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Least squares orthogonal distance fitting of implicit curves and surfaces

: Ahn, S.J.; Rauh, W.; Recknagel, M.


Radig, B. ; Deutsche Arbeitsgemeinschaft für Mustererkennung -DAGM-:
Pattern Recognition 2001. Proceedings 23rd DAGM Symposium : Munich, Germany, September 12 - 14, 2001 ; proceedings
Berlin: Springer, 2001 (Lecture Notes in Computer Science 2191)
ISBN: 3-540-42596-9
ISBN: 978-3-540-42596-0
ISSN: 0302-9743
Deutsche Arbeitsgemeinschaft für Mustererkennung (Symposium) <23, 2001, München>
Conference Paper
Fraunhofer IPA ()
Gauss-Newton iteration; Orthogonal Distance Fitting; Nonlinear Least Squares; Circle Fitting; Ellipsometrie; Geometrische Form; Messen

Curve and surface fitting is a relevant subject in computer vision and coordinate metrology. In this paper, we present a new fitting algorithm for implicit surfaces and plane curves which minimizes the sqaures sum of the orthogonal error distances between the model feature and the given data points. By the new algorithm, the model feature parameters are grouped and simultaneously estimated in terms of form, position, and rotation parameters. The form parameters determine the shape of the model feature, and the position/rotation parameters describe the rigid body motion of the model feature. The proposed algorithm is applicable to any kind of implicit surface and plane curve.