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Generalized Normalized Cross Correlation

version (5.3 KB) by Dirk Padfield
Computes the correct NCC at all locations regardless of the relative size of A and TEMPLATE


Updated 19 Apr 2012

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normxcorr2_general computes the normalized cross-correlation of matrices TEMPLATE and A. The resulting matrix C contains correlation coefficients and its values may range from -1.0 to 1.0.

Limitations of normxcorr2:
The documentation of normxcorr2 states that, "The matrix A must be larger than the matrix TEMPLATE for the normalization to be meaningful." It is implemented following the details of the paper "Fast Normalized Cross-Correlation", by J. P. Lewis, Industrial Light & Magic. This approach assumes the template is small relative to the image and proceeds to calculate the normalization across the entire template. This leads to correct computations wherever the template is wholly overlapping with the image, but the computation is incorrect in the borders of the output (the border size is proportional to the template size). This problem is therefore worse for larger templates to the point that, when the template is the same size as the image, the only correct value is at the center pixel (where the images are fully overlapping). Thus, if normxcorr2 is used for such things as registering images of the same size, the result will be incorrect.

The new normxcorr2_general:
normxcorr2_general is more general than normxcorr2 in that it gives correct results everywhere regardless of the relative size of A and TEMPLATE. It accomplishes this by computing the normalized correlation only in the overlap regions between the two matrices. Thus, the result is correct for all locations of correlation. The result is the same as if the NCC were carried out in the spatial domain (which would take a long time to compute for large matrices).

Comments and Ratings (16)

the same issue as Y Fu. I try to estimate the spatial transformation (translation, rotation, and scale) between images. However, the code on your website only return the translation parameter. Could you please release the source code? Thanks for your reply and this excellent work.


The values of TEMPLATE cannot all be the same.
I get this error and I don't know how to get around

Y Fu

Dear Professor
My research is focused on Image Registration. I have recently read your paper "Masked Object Registration in the Fourier Domain ". I find a part of coda on your website However, the code can only get translate parameters between images. I try to validate your simulation results(translation,rotation and scale between images) in my study, but no progress. I am wondering if you could kindly send me all the sources source program and the necessary information about this paper. I promise they will be used only for research purposes.
Thank you very much for your kind consideration and I am looking forward to your early reply.

Leo Shi


Dirk Padfield

In response to Karlien's question, I answered this in detail in the paper "Masked Object Registration in the Fourier Domain", which you can find on my website


Works well. Could you comment on why you are using the rotated template to calculate the local sums of T and T^2? This isn't completely clear to me from the paper of J.P. Lewis. I do understand you need to use the rotated template in the convolution but why should you use it in the local sum calculations as well? Thanks in advance for your answer.

Excellent, better than the built-in normxcorr2


How to Run this Code????
I'm new to this , please some one help me ????


Please indicate that the Image Processing Toolbox is required as it uses functions thereof (at least iptchecknargin).

John B.

Seems to work well. Seems faster than normxcorr2_mex for larger arrays, which is no longer on Matlab Central but is around on the internet.


Made the code independent of the image processing toolbox (IPT). Note that the IPT is needed to run the example since normxcorr2 is part of that toolbox. However, normxcorr2_general does not require the IPT.

Added a new optional parameter. requiredNumberOfOverlapPixels sets to 0 all locations in C computed from positions where A and T overlap less than requiredNumberOfOverlapPixels.

MATLAB Release Compatibility
Created with R2008a
Compatible with any release
Platform Compatibility
Windows macOS Linux