64,598 research outputs found

    Spatial refinement as collection order relations

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    An abstract examination of refinement (and conversely, coarsening) with respect to the involved spatial relations gives rise to formulated order relations between spatial coverings, which are defined as complete-coverage representations composed of regional granules. Coverings, which generalize partitions by allowing granules to overlap, enhance hierarchical geocomputations in several ways. Refinement between spatial coverings has underlying patterns with respect to inclusion—formalized as binary topological relations—between their granules. The patterns are captured by collection relations of inclusion, which are obtained by constraining relevant topological relations with cardinality properties such as uniqueness and totality. Conjoining relevant collection relations of equality and proper inclusion with the overlappedness (non-overlapped or overlapped) of the refining and the refined covering yields collection order relations, which serve as specific types of refinement between spatial coverings. The examination results in 75 collection order relations including seven types of equality and 34 pairs of strict or non-strict types of refinement and coarsening, out of which 19 pairs form partial collection orders

    Discovery of topological constraints on spatial object classes using a refined topological model

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    In a typical data collection process, a surveyed spatial object is annotated upon creation, and is classified based on its attributes. This annotation can also be guided by textual definitions of objects. However, interpretations of such definitions may differ among people, and thus result in subjective and inconsistent classification of objects. This problem becomes even more pronounced if the cultural and linguistic differences are considered. As a solution, this paper investigates the role of topology as the defining characteristic of a class of spatial objects. We propose a data mining approach based on frequent itemset mining to learn patterns in topological relations between objects of a given class and other spatial objects. In order to capture topological relations between more than two (linear) objects, this paper further proposes a refinement of the 9-intersection model for topological relations of line geometries. The discovered topological relations form topological constraints of an object class that can be used for spatial object classification. A case study has been carried out on bridges in the OpenStreetMap dataset for the state of Victoria, Australia. The results show that the proposed approach can successfully learn topological constraints for the class bridge, and that the proposed refined topological model for line geometries outperforms the 9-intersection model in this task

    Directly depicting granular ontologies

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    Published in extended form as "Endurants and Perdurants in Directly Depicting Ontologies", We propose an ontological theory that is powerful enough to describe both complex spatio-temporal processes and the enduring entities that participate in such processes. For this purpose we distinguish between ontologies and metaontology. Ontologies are based on very simple directly depicting languages and fall into two major categories: ontologies of type SPAN and ontologies of type SNAP. These represent two complementary perspectives on reality and result in distinct though compatible systems of categories. In a SNAP (snapshot) ontology we have the enduring entities in a given domain as they exist to be inventoried at some given moment of time. In a SPAN ontology we have perduring entities such as processes and their parts and aggregates. We argue that both kinds of ontology are required, together with the meta-ontology which joins them together. On the level of meta-ontology we are able to impose constraints on ontologies of a sort which can support efïŹcient processing of large amounts of data

    A Parallel Mesh-Adaptive Framework for Hyperbolic Conservation Laws

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    We report on the development of a computational framework for the parallel, mesh-adaptive solution of systems of hyperbolic conservation laws like the time-dependent Euler equations in compressible gas dynamics or Magneto-Hydrodynamics (MHD) and similar models in plasma physics. Local mesh refinement is realized by the recursive bisection of grid blocks along each spatial dimension, implemented numerical schemes include standard finite-differences as well as shock-capturing central schemes, both in connection with Runge-Kutta type integrators. Parallel execution is achieved through a configurable hybrid of POSIX-multi-threading and MPI-distribution with dynamic load balancing. One- two- and three-dimensional test computations for the Euler equations have been carried out and show good parallel scaling behavior. The Racoon framework is currently used to study the formation of singularities in plasmas and fluids.Comment: late submissio

    A geometry of information, I: Nerves, posets and differential forms

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    The main theme of this workshop (Dagstuhl seminar 04351) is `Spatial Representation: Continuous vs. Discrete'. Spatial representation has two contrasting but interacting aspects (i) representation of spaces' and (ii) representation by spaces. In this paper, we will examine two aspects that are common to both interpretations of the theme, namely nerve constructions and refinement. Representations change, data changes, spaces change. We will examine the possibility of a `differential geometry' of spatial representations of both types, and in the sequel give an algebra of differential forms that has the potential to handle the dynamical aspect of such a geometry. We will discuss briefly a conjectured class of spaces, generalising the Cantor set which would seem ideal as a test-bed for the set of tools we are developing.Comment: 28 pages. A version of this paper appears also on the Dagstuhl seminar portal http://drops.dagstuhl.de/portals/04351

    Structured Knowledge Representation for Image Retrieval

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    We propose a structured approach to the problem of retrieval of images by content and present a description logic that has been devised for the semantic indexing and retrieval of images containing complex objects. As other approaches do, we start from low-level features extracted with image analysis to detect and characterize regions in an image. However, in contrast with feature-based approaches, we provide a syntax to describe segmented regions as basic objects and complex objects as compositions of basic ones. Then we introduce a companion extensional semantics for defining reasoning services, such as retrieval, classification, and subsumption. These services can be used for both exact and approximate matching, using similarity measures. Using our logical approach as a formal specification, we implemented a complete client-server image retrieval system, which allows a user to pose both queries by sketch and queries by example. A set of experiments has been carried out on a testbed of images to assess the retrieval capabilities of the system in comparison with expert users ranking. Results are presented adopting a well-established measure of quality borrowed from textual information retrieval
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