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medpy.metric.histogram.correlate

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

Correlation between two histograms.

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

\[d_{corr}(H, H') = \frac{ \sum_{m=1}^M (H_m-\bar{H}) \cdot (H'_m-\bar{H'}) }{ \sqrt{\sum_{m=1}^M (H_m-\bar{H})^2 \cdot \sum_{m=1}^M (H'_m-\bar{H'})^2} }\]

with \(\bar{H}\) and \(\bar{H'}\) being the mean values of \(H\) resp. \(H'\)

Attributes:

  • not a metric, a similarity

Attributes for normalized histograms:

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

Attributes for not-normalized histograms:

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

Attributes for not-equal histograms:

  • not applicable
Parameters:

h1 : sequence

The first histogram.

h2 : sequence

The second histogram, same bins as h1.

Returns:

correlate : float

Correlation between the histograms.

Notes

Returns 0 if one of h1 or h2 contain only zeros.