Imputation for point patterns: measure variation approach
نویسندگان
چکیده
Given an observed point pattern in a window W0 ⊂ R we address the following two questions: How can one extend in a ‘reasonable way’ the pattern to a larger window W ⊃ W0? Can one predict possible gaps in the observed point configuration where points were ‘expected’ but somehow failed to realise? By assuming that the point pattern is an observed part of a realisation of a non-homogeneous Poisson process in W , we estimate its intensity measure so that to mimic a given distributional characteristic of the pattern, for instance, its sample nearest neighbour distribution. The main tool is variational analysis of measures and corresponding steepest descent type algorithms.
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