“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)]
