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This paper addresses the weighted orthogonal Procrustes problem of matching stochastically perturbed point clouds, formulated as an optimization problem with a closed-form solution. A novel uncertainty characterization of the solution of this problem is proposed resorting to perturbation theory concepts, which admits arbitrary transformations between point clouds and individual covariance and cross-covariance matrices for the points of each cloud. The method is thoroughly validated through extensive Monte Carlo simulations, and particularly interesting cases where nonlinearities may arise are further analyzed. [ABSTRACT FROM AUTHOR]

Highlights: [•] Maps provide a suitable cartographic base for historical analyses. [•] The main problem is the heterogeneity of the quality of historical data. [•] The quality of historical maps must be analyzed prior to the application of their information. [•] The evolutionary algorithms NSGA-II and msPESA are assessed in this study. [•] Solutions obtained by NSGA-II dominate solutions obtained by msPESA. [Copyright &y& Elsevier]

Abstract: Adaptive mapping and real-time spatial data delivery are currently major research topics in the fields of Web-GIS and Location Based Services (LBS). In order to successfully implement these paradigms a methodology to progressively adopt or transform an arbitrary map representation in an arbitrary fashion on-the-fly is necessary. Such a methodology was previously considered not feasible due to the high computational complexity associated with existing automated map generalisation methodologies. This paper presents a methodology, inspired by related research in the field of computer graphics, which offers the potential to reduce such associated computational complexity. This is achieved using an approach to map transformation which takes advantage of the geometric coherence between a user''s spatial data requirements. [Copyright &y& Elsevier]