Keypoint

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, $J_x$ and $J_y$ 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!

• Sobel Operator
• Scharr Operator

Use these two approximations:

• $J_x=D_x\ast I$
• $J_y=D_y\ast I$

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.