Hypersphere Fitting from Noisy Data Using an EM Algorithm

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

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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.
Original languageEnglish
Pages (from-to)314-318
Number of pages5
JournalIEEE Signal Processing Letters
Volume28
Early online date14 Jan 2021
DOIs
Publication statusPublished - 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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