Best (orthogonal) fitting ellipsoid with quaternions

BEKTAŞ S.

SURVEY REVIEW, vol.56, no.396, pp.249-264, 2024 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 56 Issue: 396
  • Publication Date: 2024
  • Doi Number: 10.1080/00396265.2023.2225899
  • Journal Name: SURVEY REVIEW
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Environment Index, Geobase, INSPEC
  • Page Numbers: pp.249-264
  • Keywords: Algebraic fitting, Geometric parameters of fitted ellipsoid, Least squares method, Orthogonal fitting, Quaternion, Variance–covariance matrix
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

The aim of this study is the determination of the best fit ellipsoid to given points by quaternions. The problem of the fitting ellipsoid is frequently encountered in image processing, computer games, medicine, engineering and science applications, geodesy, etc. The ellipsoid fitting problem is the process of determining the ellipsoid that best fits a given set of points in 3D. In the fitting process, it is generally done over two models. The first of these is the algebraic method and the second one is orthogonal (geometric) method. In this study, we tried to solve the problem of algebraic and orthogonal ellipsoid fitting based on Euler angles for the first time over quaternions. The superiority of quaternions over Euler rotation angles is well known. In addition, the variance-covariance matrix of the parameters of the fitted ellipsoid will also be calculated. Numerical applications show that the proposed method can be used successfully.