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Hypersphere Fitting From Noisy Data Using an EM Algorithm
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DOI：10.1109/LSP.2021.3051851.png)
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Abstract
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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.
Keywords:
Signal processing algorithms
Maximum likelihood estimation
Noise measurement
Three-dimensional displays
Fitting
Iterative algorithms
Distributed databases
Hypersphere Fitting
Maximum Likelihood Estimation
Expectation-Maximization Algorithm
von Mises-Fisher distribution
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