# What does structure matrix do

can anybody explain to me what does structure matrix exactly do in image processing? What happens to the pixels?

By structure matrix I mean:

$$S_w[p] = \begin{pmatrix} \sum_{r}w(r)[I_x(p-r)]^2 & \sum_{r}w(r)[I_x(p-r) I_y(p-r)] \\ \sum_{r}w(r)[I_x(p-r) I_y(p-r)] & \sum_{r}w(r)[I_y(p-r)]^2 \end{pmatrix}$$

• Could you please tell us what you do consider to be a structure matrix, and where you found the reference? – Laurent Duval Sep 24 '19 at 15:40
• I have added the definition of that to my question and it is from Wikipedia – Keivan Sep 24 '19 at 17:06
• OK, I know it under the names: structure tensor or second-order matrix – Laurent Duval Sep 24 '19 at 17:09

At each pixel $$p$$, this $$2\times 2$$ matrix summarizes the local behavior of the image (structure) inside a neighborhood of pixel $$p$$ (a neighborhood weighted by function $$w$$.