Basic Measures for Imprecise Point Sets in R d

Most algorithms in computational geometry tend to assume that all input is exact, with no imprecision or error. Most real-world data however, has some imprecision (for example due to measurement error). Thus, there exists a need for algorithms that can produce meaningful output for imprecise input data. In this thesis, I present results on the computation of upper and lower bounds on various basic measures (such as diameter, width, closest pair, volume of smallest enclosing ball and volume of minimum axis aligned bounding box) for imprecise point sets in Rd. I model the imprecision by representing an imprecise point set as a set of regions (balls or polytopes), such that each point may lie anywhere within one of the regions. This work is an extension of previous research by Löffler and van Kreveld on imprecise point sets in R2, to higher dimensions.

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