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Is SIFT scale invariant? (English) Zbl 1217.68195

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.

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

Software:

ASIFT
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