Abstract
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 nonlinear 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 language  English 

Title of host publication  Computer Vision, Imaging and Computer Graphics: Theory and Applications  International Joint Conference, VISIGRAPP 2009, Revised Selected Papers 
Pages  255268 
Number of pages  14 
Volume  68 CCIS 
DOIs  
Publication status  Published  2010 
Event  International Conference on Vision Theory and Applications 2009  Lisboa, Portugal Duration: 5 Feb 2009 → 8 Feb 2009 Conference number: 4th https://link.springer.com/book/10.1007/9783642118401 (Proceedings) 
Publication series
Name  Communications in Computer and Information Science 

Volume  68 CCIS 
ISSN (Print)  18650929 
Conference
Conference  International Conference on Vision Theory and Applications 2009 

Abbreviated title  VISAPP 2009 
Country/Territory  Portugal 
City  Lisboa 
Period  5/02/09 → 8/02/09 
Internet address 

Keywords
 Conic fitting
 Orthogonal distance least squares fitting
 Quadric fitting