Feature detection is an essential task in low-level vision.
Good features are those that resist to different perturbations such as
- noise addition,
- geometric transforms (3D rotation with perspective, scaling),
- radiometric transforms (monotonic or non-monotonic grayscale remapping).
By resistance, I mean that despite those alterations, the same features will continue to be detected.
My question is how can we mathematically express these types of resistance in general terms ? What would be the form of the equations, assuming grayscale images and features defined from the pixel values in a region of arbitrary shape ? (I am not asking for an assessment of the stability of known features described in the literature.)
Answering the question for a 1D signal would already be a good start.
Can anyone help ?