# Pearson’s Correlation

Calculate correlations between two channels within regions of interest. Returns Pearson’s product-moment correlation coefficient for pixel values on two channels within each region of interest (ROI).

## Input Parameters

#### Image

Expects arbitrary bit-depth images with at least 2 channels.

Type: Image File (`imagej.data.Dataset`)

#### Region of Interest

Set of ROIs defining the regions for which correlations will be calculated.

Type: ROI Set (file) (`imagej.data.overlay.AbstractOverlay[]`)

#### Channel 1 (1-based index)

First channel on which to calculate correlations. Specified using a 1-based index (`1 ≤ x ≤ # of channels`).

Type: Integer (`int`)

#### Channel 2 (1-based index)

Second channel on which to calculate correlations. Specified using a 1-based index (`1 ≤ x ≤ # of channels`).

Type: Integer (`int`)

## Results

One result row is produced for each ROI.

#### R

Correlation coefficient computed for pixel values on the selected two channels within the ROI.

∑[(A_{i} − mean(A)) × (B_{i} − mean(B))] ⁄ sqrt[(A_{i} − mean(A))^{2} × B_{i} − mean(B))^{2}]

`A`_{i}, pixel value on first channel

`B`_{i}, pixel value on second channel

`mean(A)`, mean value on first channel within the ROI

`mean(B)`, mean value on second channel within the ROI

Type: Numeric (`float`)