SIFT, keypoints, F-transform, non-local Laplacian

We propose a sound theoretical justification for the widely accepted heuristic of choosing keypoints. We show that if the keypoints are selected as points where a non-local Laplacian reaches its extreme values, then there exists an inverse F-transform operator that computes an approximation of an original image with a suitable (high) quality. Theoretical results are supported by numerical tests and illustrations.