normxcorr2

Normalized 2-D cross-correlation

Syntax

C = normxcorr2(template,A)

Description

C = normxcorr2(template,A) computes the normalized cross-correlation of the matrices template and A. The resulting matrix C contains the correlation coefficients.

Examples

Use Cross-Correlation to Find Template in Image

Read two images into the workspace, and convert them to grayscale for use with normxcorr2. Display the images side-by-side.

onion = im2gray(imread('onion.png'));
peppers = im2gray(imread('peppers.png'));
montage({peppers,onion})

Perform cross-correlation, and display the result as a surface.

c = normxcorr2(onion,peppers);
surf(c)
shading flat

Find the peak in cross-correlation.

[ypeak,xpeak] = find(c==max(c(:)));

Account for the padding that normxcorr2 adds.

yoffSet = ypeak-size(onion,1);
xoffSet = xpeak-size(onion,2);

Display the matched area by using the drawrectangle function. The 'Position' name-value pair argument specifies the upper left coordinate, width, and height of the ROI as the 4-element vector [xmin,ymin,width,height]. Specify the face of the ROI as fully transparent.

imshow(peppers)
drawrectangle(gca,'Position',[xoffSet,yoffSet,size(onion,2),size(onion,1)], ...
    'FaceAlpha',0);

Input Arguments

template — Input template

numeric matrix

Input template, specified as a numeric matrix. The values of template cannot all be the same.

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

A — Input image

numeric matrix

Input image, specified as a numeric image. A must be larger than the matrix template for the normalization to be meaningful.

Normalized cross-correlation is an undefined operation in regions where A has zero variance over the full extent of the template. In these regions, normxcorr2 assigns correlation coefficients of zero to the output C.

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

Output Arguments

C — Correlation coefficients

numeric matrix

Correlation coefficients, returned as a numeric matrix with values in the range [-1, 1].

Data Types: double

Algorithms

normxcorr2 uses the following general procedure [1], [2]:

1. Calculate cross-correlation in the spatial or the frequency domain, depending on size of images.

2. Calculate local sums by precomputing running sums [1].

3. Use local sums to normalize the cross-correlation to get correlation coefficients.

The implementation closely follows the formula from [1]:

$$\gamma (u,v)=\frac{{\displaystyle {\sum }_{x,y}\left[f\left(x,y\right)-{\overline{f}}_{u,v}\right]\left[t\left(x-u,y-v\right)-\overline{t}\right]}}{{\left\{{{\displaystyle {\sum }_{x,y}\left[f\left(x,y\right)-{\overline{f}}_{u,v}\right]}}^2{\displaystyle {\sum }_{x,y}{\left[t(x-u,y-v)-\overline{t}\right]}^2}\right\}}^{0.5}}$$

where

• $$f$$ is the image.

• $$\overline{t}$$ is the mean of the template

• $${\overline{f}}_{u,v}$$ is the mean of $$f(x,y)$$ in the region under the template.

References

[1] Lewis, J. P., "Fast Normalized Cross-Correlation," Industrial Light & Magic

[2] Haralick, Robert M., and Linda G. Shapiro, Computer and Robot Vision, Volume II, Addison-Wesley, 1992, pp. 316-317.

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.