calculating the provide integral

hello all. I want to calculate this integral. this formula is for image registration, but for practice, I work with 1D signla.I have I1 and I2 and u(x). I1 and I2 are a 3000*1 matrices. I meshed 1d signal and divided into the 600 element. I am wondering how I should calculate this integral. thank you.

[Matt J]

Is there any reason you are pursuing your own implementation, as opposed to using imregister()?

[Walter Roberson]

When I look at that integral, it looks to me as if I1 and I2 are intended to be functions, not matrices.

If they are matrices then we have to ask whether x is a scalar or a matrix, and whether u(x) is a scalar or a matrix, so that we can tell if is an element-by-element multiplication or a matrix multiplication.

Answer 1

[Matt J]

A common approach is to discretize the integral and instead compute sum of squared differences (SSD), e.g.,

SSD=norm( interp1(x,I2,x+u,'cubic',0) -I1).^2/2