原著論文リスト[A1]: “The final publication is available at Springer via http://dx.doi.org/10.1007/s11075-012-9607-5.”. [A2]: “The final publication is available at Springer via http://dx.doi.org/10.1007/s10092-013-0085-5.”, [A3]: DOI“10.1016/j.camwa.2015.11.022” / 京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第19859号 / 情博第610号 / 新制||情||106(附属図書館) / 32895 / 京都大学大学院情報学研究科数理工学専攻 / (主査)教授 中村 佳正, 教授 矢ｹ崎 一幸, 教授 山下 信雄 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

Automated map generalization is a necessary technique for the construction of multi-scale vector map databases that are crucial components in spatial data infrastructure of cities, provinces, and countries. Nevertheless, this is still a dream because many algorithms for map feature generalization are not parameter-free and therefore need human’s interference. One of the major reasons is that map generalization is a process of spatial similarity transformation in multi-scale map spaces; however, no theory can be found to support such kind of transformation. This thesis focuses on the theory of spatial similarity relations in multi-scale map spaces, aiming at proposing the approaches and models that can be used to automate some relevant algorithms in map generalization. After a systematic review of existing achievements including the definitions and features of similarity in various communities, a classification system of spatial similarity relations, and the calculation models of similarity relations in the communities of psychology, computer science, music, and geography, as well as a number of raster-based approaches for calculating similarity degrees between images, the thesis achieves the following innovative contributions. First, the fundamental issues of spatial similarity relations are explored, i.e. (1) a classification system is proposed that classifies the objects processed by map generalization algorithms into ten categories; (2) the Set Theory-based definitions of similarity, spatial similarity, and spatial similarity relation in multi-scale map spaces are given; (3) mathematical language-based descriptions of the features of spatial similarity relations in multi-scale map spaces are addressed; (4) the factors that affect human’s judgments of spatial similarity relations are proposed, and their weights are also obtained by psychological experiments; and (5) a classification system for spatial similarity relations in multi-scale map spaces is proposed. Second, the models that can calculate spatial similarity degrees for the ten types of objects in multi-scale map spaces are proposed, and their validity is tested by psychological experiments. If a map (or an individual object, or an object group) and its generalized counterpart are given, the models can be used to calculate the spatial similarity degrees between them. Third, the proposed models are used to solve problems in map generalization: (1) ten formulae are constructed that can calculate spatial similarity degrees by map scale changes in map generalization; (2) an approach based on spatial similarity degree is proposed that can determine when to terminate a map generalization system or an algorithm when it is executed to generalize objects on maps, which may fully automate some relevant algorithms and therefore improve the efficiency of map generalization; and (3) an approach is proposed to calculate the distance tolerance of the Douglas-Peucker Algorithm so that the Douglas-Peucker Algorithm may become fully automatic. Nevertheless, the theory and the approaches proposed in this study possess two limitations and needs further exploration. • More experiments should be done to improve the accuracy and adaptability of the proposed models and formulae. The new experiments should select more typical maps and map objects as samples, and find more subjects with different cultural backgrounds. • Whether it is feasible to integrate the ten models/formulae for calculating spatial similarity degrees into an identical model/formula needs further investigation. In addition, it is important to find out the other algorithms, like the Douglas-Peucker Algorithm, that are not parameter-free and closely related to spatial similarity relation, and explore the approaches to calculating the parameters used in these algorithms with the help of the models and formulae proposed in this thesis.

Transformations between different geodetic reference frames are often performed such that first the transformation parameters are determined from control points. If in the first place we do not know which of the numerous transformation models is appropriate then we can set up a multiple hypotheses test. The paper extends the common method of testing transformation parameters for significance, to the case that also constraints for such parameters are tested. This provides more flexibility when setting up such a test. One can formulate a general model with a maximum number of transformation parameters and specialize it by adding constraints to those parameters, which need to be tested. The proper test statistic in a multiple test is shown to be either the extreme normalized or the extreme studentized Lagrange multiplier. They are shown to perform superior to the more intuitive test statistics derived from misclosures. It is shown how model selection by multiple hypotheses testing relates to the use of information criteria like AICc and Mallows’ Cp, which are based on an information theoretic approach. Nevertheless, whenever comparable, the results of an exemplary computation almost coincide.

Transformations between different geodetic reference frames are often performed such that first the transformation parameters are determined from control points. If in the first place we do not know which of the numerous transformation models is appropriate then we can set up a multiple hypotheses test. The paper extends the common method of testing transformation parameters for significance, to the case that also constraints for such parameters are tested. This provides more flexibility when setting up such a test. One can formulate a general model with a maximum number of transformation parameters and specialize it by adding constraints to those parameters, which need to be tested. The proper test statistic in a multiple test is shown to be either the extreme normalized or the extreme studentized Lagrange multiplier. They are shown to perform superior to the more intuitive test statistics derived from misclosures. It is shown how model selection by multiple hypotheses testing relates to the use of information criteria like AICc and Mallows’ Cp, which are based on an information theoretic approach. Nevertheless, whenever comparable, the results of an exemplary computation almost coincide.

Die vorliegende Arbeit befasst sich mit der Fragestellung, inwiefern sich gegebene Verfahren zur Approximation von rationalen Krylow-Räumen zur Berechnung von Matrixfunktionen eignen. Als Modellproblem wird dazu eine 2.5D-Formulierung eines Problems aus der Gleichstrom-Geoelektrik mit finiten Elementen formuliert und dann mittels Matrixfunktionen auf rationalen Krylow-Unterräumen gelöst. Ein weiterer Teil beschäftigt sich mit dem Vergleich zweier Verfahren zur Transformation bestehender rationaler Krylow-Räume. Bei beiden Varianten werden die zugrunde liegenden Pole getauscht ohne dass ein explizites Invertieren von Matrizen notwendig ist. In dieser Arbeit werden die über mehrere Publikationen verteilten Grundlagen einheitlich zusammengetragen und fehlende Zusammenhänge ergänzt. Beide Verfahren eignen sich prinzipiell um rationale Krylow-Räume zu approximieren. Dies wird anhand mehrerer Beispiele gezeigt. Anhand des Modellproblems werden Beschränkungen der Methoden verdeutlicht.