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Fisher-Rao Metric

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Computer Vision

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Synonyms

Rao metric

Related Concepts

Definition

The Fisher-Rao metric is a particular Riemannian metric defined on a parameterized family of conditional probability density functions (pdfs). If two conditional pdfs are near to each other under the Fisher-Rao metric, then the square of the distance between them is approximately equal to twice the average value of the log likelihood ratio of the conditional pdfs. If the log likelihood ratio of the two pdfs is near to zero, then it is difficult to distinguish between them using only sampled values.

Background

Suppose that a parameterized family of conditional pdfs is given and it is required to find the parameter value corresponding to the conditional pdf that best fits a given set of data. It is useful to have a distance function defined on pairs of conditional pdfs, such that if a given conditional pdf is...

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References

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Author information

Authors and Affiliations

  1. Department of Computer Science and Information Systems, Birkbeck College University of London, London, UK

    Stephen J. Maybank

Authors
  1. Stephen J. Maybank
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Corresponding author

Correspondence to Stephen J. Maybank .

Section Editor information

  1. Okayama University, Okayama, Japan

    Kenichi Kanatani

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Maybank, S.J. (2020). Fisher-Rao Metric. In: Computer Vision. Springer, Cham. https://doi.org/10.1007/978-3-030-03243-2_657-1

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  • DOI: https://doi.org/10.1007/978-3-030-03243-2_657-1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-03243-2

  • Online ISBN: 978-3-030-03243-2

  • eBook Packages: Springer Reference Computer SciencesReference Module Computer Science and Engineering

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