Qualitative Spatial Reasoning with Holed Regions

The intricacies of real-world and constructed spatial entities call for versatile spatial data types to model complex spatial objects, often characterized by the presence of holes. To date, however, relations of simple, hole-free regions have been the prevailing approaches for spatial qualitative reasoning. Even though such relations may be applied to holed regions, they do not take into consideration the consequences of the existence of the holes, limiting the ability to query and compare more complex spatial configurations. To overcome such limitations, this thesis develops a formal framework for spatial reasoning with topological relations over two-dimensional holed regions, called the Holed Regions Model (HRM), and a similarity evaluation method for comparing relations featuring a multi-holed region, called the Frequency Distribution Method (FDM). The HRM comprises a set of 23 relations between a hole-free and a single-holed region, a set of 152 relations between two single-holed regions, as well as the composition inferences enabled from both sets of relations. The inference results reveal that the fine-grained topological relations over holed regions provide more refined composition results in over 50% of the cases when compared with the results of hole-free regions relations. The HRM also accommodates the relations between a hole-free region and a multi-holed region. Each such relation is called a multi-element relation, as it can be deconstructed into a number of elements—relations between a hole-free and a singleholed region—that is equal to the number of holes, regarding each hole as if it were the only one. FDM facilitates the similarity assessment among multi-element relations. The similarity is evaluated by comparing the frequency summaries of the single-holed region relations. The multi-holed regions of the relations under comparison may differ in the number of holes. In order to assess the similarity of such relations, one multi-holed region is considered as the result of dropping from or adding holes to the other region. Therefore, the effect that two concurrent changes have on the similarity of the relations is evaluated. The first is the change in the topological relation between the regions, and the second is the change in a region’s topology brought upon by elimination or addition of holes. The results from the similarity evaluations examined in this thesis show that the topological placement of the holes in relation to the hole-free region influences relation similarity as much as the relation between the hole-free region and the host of the holes. When the relations under comparison have fewer characteristics in common, the placement of the holes is the determining factor for the similarity rankings among relations. The distilled and more correct composition and similarity evaluation results enabled by the relations over holed regions indicate that spatial reasoning over such regions differs from the prevailing reasoning over hole-free regions. Insights from such results are expected to contribute to the design of future geographic information systems that more adequately process complex spatial phenomena, and are better equipped for advanced database query answering

Qualitative Spatial Reasoning with Holed Regions

The intricacies of real-world and constructed spatial entities call for versatile spatial data types to model complex spatial objects, often characterized by the presence of holes. To date, however, relations of simple, hole-free regions have been the prevailing approaches for spatial qualitative reasoning. Even though such relations may be applied to holed regions, they do not take into consideration the consequences of the existence of the holes, limiting the ability to query and compare more complex spatial configurations. To overcome such limitations, this thesis develops a formal framework for spatial reasoning with topological relations over two-dimensional holed regions, called the Holed Regions Model (HRM), and a similarity evaluation method for comparing relations featuring a multi-holed region, called the Frequency Distribution Method (FDM). The HRM comprises a set of 23 relations between a hole-free and a single-holed region, a set of 152 relations between two single-holed regions, as well as the composition inferences enabled from both sets of relations. The inference results reveal that the fine-grained topological relations over holed regions provide more refined composition results in over 50% of the cases when compared with the results of hole-free regions relations. The HRM also accommodates the relations between a hole-free region and a multi-holed region. Each such relation is called a multi-element relation, as it can be deconstructed into a number of elements—relations between a hole-free and a singleholed region—that is equal to the number of holes, regarding each hole as if it were the only one. FDM facilitates the similarity assessment among multi-element relations. The similarity is evaluated by comparing the frequency summaries of the single-holed region relations. The multi-holed regions of the relations under comparison may differ in the number of holes. In order to assess the similarity of such relations, one multi-holed region is considered as the result of dropping from or adding holes to the other region. Therefore, the effect that two concurrent changes have on the similarity of the relations is evaluated. The first is the change in the topological relation between the regions, and the second is the change in a region’s topology brought upon by elimination or addition of holes. The results from the similarity evaluations examined in this thesis show that the topological placement of the holes in relation to the hole-free region influences relation similarity as much as the relation between the hole-free region and the host of the holes. When the relations under comparison have fewer characteristics in common, the placement of the holes is the determining factor for the similarity rankings among relations. The distilled and more correct composition and similarity evaluation results enabled by the relations over holed regions indicate that spatial reasoning over such regions differs from the prevailing reasoning over hole-free regions. Insights from such results are expected to contribute to the design of future geographic information systems that more adequately process complex spatial phenomena, and are better equipped for advanced database query answering

Theory of Spatial Similarity Relations and Its Applications in Automated Map Generalization

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

Réception des données spatiales et leurs traitements : analyse d'images satellites pour la mise à jour des SIG par enrichissement du système de raisonnement spatial RCC8

De nos jours, la résolution des images satellites et le volume des bases de données géographiques disponibles sont en constante augmentation. Les images de télédétection à haute résolution représentent des sources de données hétérogènes de plus en plus nécessaires et difficiles à exploiter. Ces images sont considérées comme des sources très riches et utiles pour la mise à jour des Systèmes d'Information Géographique (SIG). Afin de mettre à jour ces bases de données, une étape de détection de changements est nécessaire. Cette thèse s'attache à l'étude de l'analyse d'images satellites par enrichissement du système de raisonnement spatial RCC8 (Region Connection Calculus) pour la détection des changements topologiques dans le but de mettre à jour des SIG. L'objectif à terme de cette étude est d'exploiter, de détailler et d'enrichir les relations topologiques du système RCC8. L'intérêt de l'enrichissement, l'exploitation et la description détaillée des relations du système RCC8 réside dans le fait qu'elles permettent de détecter automatiquement les différents niveaux de détails topologiques et les changements topologiques entre des régions géographiques représentées sur des cartes numériques (CN) et dans des images satellitaires. Dans cette thèse, nous proposons et développons une extension du modèle topologique d'Intersection et Différence (ID) par des invariants topologiques qui sont : le nombre de séparations, le voisinage et le type des éléments spatiaux. Cette extension vient enrichir et détailler les relations du système RCC8 à deux niveaux de détail. Au premier niveau, l'enrichissement du système RCC8 est fait par l'invariant topologique du nombre de séparations, et le nouveau système est appelé "système RCC-16 au niveau-1". Pour éviter des problèmes de confusion entre les relations de ce nouveau système, au deuxième niveau, l'enrichissement du "RCC-16 au niveau-1" est fait par l'invariant topologique du type d'éléments spatiaux et le nouveau système est appelé "système RCC-16 au niveau-2". Ces deux systèmes RCC-16 (au niveau-1 et au niveau-2) seront appliqués pour l'analyse d'images satellites, la détection de changements et l'analyse spatiale dans des SIG. Nous proposons à partir de celà une nouvelle méthode de détection de changements entre une nouvelle image satellite et une ancienne carte numérique des SIG qui intègre l'analyse topologique par le système RCC-16 afin de détecter et d'identifier les changements entre deux images satellites, ou entre deux cartes vectorielles produites à différentes dates. Dans cette étude de l'enrichissement du système RCC8, les régions spatiales ont de simples représentations spatiales. Cependant, la représentation spatiale et les relations topologiques entre régions dans des images satellites et des données des SIG sont plus complexes, floues et incertaines. Dans l'objectif d'étudier les relations topologiques entre régions floues, un modèle appelé le modèle topologique Flou d'Intersection et Différence (FID) pour la description des relations topologiques entre régions floues sera proposé et développé. 152 relations topologiques peuvent être extraites à l'aide de ce modèle FID. Ces 152 relations sont regroupées dans huit clusters qualitatifs du système RCC8 : Disjoint (Déconnexion), Meets (Connexion Extérieure), Overlaps (Chevauchement), CoveredBy (Inclusion Tangentielle), Inside (Inclusion Non-Tangentielle), Covers (Inclusion Tangentielle Inverse), Contains (Inclusion Non-Tangentielle Inverse), et Equal (Égalité). Ces relations seront évaluées et extraites à partir des images satellites pour donner des exemples de leur intérêt dans le domaine de l'analyse d'image et dans des SIG. La contribution de cette thèse est marquée par l'enrichissement du système RCC8 donnant lieu à un nouveau système, RCC-16, mettant en ouvre une nouvelle méthode de détection de changements, le modèle FID, et regroupant les 152 relations topologiques floues dans les huit clusters qualitatifs du système RCC8.Nowadays, the resolution of satellite images and the volume of available geographic databases are constantly growing. Images of high resolution remote sensing represent sources of heterogeneous data increasingly necessary and difficult to exploit. These images are considered very rich and useful sources for updating Geographic Information Systems (GIS). To update these databases, a step of change detection is necessary and required. This thesis focuses on the study of satellite image analysis by enriching the spatial reasoning system RCC8 (Region Connection Calculus) for the detection of topological changes in order to update GIS databases. The ultimate goal of this study is to exploit and enrich the topological relations of the system RCC8. The interest of the enrichment and detailed description of RCC8 system relations lies in the fact that they can automatically detect the different levels of topological details and topological changes between geographical regions represented on GIS digital maps and satellite images. In this thesis, we propose and develop an extension of the Intersection and Difference (ID) topological model by using topological invariants which are : the separation number, the neighborhood and the spatial element type. This extension enriches and details the relations of the system RCC8 at two levels of detail. At the first level, the enrichment of the system RCC8 is made by using the topological invariant of the separation number and the new system is called "system RCC-16 at level-1". To avoid confusion problems between the topological relations of this new system, the second level by enriching the "system RCC-16 at level-1" is done by using the topological invariant of the spatial element type and the new system is called "system RCC-16 at level-2". These two systems RCC-16 (at two levels : level-1 and level-2) will be applied to satellite image analysis, change detection and spatial analysis in GIS. We propose a new method for detecting changes between a new satellite image and a GIS old digital map. This method integrates the topological analysis of the system RCC-16 to detect and identify changes between two satellite images, or between two vector maps produced at different dates. In this study of the enrichment of the system RCC8, spatial regions have simple spatial representations. However, the spatial and topological relations between regions in satellite images and GIS data are more complex, vague and uncertain. With the aim of studying the topological relations between fuzzy regions, a model called the Fuzzy topological model of Intersection and Difference (FID) for the description of topological relations between fuzzy regions is proposed and developed. 152 topological relations can be extracted using this model FID. These 152 relations are grouped into eight clusters of the qualitative relations of the system RCC8 : Disjoint (Disconnected), Meets (Externally Connected), Overlaps (Partially Overlapping), CoveredBy (Tangential Proper Part), Inside (Non-Tangential Proper Part), Covers (Tangential Proper Part Inverse), Contains (Non-Tangential Proper Part Inverse), and Equal. These relations will be evaluated and extracted from satellite images to give examples of their interest in the image analysis field and GIS. The contribution of this thesis is marked by enriching the qualitative spatial reasoning system RCC8 giving rise to a new system, RCC-16, implementing a new method of change detection, the model FID, and clustering the 152 fuzzy topological relations in eight qualitative clusters of the system RCC8