Image Processing Toolbox™

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 matrix A must be larger than the matrix template for the normalization to be meaningful. The values of template cannot all be the same. The resulting matrix C contains the correlation coefficients, which can range in value from -1.0 to 1.0.

Class Support

The input matrices can be numeric. The output matrix C is double.

Algorithm

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

Calculate cross-correlation in the spatial or the frequency domain, depending on size of images.
Calculate local sums by precomputing running sums. [1]
Use local sums to normalize the cross-correlation to get correlation coefficients.

The implementation closely follows following formula from [1]:

where

is the image.
is the mean of the template
is the mean of in the region under the template.

Examples

template = .2*ones(11); % Make light gray plus on dark gray background
template(6,3:9) = .6;   
template(3:9,6) = .6;
BW = template > 0.5;      % Make white plus on black background
figure, imshow(BW), figure, imshow(template)
% Make new image that offsets the template
offsetTemplate = .2*ones(21); 
offset = [3 5];  % Shift by 3 rows, 5 columns
offsetTemplate( (1:size(template,1))+offset(1),...
                (1:size(template,2))+offset(2) ) = template;
figure, imshow(offsetTemplate)
    
% Cross-correlate BW and offsetTemplate to recover offset  
cc = normxcorr2(BW,offsetTemplate); 
[max_cc, imax] = max(abs(cc(:)));
[ypeak, xpeak] = ind2sub(size(cc),imax(1));
corr_offset = [ (ypeak-size(template,1)) (xpeak-size(template,2)) ];
isequal(corr_offset,offset) % 1 means offset was recovered

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.

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