INTRODUCTION 1 On the consistency of the SIFT Method

This note is devoted to the mathematical arguments proving that Lowe’s Scale-Invariant Feature Transform (SIFT [23]), a very successful image matching method, is indeed similarity invariant. The mathematical proof is given under the assumption that the gaussian smoothing performed by SIFT gives aliasing free sampling. The validity of this main assumption is confirmed by a rigorous experimental procedure. These results explain why SIFT outperforms all other image feature extraction methods when it comes to scale invariance.

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