# Structure Matrix

Taught to me by Cyrill Stachniss.

The structure matrix is key to finding edges and corners in an image. It encodes the changes in image intensities in a local area.

- summarizes the dominant directions of the gradient around a point

The structure matrix is constructed by computing gradients (partial derivatives) of the image in both $x$ and $y$ direction

- Here, $J_{x}โ$ and $J_{y}โ$ are the gradients (jacobians) of the image at that local patch $W$

How can we calculate these gradients? It seems super intimidating, but you can simply use a kernel!

Use these two approximations:

- $J_{x}=D_{x}โI$
- $J_{y}=D_{y}โI$

https://www.ipb.uni-bonn.de/html/teaching/photo12-2021/2021-pho1-10-features-keypoints.pptx.pdf

Go to Keypoint to see more about the ways this structure matrix is precisely calculated.

### Derivation

The derivation of a structure matrix comes from the idea that we need to search for intensity changes in two directions.