Imposing a prescribed motion field to a grayscale image

I have a grayscale image with intensity distribution I1(i,j). I am trying apply a motion field

 u(i,j), v(i,j)

where (i,j) is the index coordinates in the image, u is the horizontal velocity, and v is the vertical velocity. I want to obtain the intensity at the next frame, I2(i,j), after being imposed by the prescribed motion field. In other word, by processing I1 and I2, one should get the motion field u,v. This is how I approached but it does not work:

 % Creating a grayscale image.
 a = 0;
 b = 1;
 I1 = (b-a).*rand(numel(u),1) + a;
 I1 = reshape(I1, size(u));
 I2 = zeros(size(I1));

 InRows    = size(I1, 1);
 InCols    = size(I1, 2);

 % Estimating the intensity field in the next frame.
 for j = 1:size(I1,2)
     for i = 1:size(I1,1)
         i1 = i + (round(v(i,j)));
         j1 = j + (round(u(i,j)));
        
         if i1 > 0 && i1 < (InRows+1) && j1 > 0 && j1 < (InCols+1)
             I2(i1, j1) = max(I2(i1, j1),I1(i, j));
         end
     end
 end

Could someone help me how this can be approached?

[David Young]

You say it does not work - what exactly goes wrong?

Answer 1

[Guillaume]

As David asks, what exactly does not work with your code?

In any case, it looks like a job for imwarp:

I2 = imwarp(I1, cat(3, u, v)); %imwarp with displacement field

Answer 2

[Image Analyst]

Attached is an example for how to shift/move/translate an image with imwarp().