# “Feature detection 2”

## Image transformation

- Geometric: Rotation, Scale
- Photometric: Intensity change

## Invariance and equivariance

We want corner locations to be invariant to photometric transformations and equivariant to geometric transformations

- Invariance: image is transformed and corner locations do not change
- Equavariance: if we have two transformed versions of the same image, features should be detected in corresponding locations

## Some operartion and their characteristic

- Derivatives and window function are equivariant
- Corner location is equivariant w.r.t. translation
- Corner location is equivariant w.r.t. image rotation
- Affine intensity change: Partially invariant to affine intensity change
- Scaling is neither invariant nor equivariant to scaling

## Key idea to scale invariant

find scale that gives local maximum of f

- in both position and scale
- one definition of f: the Harris operator
- Instead of computing f for larger and larger windows, we can implement using a fixed window size with a Gaussian pyramid

## Laplacian of Gaussian

\(\nabla^{2} g=\frac{\partial^{2} g}{\partial x^{2}}+\frac{\partial^{2} g}{\partial y^{2}}\)

This is a “Blob” detector, the maxima and minima of LoG operator in space and scale are blobs in the image

## An alternative

DoG: Difference of Gaussians

[D o G=G(x, y, k \sigma)-G(x, y, \sigma)]