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Best-Fit of Implicit Curves and Surfaces

: Ahn, S.J.; Westkämper, E.; Rauh, W.

Gruen, A. ; TU Wien, Institut für Geodäsie und Geophysik; TH Zürich -ETH-, Institut für Geodäsie und Photogrammetrie:
Optical 3-D Measurement Techniques V : Applications in manufacturing, quality control, robotics, navigation, mobile mapping, medical imaging, animation. Papers presented at the Conference organized at Vienna, Oktober 1-4, 2001
Wien, 2001
ISBN: 3-9501492-0-1
Conference "Optical 3-D Measurement Techniques" <5, 2001, Wien>
Conference Paper
Fraunhofer IPA ()
curve fitting; Surface Fitting; geometric distance; Orthogonal Distance Fitting; Object reconstruction; Gauss-Newton-Method; implicit curve; Implicit Surfaces; Oberfläche; Mathematisches Verfahren

Curve and surface fitting find their applications in various fields of science and engineering, and, are relevant subjects in coordinate metrology. In this paper, we present two new fitting algorithms for implicit surfaces and plane curves, which minimize the square sum of the orthogonal error distances between the model feature and the given data points. By the new algorithms, 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 algorithms are applicable to any kind of implicit surface and plane curve. We give fitting examples for cylinder, cone, and torus.