paper critique & summarization : Scale & Affine Invariant Interest Point Detectors

Title : Scale & Affine Invariant Interest Point Detectors
Author: K. Mikolajczyk and C. Schmid

This paper proposes a method for detecting interest points invariant to scale and affine transformations. It combines the Harris detector with Laplacian to get the goal.

Harris detector is a interest point detector, but it is not invariant to scale changes. To solve this problem, they generate multi-scale for each point, and use Laplacian-of-Faussians to find the highest percentage of correct characteristic scales. Then can generate a scale invariant detector, and they call it "Harris-Laplace detector".

And for the affine invariant interest point detector, because the Harris-Laplace detector could not reflect the real transformation of a point when it has not only scale change but also affine transformation. They use the "Second Moment Matrix" to fix the problem. But in fact, the math formulas is hard for me.

And the "Harris-Affine Interest Point Detector" which they propose have the following parts:
1. spatial localization - determined by the local maximum of the Harris function.
2. integration scale - selected at the extremum over scale of the normalized Laplacian.
3. differentiation scale - selected at the maximum of normalized isotropy
4. shape adaptation matrix - estimated with the second moment matrix.