Interpolation and extrapolation of point patterns based on variation analysis on measures

• Main Author: Khatun, Mahmuda
• Published: University of Strathclyde 2008
• Subjects: 511.8
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.502280

Suppose that we observe a point pattern in an observation window W₀ C Rd. In this study we pose ourselves the following two main questions: How can one extend the pattern in a 'reasonable way' to a larger window W ) W₀? Can one predict possible gaps in the observed point pattern where points were 'expected' but somehow failed to realise. We address these questions by assuming that the point pattern is an observed part of a realisation of a non-homogeneous Poisson process in W and estimate its intensity so that to mimic a given distributional characteristic of the pattern, for instance, its sample nearest neighbour distribution. The project aims to develop prediction and extrapolation techniques for random points processes and related techniques of optimisation of functionals depending on a measure. Applications are numerous and important, including restoration of images, detection of impurities in material science, prediction of anomalies in geology, etc.