Hypersphere Fitting From Noisy Data Using an EM Algorithm

This letter studies a new expectation maximization (EM) algorithm to solve the problem of circle, sphere and more generally hypersphere fitting. This algorithm relies on the introduction of random latent vectors having a priori independent von Mises-Fisher distributions defined on the hypersphere. T...

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Bibliographic Details
Published in:IEEE signal processing letters Vol. 28; pp. 314 - 318
Main Authors: Lesouple, Julien, Pilastre, Barbara, Altmann, Yoann, Tourneret, Jean-Yves
Format: Journal Article
Language:English
Published: New York IEEE 01.01.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Institute of Electrical and Electronics Engineers
Subjects:
Algorithms
Computer Science
Distributed databases
Engineering Sciences
Expectation-Maximization Algorithm
Fitting
Hypersphere Fitting
Hyperspheres
Iterative algorithms
Maximum likelihood estimation
Noise measurement
Signal and Image Processing
Signal processing algorithms
Statistical models
Three-dimensional displays
von Mises-Fisher distribution
Maximum likelihood estimation
von Mises-Fisher distribution
Expectation-maximization algorithm
Hypersphere fitting
ISSN:1070-9908, 1558-2361
Online Access:Get full text
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Summary:This letter studies a new expectation maximization (EM) algorithm to solve the problem of circle, sphere and more generally hypersphere fitting. This algorithm relies on the introduction of random latent vectors having a priori independent von Mises-Fisher distributions defined on the hypersphere. This statistical model leads to a complete data likelihood whose expected value, conditioned on the observed data, has a Von Mises-Fisher distribution. As a result, the inference problem can be solved with a simple EM algorithm. The performance of the resulting hypersphere fitting algorithm is evaluated for circle and sphere fitting.
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ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2021.3051851