Computation And Applications Of Boltzmann Entropy For Raster Data

“The vast sky still has many unknown mysteries to be explored,and the comprehensive development of space science,space technology,and space applications must be promoted.”Spatial information is the basis for promoting the development of space science,technology and applications,and its bottleneck lies in the measurement of spatial information.Since the cartographer,Sukhov took the lead in introducing information theory into the field of cartography,spatial information measurement methods have continued to develop and have been widely used in image interpretation,map design,and cartographic generalization.Consequently,a new science,the theory of map information characterized by spatial information measurement,transmission,and application,is booming and has yielded fruitful results.At present,the spatial information measurement method for vector data is relatively mature,and the geometric,topological,and thematic information entropy measurement methods of the map have been proposed.However,the spatial information measurement method for vector data cannot be extended to raster data.The reason is that the grid expresses raster data,and the basic unit size is the same and has a fixed number of neighbours,rather than the point,line,and area map symbol with different sizes and many adjacent relationships.Toward these problems,this paper aims to propose a series of spatial Boltzmann entropy optimization algorithms and variant indicators and use them in the fields of urban expansion and remote sensing image interpretation.This thesis first systematically reviews the research status of spatial Boltzmann entropy,then evaluates the thermodynamic consistency of Boltzmann entropy indicators for categorical raster data(e.g.,landscape mosaic),including the generation of evaluation data,determination of evaluation criteria,standards,and indicators.To improve Boltzmann entropy computation efficiency,we designed and implemented an absolute Boltzmann entropy approximation algorithm using head/tail break.Further,we proposed an aggregation-based approximation algorithm for raster data with strong homogeneity.Considering the influence of the continuity characteriztics of raster data on the computation results of Boltzmann entropy,the landscape shape index and Wasserstein distance are introduced to construct a variant of Boltzmann entropy that takes into account morphology and repeated information,and we evaluated its effectiveness.Considering that the definition of adjacency relationship affects continuous area recognition,the Wassersteinbased Boltzmann entropy under four neighbourhoods is extended to eight neighbourhoods,and it is used for optimal bands selection.Results demonstrated that Wasserstein-based Boltzmann entropy under four neighbourhoods and eight neighbourhoods could be used to determine the optimal bands,and the latter is better than the former.Subsequently,the variant of Boltzmann entropy is introduced into the analysis of urban land-use change to identify urban development patterns and expansion methods.Finally,this paper develops software for computing Boltzmann entropy of raster data.This software includes data import,selection of different indicators to compute Boltzmann entropy,and calculation result processing functions.