# Harris Corners Detector squared derivatives

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

• back then I made the same assumption reading that article, but as you noticed everything element wise – MimSaad Feb 7 '20 at 15:45

## 1 Answer

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).