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Related Experiment Video

Updated: Jun 17, 2026

Precision Measurements and Parametric Models of Vertebral Endplates

Precision Measurements and Parametric Models of Vertebral Endplates

Published on: September 17, 2019

An adaptive and stable method for fitting implicit polynomial curves and surfaces.

Bo Zheng¹, Jun Takamatsu, Katsushi Ikeuchi

¹The University of Tokyo, Tokyo, Japan. zheng@cvl.iis.u-tokyo.ac.jp

IEEE Transactions on Pattern Analysis and Machine Intelligence

|January 16, 2010

Summary

This summary is machine-generated.

This study introduces a stable and accurate method for fitting implicit polynomials (IPs) to 2D and 3D data. The new approach efficiently determines the optimal IP degree, improving computational cost and fitting accuracy for computer vision applications.

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Last Updated: Jun 17, 2026

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Area of Science:

Computer Vision
Numerical Analysis
Data Fitting

Background:

Implicit polynomials (IPs) are valuable for representing 2D and 3D data in computer vision.
Existing IP fitting methods face challenges in computational cost, degree selection, and maintaining fitting accuracy and stability.

Purpose of the Study:

To develop a stable and accurate IP fitting method with automatic degree determination.
To improve computational efficiency and fitting precision compared to existing techniques.

Main Methods:

Proposes an incremental approach that increases the IP degree until satisfactory fitting is achieved.
Utilizes QR decomposition with Gram-Schmidt orthogonalization for computational efficiency.
Applies selective ridge regression constraints to unstable elements identified by the decomposition.

Main Results:

Achieves computational stability and high fitting accuracy.
Demonstrates superior performance compared to existing IP fitting methods in experimental evaluations.
Effectively determines a moderate and appropriate degree for IP representation automatically.

Conclusions:

The proposed method offers a stable, accurate, and computationally efficient solution for implicit polynomial fitting.
It addresses key limitations of prior methods in degree selection and stability.
The technique shows significant promise for advancing computer vision applications requiring precise data representation.