In some recent papers Beinat and Crosilla (2003a, 2003b) have illustrated a new direct procedure, based on Procrustes analysis techniques, for the least squares adjustment of digital cadastral map features. The method has been successfully applied to simultaneously fit a series of fiducial point networks (polygons), each one connecting at least three points measured in the field by professional surveyors, strictly preserving their geometrical shape and linking the whole polygon set to a limited number of fixed points. The proposed procedure considers the various partially or totally overlapping measured polygons as unitary component parts of the general network of fiducial cadastral points to be adjusted. Direct and independent similarity transformation models are applied to each polygon – i.e., the so called Procrustes adjustment model – so to minimise a measure of discrepancy among the various polygons. As well as for the fiducial point network, the same technique can also correctly perform the conformal mosaicking of the new surveyed cadastral parcels with those ones obtained by digitisation of the original map, satisfying further possible geometrical constraints of the map entities like alignments, orthogonality and so on. To achieve the conformal parcel mosaicking in the absence of any topological or structural information, a specific procedure is needed to automatically identify the point-to-point correspondences between the various geometric entities to be connected. Several methods to detect possible correspondences between two sets of equal number of unlabeled points have been developed and investigated. Among these, we report the Umeyama's method (1988) developed to compute the permutation that maximises the agreement between two weighted graphs by way of a singular value decomposition of the relative adjacency matrix product. Another original direct solution, based on pure geometric rules, has been implemented and successively described. For the more general problem of detecting a geometric entity entirely contained within a more complex configuration, e.g. a measured parcel belonging to a cadastral map, a "kernel growing" geometric approach has been developed. The method explained in the paper is based on the analysis and segmentation of the adjacency matrices relative to the specific parcel and to the entire map vertex coordinates, and on the computation and validation of transformation parameters performed by Procrustes analysis techniques. In addition to the cadastral cartographic purposes, the procedure seems suitable for a wider range of possible applications, spacing from the Geographic Information Systems to the industrial and civil engineering design.

An Automatic Analytical Procedure for Searching Corresponding Feature Points in a Cadastral Map - TS28.5

BEINAT, Alberto;CROSILLA, Fabio;
2004-01-01

Abstract

In some recent papers Beinat and Crosilla (2003a, 2003b) have illustrated a new direct procedure, based on Procrustes analysis techniques, for the least squares adjustment of digital cadastral map features. The method has been successfully applied to simultaneously fit a series of fiducial point networks (polygons), each one connecting at least three points measured in the field by professional surveyors, strictly preserving their geometrical shape and linking the whole polygon set to a limited number of fixed points. The proposed procedure considers the various partially or totally overlapping measured polygons as unitary component parts of the general network of fiducial cadastral points to be adjusted. Direct and independent similarity transformation models are applied to each polygon – i.e., the so called Procrustes adjustment model – so to minimise a measure of discrepancy among the various polygons. As well as for the fiducial point network, the same technique can also correctly perform the conformal mosaicking of the new surveyed cadastral parcels with those ones obtained by digitisation of the original map, satisfying further possible geometrical constraints of the map entities like alignments, orthogonality and so on. To achieve the conformal parcel mosaicking in the absence of any topological or structural information, a specific procedure is needed to automatically identify the point-to-point correspondences between the various geometric entities to be connected. Several methods to detect possible correspondences between two sets of equal number of unlabeled points have been developed and investigated. Among these, we report the Umeyama's method (1988) developed to compute the permutation that maximises the agreement between two weighted graphs by way of a singular value decomposition of the relative adjacency matrix product. Another original direct solution, based on pure geometric rules, has been implemented and successively described. For the more general problem of detecting a geometric entity entirely contained within a more complex configuration, e.g. a measured parcel belonging to a cadastral map, a "kernel growing" geometric approach has been developed. The method explained in the paper is based on the analysis and segmentation of the adjacency matrices relative to the specific parcel and to the entire map vertex coordinates, and on the computation and validation of transformation parameters performed by Procrustes analysis techniques. In addition to the cadastral cartographic purposes, the procedure seems suitable for a wider range of possible applications, spacing from the Geographic Information Systems to the industrial and civil engineering design.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11390/882313
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