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 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.
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Wijewickrema, S., Esson, C., Papliński, A. (2010). Orthogonal Distance Least Squares Fitting: A Novel Approach. In: Ranchordas, A., Pereira, J.M., Araújo, H.J., Tavares, J.M.R.S. (eds) Computer Vision, Imaging and Computer Graphics. Theory and Applications. VISIGRAPP 2009. Communications in Computer and Information Science, vol 68. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11840-1_19
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DOI: https://doi.org/10.1007/978-3-642-11840-1_19
Publisher Name: Springer, Berlin, Heidelberg
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