normxcorr2 (Image Processing Toolbox User's Guide)

Image Processing Toolbox User's Guide

Normalized two-dimensional 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 of class uint8, uint16, or double.

Algorithm

normxcorr2 uses the following general procedure:

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. [2]

Example

T = .2*ones(11); % make light gray plus on dark gray background
T(6,3:9) = .6;
T(3:9,6) = .6;
BW = T>0.5;      % make white plus on black background
imshow(BW), title('Binary')
figure, imshow(T), title('Template')

% make new image that offsets template T
T_offset = .2*ones(21);
offset = [3 5];  % shift by 3 rows, 5 columns
T_offset( (1:size(T,1))+offset(1), (1:size(T,2))+offset(2) ) = T;
imshow(T_offset), title('Offset Template')

% cross-correlate BW and T_offset to recover offset
cc = normxcorr2(BW,T_offset);
[max_cc, imax] = max(abs(cc(:)));
[ypeak, xpeak] = ind2sub(size(cc),imax(1));
corr_offset = [ (ypeak-size(T,1)) (xpeak-size(T,2)) ];
isequal(corr_offset,offset) % 1 means offset was recovered

See Also

corrcoef

References

[1] Lewis, J. P., "Fast Normalized Cross-Correlation," Industrial Light & Magic, <http://www.idiom.com/~zilla/Papers/nvisionInterface/nip.html>

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

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