Harris Corners Detector squared derivatives

Question

I have trouble understanding something (small) regarding the math behind Harris Corners Detector. (for example I looked at this explanation - https://aishack.in/tutorials/harris-corner-detector/)

In the equation we get there are squared derivative matrices - $I_x^2, I_y^2$ and also $I_x \times I_y$. I've seen code implementations of this around the web, and it seems to me that these multiplications are element-wise. My question why? I thought that when you take the square of a matrix it should be matrix multiplication, and not element-wise multiplication...

I'd really appreciate some clarifications regarding this, Thank you

Answer 1

I think this part in article is starting point of the confusion :

See how the $I(x+u, y+v)$ changed into a totally different form $I(x,y)+ uI_x + vI_y)$?

The author should have write a bit more detailed notation as:

$I(x,y)+ uI_x(x,y) + vI_y(x,y)$

i.e. pointing out that these are element-wise spatial derivatives (like Sobel) not matrix derivatives ( those x and y indicate horizontal and vertical spatial derivative).