corr2

2-D correlation coefficient

Syntax

R = corr2(A,B)

Description

R = corr2(A,B) returns the 2-D correlation coefficient R between arrays A and B.

You optionally can compute the correlation coefficient using a GPU (requires Parallel Computing Toolbox™). For more information, see Image Processing on a GPU.

Examples

Compute the correlation coefficient

Compute the correlation coefficient between an image and the same image processed with a median filter.

I = imread('pout.tif');
J = medfilt2(I);
R = corr2(I,J)

R = 0.9959

Compute the Correlation Coefficient on a GPU

Compute the correlation coefficient on a GPU between an image and the same image processed using standard deviation filtering.

I = gpuArray(imread('pout.tif'));
J = stdfilt(I);
R = corr2(I,J)

R =

    0.2762

Input Arguments

A — First input array

numeric array | logical array | gpuArray

First input array, specified as a numeric or logical array.

To perform the computation using a GPU, specify A as a gpuArray that contains a numeric or logical array.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical

B — Second input array

numeric array | logical array | gpuArray

Second input array, specified as a numeric or logical array. B has the same size as the first input array, A.

To perform the computation using a GPU, specify B as a gpuArray that contains a numeric or logical array.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical

Output Arguments

R — Correlation coefficient

numeric scalar | gpuArray

Correlation coefficient, returned as a numeric scalar.

If the correlation coefficient is computed using a GPU, then R is returned as a gpuArray containing a numeric scalar.

Data Types: double

Algorithms

corr2 computes the correlation coefficient using

$$r=\frac{{\displaystyle \sum _m{\displaystyle \sum _n(A_{mn}-\overline{A})(B_{mn}-\overline{B})}}}{\sqrt{\left({\displaystyle \sum _m{\displaystyle \sum _n{\left(A_{mn}-\overline{A}\right)}^2}}\right)\left({\displaystyle \sum _m{\displaystyle \sum _n{\left(B_{mn}-\overline{B}\right)}^2}}\right)}}$$

where $$\overline{A}$$ = mean2(A), and $$\overline{B}$$ = mean2(B).

Extended Capabilities

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Image Processing on a GPU.