# Sum two matrices shifted by a non integer number?

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MementoMori on 26 Mar 2023
Edited: Matt J on 26 Mar 2023
Suppose we have two matrices A and B, and I want to sum them shifted by a non-integer number of pixels. How can I do it?
For example for a 0.5 shift. We can enlarge them by a factor of 2, sum them shifted by 1 pixel and reduce it by a factor 2.
But this way can be very computational expensive, in particular for a low pixel shift.

Matt J on 26 Mar 2023
Edited: Matt J on 26 Mar 2023
Because of the linearity of interpolation, you should not interpolate each matrix. You should sum the matrices first, then interpolate the result, e.g,
C=imtranslate(A+B,[0.5,0]);
which will cut down the computation by half.

John D'Errico on 26 Mar 2023
There is no magic, whereby you can do things that take computational time, and do them instantly.
What you want to do is implicitly interpolate the images, at sub-pixel levels. You can use interp2 to interpolate one array at a shift of some fractional amount. Then add the results. But no matter what, you will need to perform an interpolation.
MementoMori on 26 Mar 2023
Yes I know, I was wondering if there was a faster way than my idea or interpolation

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