Sum two matrices shifted by a non integer number?

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.

Answer 1

[Matt J]

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.

Answer 2

[John D'Errico]

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]

Yes I know, I was wondering if there was a faster way than my idea or interpolation