面向栅格数据空间信息测度的玻尔兹曼熵研究

The fundamental importance of spatial (or geographical) information theory has been recognized for many years. This theory has been highlighted as the core of the geographical information science defined by Goodchild in 1992. It was also the theme of a famous conference—International Conference on Spatial Information Theory (COSIT)—which has been held biennially since 1993...In spatial information theory, however, there is a basic scientific question that still requires an answer: How to measure spatial information? (or specifically, how to measure the information of a spatial dataset?) This question has been expected to be answered by information theory, which has been established as early as 1948, but it remains until this very day. The problem is that the measure of information—Shannon entropy—is capable of measuring only statistical information, rather than spatial information. Considerable efforts have been made to solve this problem. The result is as follows. For vector data, Shannon entropy has been improved to be a suitable measure of spatial information. For raster data, however, Shannon entropy is found to be not effective...Instead of adopting Shannon entropy, this project aims to measure the spatial information of raster data using Boltzmann entropy. The concept of Boltzmann entropy was proposed by the Austrian physicist Ludwig Eduard Boltzmann in 1872. It is the conceptual model of disorder and a theoretically sound measure of spatial information. Its computation has been a problem for one and a half centuries, but some developments have been achieved recently in landscape ecology. Inspired by these developments, this project intends to introduce Boltzmann entropy to spatial information theory. Specifically, this project has three objectives: to develop a computational model of Boltzmann entropy for measuring the spatial information of raster data, to develop efficient algorithms for computing Boltzmann entropy, and to apply Boltzmann entropy to the processing of spatial data...The successful completion of this project will provide new insight into the development of spatial information theory. Based on Boltzmann entropy, a series of methods can be developed for geospatial processing in the future.

从1992年Goodchild提出“地理信息科学”概念开始，地理（或空间）信息的理论研究便被赋予了新的使命和广泛重视。1993年起，空间信息理论国际会议在欧洲创办、延续至今、影响巨大。然而时至今日，依然有基础理论问题未能充分回答：如何测度空间信息？这一问题本应从信息论中得到解答，但信息论的核心——香农熵——并不适用于空间信息的测度。在后续大量的研究中，面向矢量数据的空间信息测度已突破，但面向栅格的测度遇到瓶颈。受生态学界近来研究计算玻尔兹曼熵（玻熵）的启发，本项目提出尝试从香农熵重返其热力学中的概念模型玻熵，利用玻熵测度栅格数据的空间信息。理论上，玻熵具备全面刻画无序、完整测度空间信息的潜力，但其计算是从1872年诞生以来的难点。项目设置层次递进的三项研究内容：面向栅格数据空间信息测度的玻熵计算模型、高效算法、应用示范。项目的成功执行预期将为地理/空间信息科学的理论与方法建设提供新视角。

从1992年Goodchild提出“地理信息科学”概念开始，地理（或空间）信息的理论研究便被赋予了新的使命和广泛重视。1993年起，空间信息理论国际会议在欧洲创办、延续至今、影响巨大。然而时至今日，依然有基础理论问题未能充分回答：如何测度空间信息？这一问题本应从信息论中得到解答，但信息论的核心（即信息熵、又称香农熵）并不适用于空间信息的测度。在后续大量的研究中，面向矢量数据的空间信息测度已突破，但面向栅格的测度遇到瓶颈。受生态学界近来研究计算热力学熵（又称玻尔兹曼熵）的启发，本项目提出尝试从信息熵重返其概念模型——热力学熵，利用热力学熵测度栅格数据的空间信息。理论上，热力学熵具备全面刻画无序、完整测度空间信息的潜力，但其计算是从1872年诞生以来的难点。项目设置层次递进的三项研究内容：面向栅格数据空间信息测度的热力学熵计算模型、高效算法、遥感图像处理应用示范。项目已圆满完成所有研究任务。所提出的热力学熵在国际上被命名为“The Gao Method”。