How to use SIFT algorithm to compute how similar two images are?

Question

I have used the SIFT implementation of Andrea Vedaldi, to calculate the sift descriptors of two similar images (the second image is actually a zoomed in picture of the same

Answer 1

If you want just compare zoomed and rotated image with known center of rotation you can use phase correlation in log-polar coordinates. By sharpness of peak and histogram of phase correlation you can judge how close images are. You can also use euclidean distance on absolute value of Fourier coefficients.

If you want compare SIFT descriptor, beside euclidean distance you can also use "diffuse distance" - getting descriptor on progressively more rough scale and concatenating them with original descriptor. That way "large scale" feature similarity would have more weight.