Harris corner detector
[Derivative Filter](https://texonom.com/derivative-filter-1c54bd4735874bfabc93b6946b019936) 


### Using that significant change exists to all direction in Derivative Filter at the corner
It shows orientation and magnitude
- Harris corner response is invariant to rotation ([Eigenvalue](https://texonom.com/eigenvalue-4dff6b022dd94d19b3791eef258bf9c5) is same)
- Harris corner detector is not invariant to scale
The surface $E(u,v)$ is locally approximated by a quadratic form

[Second Moment Matrix](https://texonom.com/second-moment-matrix-11b24324bf3c480eaa71412dab72369e)

## Error Function
### for each point

1. pick small region [Window Function](https://texonom.com/window-function-84df809a43bb436c8e95a78198dea06f) or [Gaussian Filter](https://texonom.com/gaussian-filter-f20f04a4f6964292a8032243414766e1) 
2. compute derivatives
3. compute products of derivatives at every pixel
4. compute the sums of products of derivatives at each pixel and subtract it [DC bias](https://texonom.com/dc-bias-718d4831a85b482db2f7f7290d07bdef) 
5. Compute the covariance matrix (M 모양)
6. Compute [Eigenvector](https://texonom.com/eigenvector-d2424f7eaea4443d81105606ebf4e975) and eigenvalues
> ![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F14793ae2-7822-4010-b2aa-d1f4751124c4%2FUntitled.png?table=block&id=a47a3af1-f9d4-420d-8dd7-9857b10463e2&cache=v2)
7. Use threshold on a function of eigenvalues to detect corners
> ![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2Ff4940fbe-cbf7-40d0-9881-5bb5d378129e%2FUntitled.png?table=block&id=7b6a2c18-f2aa-4097-8127-2a9ae136d155&cache=v2)
> ![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2Febc8d0ec-f7ac-46dc-a1b8-59a5e3164312%2FUntitled.png?table=block&id=00008d8e-993b-4ca2-985e-2d00ea2768b2&cache=v2)
![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2Fb1c11886-71ff-4a8e-b945-7ae0822d2822%2FUntitled.png?table=block&id=715b4172-d1e2-444c-a6e3-f6b3c38f7148&cache=v2)
[Paraboloid](https://texonom.com/paraboloid-ea4b361db9d342909a517fdabbf50ef6) 

![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2Fbf5e03f0-ca96-4da9-8955-0d8ba1dd3c88%2FUntitled.png?table=block&id=5ef1b944-98ea-48e8-a0eb-495a9dee98cd&cache=v2)


### Pros
- Corner response R is invariant to image rotation
- R is Partial invariance to affine intensity change (shift and intensity scale)

### Limitation
- 색변화만 감지한다
- not invariant to scale so we need multi-scale detection (can’t auto select)
- 주변만 고려한다 





