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

By structure matrix I mean:

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

  • $\begingroup$ Could you please tell us what you do consider to be a structure matrix, and where you found the reference? $\endgroup$ Sep 24, 2019 at 15:40
  • 1
    $\begingroup$ I have added the definition of that to my question and it is from Wikipedia $\endgroup$
    – Keivan
    Sep 24, 2019 at 17:06
  • $\begingroup$ OK, I know it under the names: structure tensor or second-order matrix $\endgroup$ Sep 24, 2019 at 17:09

1 Answer 1


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 $w$.

From this matrix, different quantities can be computed, that provide interesting attributes for image analysis. Structure tensors, or second-order matrices, have been used for image segmentation, especially with geodesic or level-set methods, as they can provide insights to image textures or orientations.


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