TY - JOUR
T1 - Hypersphere Fitting from Noisy Data Using an EM Algorithm
AU - Lesouple, Julien
AU - Pilastre, Barbara
AU - Altmann, Yoann
AU - Tourneret, Jean-Yves
N1 - 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 TéSA, 31500 Toulouse, France (e-mail: [email protected]; [email protected]).
Publisher Copyright:
© 1994-2012 IEEE.
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2021
Y1 - 2021
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.
AB - 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.
KW - Distributed databases
KW - Expectation-Maximization Algorithm
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
UR - http://www.scopus.com/inward/record.url?scp=85099729265&partnerID=8YFLogxK
U2 - 10.1109/LSP.2021.3051851
DO - 10.1109/LSP.2021.3051851
M3 - Article
SN - 1070-9908
VL - 28
SP - 314
EP - 318
JO - IEEE Signal Processing Letters
JF - IEEE Signal Processing Letters
ER -