Best-fit of implicit surfaces and plane curves

Authors:
Sung-Joon Ahn;Wolfgang Rauh;Hans-Jürgen Warnecke
Affiliations:
Fraunhofer Institute IPA, Stuttgart, Germany;Fraunhofer Institute IPA, Stuttgart, Germany;Fraunhofer Society, Munich, Germany
Venue:
Mathematical Methods for Curves and Surfaces
Year:
2001

Citing 5
Cited 1

Numerical recipes in C: the art of scientific computing

Numerical recipes in C: the art of scientific computing
Recovery of Parametric Models from Range Images: The Case for Superquadrics with Global Deformations

IEEE Transactions on Pattern Analysis and Machine Intelligence
Estimation of Planar Curves, Surfaces, and Nonplanar Space Curves Defined by Implicit Equations with Applications to Edge and Range Image Segmentation

IEEE Transactions on Pattern Analysis and Machine Intelligence
Using Geometric Distance Fits for 3-D Object Modeling and Recognition

IEEE Transactions on Pattern Analysis and Machine Intelligence
Orthogonal Distance Fitting of Implicit Curves and Surfaces

IEEE Transactions on Pattern Analysis and Machine Intelligence

A class of methods for fitting a curve or surface to data by minimizing the sum of squares of orthogonal distances

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

Dimensional model fitting to a set of given points is a relevant subject in various disciplines of science and engineering. In this paper, we present a universal, and very efficient, best-fit algorithm for implicit surfaces and plane curves, by which the square sum of the orthogonal error distances of the given points to the model feature will be rotation parameters, and are simultaneously estimated. The form parameters determines the shape of the model feature, and the position/rotation parameters describe the rigid body motion of the model feature. The mathematics frame of the proposed algorithm is applicable to any kind of surface and plane curve. Dimensional model fitting to a set of given points is a relevant subject in various disciplines of science and engineering. In this paper, we present a universal, and very efficient, best-fit algorithm for implicit surfaces and plane curves, by which the square sum of the orthogonal error distances of the given points to the model feature will be rotation parameters, and are simultaneously estimated. The form parameters determines the shape of the model feature, and the position/rotation parameters describe the rigid body motion of the model feature. The mathematics frame of the proposed algorithm is applicable to any kind of surface and plane curve.