithms with consideration of statistical information only, but not capable of predicting compression ratio by the algorithms with consideration of configurational information of pixels. Overall, this study indicates that new empirical (or theoretical) models for predicting lossless compression ratio can be built with metrics capturing configurational information.

Abstract. Map is an effective communication means. It carries and transmits spatial information about spatial objects and phenomena, from map makers to map users. Therefore, cartography can be regarded as a communication system. Efforts has been made on the application of Shannon Information theory developed in digital communication to cartography to establish an information theory of cartography, or simply cartographic information theory (or map information theory). There was a boom during the period from later 1960s to early 1980s. Since later 1980s, researcher have almost given up the dream of establishing the information theory of cartography because they met a bottleneck problem. That is, Shannon entropy is only able to characterize the statistical information of map symbols but not capable of characterizing the spatial configuration (patterns) of map symbols. Fortunately, break-through has been made, i.e. the building of entropy models for metric and thematic information as well as a feasible computational model for Boltzmann entropy. This paper will review the evolutional processes, examine the bottleneck problems and the solutions, and finally propose a framework for the information theory of cartography. It is expected that such a theory will become the most fundamental theory of cartography in the big data era.