To compare
pixels that are not at integer grid points, we resample the image.
Assume
image is locally bilinear.
I(x,y) =
ax + by + cxy + d = 0. Given the value
of the image at four points: I(x,y),
I(x+1,y), I(x,y+1), I(x+1,y+1) we can
solve for a,b,c,d linearly. Then, for
any u between x and x+1, for any v
between y and y+1, we use this
equation to find I(u,v).