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Normalized 2-D cross-correlation



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


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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'));

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

c = normxcorr2(onion,peppers);
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.

drawrectangle(gca,'Position',[xoffSet,yoffSet,size(onion,2),size(onion,1)], ...

Input Arguments

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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

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

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

Data Types: double


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.

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

The implementation closely follows the formula from [1]:



  • f is the image.

  • t¯ is the mean of the template

  • f¯u,v is the mean of f(x,y) in the region under the template.


[1] Lewis, J. P. "Fast Normalized Cross-Correlation." Industrial Light & Magic, 1995.

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

Extended Capabilities

Version History

Introduced before R2006a

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See Also