Feature Point

# Keypoint

Notes taken from Cyrill Stachniss.

Resources

Corner = two edges in roughly orthogonal directions Edge = a sudden brightness change

Corners are great because they are very localizable in varying lighting conditions. This is why people focus on corners to get keypoints.

##### Finding Corners

To find corners we need to search for intensity changes in two directions.

Compute the SSD of neighbour pixels around

• is the actual intensity value of the pixel at position
• and are simply small displacement values, they are NOT partial derivatives
• is a local patch around

Using Taylor expansion, we obtain that is approximately Plugging back into , we see that the taylor approximation leads to Written in a matrix form as

• the derivation for this comes from expanding

We can move the sums inside the matrix to get the Structure Matrix!

J_x J_y has become J_y J_x for one of the terms?

This is more for convenience. and are merely real numbers.

Eigenvalue and Jacobian Matrix?

Cyrill talks about Eigenvalues at 19:30 when referencing the structure matrix. What do eigenvalues have to do with the eigenvalue?? I think of it as just a large value signifies a large change, high gradient.

Also, how are we going to deal with different orientations?

βWe want to find a matrix with 2 large eigenvaluesβ. That makes it a good corner.

He thens introduces 3 similar approaches that were introduced in the 1990s for feature detection:

All of them rely on the Structure Matrix, but they use a different criterion to decide if a point is corner or not.

I don't really understand the eigenvalue part of this....

I guess I donβt really understand how eigenvalues work, so it is important to review that.

Consider points as corners if their structure matrix has two large eigenvenlues values.

Implementation Remarks

• RGB to gray-scale conversion first
• Real images are affected by noise, smoothing of the input is suggested

This is a great summary diagram, to see high level how things work

### Part 2: Difference of Gaussians

Used for SIFT descriptors

In Summary

The 2 approaches are key ingredients of most hand-designed features

Nowadays, features completely learned from data.