Mereotopological Connection

The paper outlines a model-theoretic framework for investigating and comparing a variety of mereotopological theories. In the first part we consider different ways of characterizing a mereotopology with respect to (i) the intended interpretation of the connection primitive, and (ii) the composition of the admissible domains of quantification (e.g., whether or not they include boundary elements). The second part extends this study by considering two further dimensions along which different patterns of topological connection can be classified—the strength of the connection and its multiplicity

Variations and Application Conditions Of the Data Type »Image« - The Foundation of Computational Visualistics

Few years ago, the department of computer science of the University Magdeburg invented a completely new diploma programme called 'computational visualistics', a curriculum dealing with all aspects of computational pictures. Only isolated aspects had been studied so far in computer science, particularly in the independent domains of computer graphics, image processing, information visualization, and computer vision. So is there indeed a coherent domain of research behind such a curriculum? The answer to that question depends crucially on a data structure that acts as a mediator between general visualistics and computer science: the data structure "image". The present text investigates that data structure, its components, and its application conditions, and thus elaborates the very foundations of computational visualistics as a unique and homogenous field of research. Before concentrating on that data structure, the theory of pictures in general and the definition of pictures as perceptoid signs in particular are closely examined. This includes an act-theoretic consideration about resemblance as the crucial link between image and object, the communicative function of context building as the central concept for comparing pictures and language, and several modes of reflection underlying the relation between image and image user. In the main chapter, the data structure "image" is extendedly analyzed under the perspectives of syntax, semantics, and pragmatics. While syntactic aspects mostly concern image processing, semantic questions form the core of computer graphics and computer vision. Pragmatic considerations are particularly involved with interactive pictures but also extend to the field of information visualization and even to computer art. Four case studies provide practical applications of various aspects of the analysis

A Qualitative Representation of Spatial Scenes in R2 with Regions and Lines

Regions and lines are common geographic abstractions for geographic objects. Collections of regions, lines, and other representations of spatial objects form a spatial scene, along with their relations. For instance, the states of Maine and New Hampshire can be represented by a pair of regions and related based on their topological properties. These two states are adjacent (i.e., they meet along their shared boundary), whereas Maine and Florida are not adjacent (i.e., they are disjoint). A detailed model for qualitatively describing spatial scenes should capture the essential properties of a configuration such that a description of the represented objects and their relations can be generated. Such a description should then be able to reproduce a scene in a way that preserves all topological relationships, but without regards to metric details. Coarse approaches to qualitative spatial reasoning may underspecify certain relations. For example, if two objects meet, it is unclear if they meet along an edge, at a single point, or multiple times along their boundaries. Where the boundaries of spatial objects converge, this is called a spatial intersection. This thesis develops a model for spatial scene descriptions primarily through sequences of detailed spatial intersections and object containment, capturing how complex spatial objects relate. With a theory of complex spatial scenes developed, a tool that will automatically generate a formal description of a spatial scene is prototyped, enabling the described objects to be analyzed. The strengths and weaknesses of the provided model will be discussed relative to other models of spatial scene description, along with further refinements