Automatic Point Matching of GIS Geometric Figures

GIS and digital mapping operations frequently require the automatic comparison and superimposition of geometric figures represented by sets of vertex coordinates supported by structural and topological information. When the configurations are not structured, that is the only vertex coordinates of the figures are available, manual intervention is needed in order to establish correspondences among the different geometries. To overcome this limitation, an automatic method has been developed to detect the correspondences between two or more equivalent sets of unlabeled points, representing n-dimensional geometric figures. The proposed technique performs a geometrical analysis of the adjacency matrices of the point configurations, in order to identify, for each one, the vertex of maximal asymmetry. A pairwise comparison of the sorted components of the adjacency matrix relative to these vertices, leads to the identification of the point correspondences. A directly-computed Procrustes conformal transformation is then applied to the geometric figures in order to achieve their optimal alignment. Also in case of geometric entities included into another, the problem solution starts trying to find some minimal asymmetric sub- configurations (kernels) that are similar in both figures. A Procrustes superimposition of these corresponding kernels is then applied, and extended to the remaining points of the included configuration. A shape test is finally executed in order to identify the best solution. Specific geometric rules and filters are implemented to optimise the computation process. The method has been successfully tested on cadastral cartographic matching problems. In addition, it is suitable for a wider range of possible applications, like CAD/CAM, computer vision and reverse engineering.