Solution of Nine-Parameter Affine Transformation Based on Quaternions


Uygur S. Ö. , Akyılmaz O., Aydın C.

Journal Of Surveying Engineering-Asce, vol.147, no.3, pp.1-11, 2021 (Journal Indexed in SCI Expanded)

  • Publication Type: Article / Article
  • Volume: 147 Issue: 3
  • Publication Date: 2021
  • Doi Number: 10.1061/(asce)su.1943-5428.0000364
  • Title of Journal : Journal Of Surveying Engineering-Asce
  • Page Numbers: pp.1-11

Abstract

A least-squares solution for (a)symmetric nine-parameter three-dimensional affine coordinate transformation based on quaternions is presented. Retrieval of the nine transformation parameters (three translations, three scale factors, and three Euler rotation angles) and their covariance matrix from the quaternion-based estimates is given in detail. The proposed method can successfully handle all the cases regardless of the magnitude of the parameters and full covariance matrices of the control points. Efficiency and consistency of the solution are discussed within five different case studies consisting of many numerical examples.

A least-squares solution for (a)symmetric nine-parameter three-dimensional affine coordinate transformation based on quaternions is presented. Retrieval of the nine transformation parameters (three translations, three scale factors, and three Euler rotation angles) and their covariance matrix from the quaternion-based estimates is given in detail. The proposed method can successfully handle all the cases regardless of the magnitude of the parameters and full covariance matrices of the control points. Efficiency and consistency of the solution are discussed within five different case studies consisting of many numerical examples.