# Computer Vision - What are the possible values for indices in auto correlation function for Harris Corner Detector?

The auto correlation function for Harris Corner Detector is defined as

$$E(u, v) = \Sigma_{x, y} w(x, y) [I(x + u, y + v) - I(x, y)]^ 2$$

The idea here is that we will consider a patch around a point in the image and we will displace this patch to a small extent to see the variation in the $$E$$. If the variation is large in all directions, the point/ patch can be considered as a corner. We also use a window or weight function, for smoothing or averaging. Here $$(u, v)$$ are displacement and $$(x, y)$$ are pixel coordinates/ indices. I am trying to understand what range of values can these variables have and how this auto correlation function works. The $$I$$ indicates image and $$w$$ indicates window/ weight function.

Let's consider an image of size 10 x 10 and patches of size 3 x 3. The value of both $$u$$ and $$v$$ can be in the range {-1, 0, 1}. Let us say we are trying to see if a point (3, 3) and associated patch is a corner or not. In this case, the $$x$$ and $$y$$ will have values in the range {2, 3, 4}. I am making an assumption that $$x$$ and $$y$$ will always belong to a set of original image pixel coordinates. However, for a particular patch, this set will have only 3 values since the patch size is 3.

Q1) Does $$u$$ and $$v$$ have the right range of values?

Q2) Is the assumption regarding values of $$x$$ and $$y$$ correct?

Q3) Are we evaluating a point or a patch to be called a corner?

I believe that my story regarding the values acquired by $$x$$, $$y$$, $$u$$ and $$v$$ are consistent upto this point. However, the values of $$x$$ and $$y$$ does not make sense when we consider the window or weight function.

Q4) Shouldn't weight function have another set of variables to indicate its indices or am I selecting the values for $$x$$ and $$y$$ wrong?