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medpy.metric.histogram.fidelity_based

medpy.metric.histogram.fidelity_based(h1, h2)[source]

Fidelity based distance.

Also Bhattacharyya distance; see also the extensions noelle_1 to noelle_5.

The metric between two histograms \(H\) and \(H'\) of size \(m\) is defined as:

\[d_{F}(H, H') = \sum_{m=1}^M\sqrt{H_m * H'_m}\]

Attributes:

  • not a metric, a similarity

Attributes for normalized histograms:

  • \(d(H, H')\in[0, 1]\)
  • \(d(H, H) = 1\)
  • \(d(H, H') = d(H', H)\)

Attributes for not-normalized histograms:

  • not applicable

Attributes for not-equal histograms:

  • not applicable
Parameters:

h1 : sequence

The first histogram, normalized.

h2 : sequence

The second histogram, normalized, same bins as h1.

Returns:

fidelity_based : float

Fidelity based distance.

Notes

The fidelity between two histograms \(H\) and \(H'\) is the same as the cosine between their square roots \(\sqrt{H}\) and \(\sqrt{H'}\).