Orthogonal distance least squares fitting: A novel approach

Sudanthi Wijewickrema, Charles Esson, Andrew Papliński

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

11 Citations (Scopus)


Least squares is a common method of conic fitting that minimizes the squared sum of a distance measure between a set of points and a conic. Orthogonal distance, when used as the distance that is minimized, provides more accurate fits as it is the shortest distance between a point and a conic. The problem however lies in the calculation of the orthogonal distance for a general conic, which results in an unstable closed form solution. Existing methods avoid this closed form solution by using non-linear iterative procedures or incorporating conic specific information. This paper introduces a novel method to directly calculate the orthogonal distance for an arbitrary conic, thereby eliminating the need for iterative procedures and conic specific information. It further describes a least squares fitting algorithm that uses the orthogonal distance thus calculated, to fit general conics. This technique is then extended to fit quadrics to three dimensional data.

Original languageEnglish
Title of host publicationComputer Vision, Imaging and Computer Graphics: Theory and Applications - International Joint Conference, VISIGRAPP 2009, Revised Selected Papers
Number of pages14
Volume68 CCIS
Publication statusPublished - 2010
EventInternational Conference on Vision Theory and Applications 2009 - Lisboa, Portugal
Duration: 5 Feb 20098 Feb 2009
Conference number: 4th
https://link.springer.com/book/10.1007/978-3-642-11840-1 (Proceedings)

Publication series

NameCommunications in Computer and Information Science
Volume68 CCIS
ISSN (Print)18650929


ConferenceInternational Conference on Vision Theory and Applications 2009
Abbreviated titleVISAPP 2009
Internet address


  • Conic fitting
  • Orthogonal distance least squares fitting
  • Quadric fitting

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