A method for local approximation of a planar deformation field

• Autorzy: Ligas Marcin , Banaś Marek , Szafarczyk Anna

Identyfikatory

DOI

10.2478/rgg-2019-0007

• Języki publikacji: EN

Abstrakty

EN

We present a method of approximation of a deformation eld based on the local ane transformations constructed based on n nearest neighbors with respect to points of adopted grid. The local ane transformations are weighted by means of inverse distance squared between each grid point and observed points (nearest neighbors). This work uses a deformation gradient, although it is possible to use a displacement gradient instead – the two approaches are equivalent. To decompose the deformation gradient into components related to rigid motions (rotations, translations are excluded from the deformation gradient through dierentiation process) and deformations, we used a polar decomposition and decomposition into a sum of symmetric and an anti-symmetric matrices (tensors). We discuss the results from both decompositions. Calibration of a local ane transformations model (i.e., number of nearest neighbors) is performed on observed points and is carried out in a cross-validation procedure. Verication of the method was conducted on simulated data-grids subjected to known (functionally generated) deformations, hence, known in every point of a study area.

Słowa kluczowe

EN

deformation analysis; polar decomposition; affine transformation; rotation matrix; stretch tensor

PL

analiza deformacji; rozkład biegunowy operatora; transformacja afiniczna; macierz obrotu

• Wydawca: Wydział Geodezji i Kartografii Politechniki Warszawskiej
• Czasopismo: Reports on Geodesy and Geoinformatics
• Rocznik: 2019
• Tom: Vol. 108
• Strony: 1--8
• Opis fizyczny: Bibliogr. 15 poz., rys., tab.

Twórcy

autor

Ligas Marcin

• Department of Integrated Geodesy and Cartography, Faculty of Mining Surveying and Environmental Engineering, AGH University of Science and Technology, 30 A. Mickiewicza Avenue, 30-059, Cracow, Poland

autor

Banaś Marek

• Institute of Technical Engineering, Bronisław Markiewicz State Higher School of Technology and Economics in Jarosław, 16 Czarnieckiego Street, 37-500, Jarosław, Poland

autor

Szafarczyk Anna

• Department of Mine Areas Protection, Geoinformatics and Mine Surveying, Faculty of Mining Surveying and Environmental Engineering, AGH University of Science and Technology, 30 A. Mickiewicza Avenue, 30-059, Cracow, Poland

Bibliografia

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