Least Squares Orthogonal Distance Fitting of Implicit Curves and Surfaces

Authors:
Sung Joon Ahn;Wolfgang Rauh;Matthias Recknagel
Affiliations:
-;-;-
Venue:
Proceedings of the 23rd DAGM-Symposium on Pattern Recognition
Year:
2001

Citing 6
Cited 1

Practical methods of optimization; (2nd ed.)

Practical methods of optimization; (2nd ed.)
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
Superquadrics and Angle-Preserving Transformations

IEEE Computer Graphics and Applications

Algorithms for projecting points onto conics

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

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 square 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.