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- W10002721 abstract "We define a simple model of a map and formulate geometrical integration as a transformation problem between one idealized true map only known partially and multiple realizations of the map perturbed by random noise and unknown systematic effects. In the statistical model the connection between the true map and its realizations is interpreted as a multivariate spatial random process and further investigated by geostatistical and classical estimation methods. As a main result a model of the distance-dependent relative accuracy (neighborhood accuracy) in spatial datasets is obtained. On the basis of this statistical hypothesis two models for the estimation of the true map, namely intrinsic kriging and collocation, are suggested. As an alternative to the stochastical model we suggest the deterministic model of the topology of the euclidean plane where the connection between the maps is treated as a homeomorphism. The consideration of constraints in form of a bijection for homologous points and nonlinear functions for geometrical constraints leads to the formal definition of the homogenization of maps. An extension of the collocation model allows us to estimate the unknown parameters (coordinates) in the system of the true map and to simultaneously consider geometrical constraints, the linear trend, the nonlinear signal and the random noise. Due to the high density of its design matrix the suggested model is unsuitable for practical applications with mass data. The hybrid approach of Benning appears to be an optimal compromise between the extended collocation model and other alternatives. It has the advantage that statistical least squares methods can be combined with (efficient) deterministic interpolation methods and furthermore leads to a sparse design matrix." @default.
- W10002721 created "2016-06-24" @default.
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- W10002721 date "2005-01-01" @default.
- W10002721 modified "2023-10-18" @default.
- W10002721 title "MATHEMATICAL MODELS FOR GEOMETRICAL INTEGRATION" @default.
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