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Hypersphere fitting from noisy data using an EM algorithm

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 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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Submitted on : Monday, August 30, 2021 - 8:36:06 PM
Last modification on : Tuesday, October 19, 2021 - 2:24:25 PM

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Julien Lesouple, Barbara Pilastre, Yoann Altmann, Jean-Yves Tourneret. Hypersphere fitting from noisy data using an EM algorithm. IEEE Signal Processing Letters, Institute of Electrical and Electronics Engineers, 2021, 28, pp.314-318. ⟨10.1109/LSP.2021.3051851⟩. ⟨hal-03329377⟩

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