Hypersphere Fitting from Noisy Data Using an EM Algorithm

Julien Lesouple; Barbara Pilastre; Yoann Altmann; Jean-Yves Tourneret

doi:10.1109/LSP.2021.3051851

Hypersphere Fitting from Noisy Data Using an EM Algorithm

Julien Lesouple
, Barbara Pilastre
, Yoann Altmann
, Jean-Yves Tourneret

Research output: Contribution to journal › Article

14 Citations (Scopus)

168 Downloads (Pure)

Abstract

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 indepen- dent 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.

Original language	English
Pages (from-to)	314-318
Number of pages	5
Journal	IEEE Signal Processing Letters
Volume	28
Early online date	14 Jan 2021
DOIs	https://doi.org/10.1109/LSP.2021.3051851
Publication status	Published - 2021

Keywords

Distributed databases
Expectation-Maximization Algorithm
Fitting
Hypersphere Fitting
Iterative algorithms
Maximum Likelihood Estimation
Maximum likelihood estimation
Noise measurement
Signal processing algorithms
Three-dimensional displays
von Mises-Fisher distribution

ASJC Scopus subject areas

Signal Processing
Electrical and Electronic Engineering
Applied Mathematics

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abstract = "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 indepen- dent 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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note = "Funding Information: Manuscript received November 18, 2020; revised January 6, 2021; accepted January 11, 2021. Date of publication January 14, 2021; date of current version February 10, 2021. This work was supported by the Royal Academy of Engineering under the Research Fellowship scheme RF201617/16/31. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Pu Wang. (Corresponding author: Julien Lesouple.) Julien Lesouple and Barbara Pilastre are with the T{\'e}SA, 31500 Toulouse, France (e-mail: [email protected]; [email protected]). Publisher Copyright: {\textcopyright} 1994-2012 IEEE. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",

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PY - 2021

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N2 - 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 indepen- dent 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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KW - Fitting

KW - Hypersphere Fitting

KW - Iterative algorithms

KW - Maximum Likelihood Estimation

KW - Maximum likelihood estimation

KW - Noise measurement

KW - Signal processing algorithms

KW - Three-dimensional displays

KW - von Mises-Fisher distribution

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JO - IEEE Signal Processing Letters

JF - IEEE Signal Processing Letters

ER -

Hypersphere Fitting from Noisy Data Using an EM Algorithm

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Keywords

ASJC Scopus subject areas

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