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Fitting of parametric space curves and surfaces by using the geometric error measure

: Ahn, S.J.; Rauh, W.; Westkämper, E.


Gool, L. van ; Deutsche Arbeitsgemeinschaft für Mustererkennung -DAGM-:
Pattern recognition : Zürich, Switzerland, September 16 - 18, 2002. Proceedings. 24th DAGM Symposium
Berlin: Springer, 2002 (Lecture Notes in Computer Science 2449)
ISBN: 3-540-44209-X
ISSN: 0302-9743
Deutsche Arbeitsgemeinschaft für Mustererkennung (Symposium) <24, 2002, Zürich>
Fraunhofer IPA ()
parametric curve; surface; parameter spaces; curve; curve fitting; computer vision; pattern recognition

For pattern recognition and computer vision, fitting of curves and surfaces to a set of given data points in space is a relevant subject. In this paper, we review the current orthogonal distance fitting algorithms for parametric model features, and, present two new algorithms in a well organized and easily understandable manner. Each of these algorithms estimates the model parameters which minimize the square sum of the shortest error distances between the model feature and the given data points. The model parameters are grouped and simultaneously estimated in terms of form, position, and rotation parameters. We give various examples of fitting curves and surfaces to a point set in space.