Morel, Jean-Michel; Yu, Guoshen Is SIFT scale invariant? (English) Zbl 1217.68195 Inverse Probl. Imaging 5, No. 1, 115-136 (2011). Summary: This note is devoted to a mathematical exploration of whether Lowe’s Scale-Invariant Feature Transform (SIFT), a very successful image matching method, is similarity invariant as claimed. It is proved that the method is scale invariant only if the initial image blurs are exactly guessed. Yet, even a large error on the initial blur is quickly attenuated by this multiscale method, when the scale of analysis increases. In consequence, its scale invariance is almost perfect. The mathematical arguments are given under the assumption that the Gaussian smoothing performed by SIFT gives an aliasing free sampling of the image evolution. The validity of this main assumption is confirmed by a rigorous experimental procedure, and by a mathematical proof. These results explain why SIFT outperforms all other image feature extraction methods when it comes to scale invariance. Cited in 5 Documents MSC: 68T10 Pattern recognition, speech recognition 68T45 Machine vision and scene understanding 68U10 Computing methodologies for image processing 94A08 Image processing (compression, reconstruction, etc.) in information and communication theory Keywords:SIFT; scale invariance; Shannon interpolation; Gaussian blur; sampling theory; aliasing Software:ASIFT PDFBibTeX XMLCite \textit{J.-M. Morel} and \textit{G. Yu}, Inverse Probl. Imaging 5, No. 1, 115--136 (2011; Zbl 1217.68195) Full Text: DOI