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Related Experiment Video

Updated: May 22, 2026

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

Published on: August 19, 2021

A fast algorithm for multidimensional ellipsoid-specific fitting by minimizing a new defined vector norm of residuals

Xianghua Ying¹, Li Yang, Hongbin Zha

¹Key Laboratory of Machine Perception (Ministry of Education), School of Electronic Engineering and Computer Science, Peking University, Beijing 100871, China. xhying@cis.pku.edu.cn

IEEE Transactions on Pattern Analysis and Machine Intelligence

|May 16, 2012

Summary

This summary is machine-generated.

This study introduces a faster algorithm for fitting multidimensional ellipsoids using semidefinite programming (SDP). The new method significantly reduces computational demands, enabling the analysis of millions of data points efficiently.

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Area of Science:

Computational Geometry
Optimization
Computer Vision

Background:

Quadratic surfaces in n-dimensional space are defined by quadratic polynomials, representable by vectors and matrices.
Ellipsoid fitting is crucial in various scientific domains, often employing semidefinite programming (SDP).
Existing SDP methods for multidimensional ellipsoid fitting are computationally intensive and memory-demanding for large datasets.

Purpose of the Study:

To develop a computationally efficient and accurate algorithm for multidimensional ellipsoid-specific fitting.
To overcome the limitations of existing SDP-based methods regarding runtime and memory usage.

Main Methods:

Proposing a novel vector norm for the algebraic residual vector in ellipsoid fitting.
Utilizing semidefinite programming (SDP) with a reduced problem size.
Developing a fast and easily implementable algorithm based on the new norm and SDP formulation.

Main Results:

The proposed algorithm drastically decreases the size of the semidefinite programming problem.
The method preserves the accuracy of multidimensional ellipsoid fitting.
The algorithm efficiently handles datasets with several million points, a significant improvement over prior methods.

Conclusions:

The novel SDP-based approach offers a significant advancement in multidimensional ellipsoid fitting.
This fast and scalable method enables the analysis of large-scale geometric data.
The algorithm is suitable for applications requiring efficient and accurate ellipsoid fitting from extensive point clouds.