3 research outputs found

    Representing space for practical reasoning

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    This paper describes a new approach to representing space and time for practical reasoning, based on space-filling cells. Unlike R n, the new models can represent a bounded region of space using only finitely many cells, so they can be manipulated directly. Unlike Z n, they have useful notions of function continuity and region connectedness. The topology of space is allowed to depend on the situation being represented, accounting for sharp changes in function values and lack of connectedness across object boundaries. Algorithms based on this model of space are neither purely region-based nor purely boundary-based, but a blend of the two. This new style of algorithm design is illustrated by a new program for finding edges in grey-scale images. Although the program is based on a relatively conventional second directional difference operator, it can detect fine texture in the presence of camera noise, produce connected boundaries around sharp corners, and return thin boundaries without "feathering. " New algorithms are presented for combining directional differences, suppressing the effects of camera noise, reconstructing image intensities from the second difference values and merging results from different scales (including suppression of spurious boundaries in staircase patterns).

    Boundaries and Topological Algorithms

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    This thesis develops a model for the topological structure of situations. In this model, the topological structure of space is altered by the presence or absence of boundaries, such as those at the edges of objects. This allows the intuitive meaning of topological concepts such as region connectivity, function continuity, and preservation of topological structure to be modeled using the standard mathematical definitions. The thesis shows that these concepts are important in a wide range of artificial intelligence problems, including low-level vision, high-level vision, natural language semantics, and high-level reasoning
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