The most popular image matching algorithm SIFT, introduced by D. Lowe adecade ago, has proven to be sufficiently scale invariant to be used innumerous applications. In practice, however, scale invariance may be weakenedby various sources of error inherent to the SIFT implementation affecting thestability and accuracy of keypoint detection. The density of the sampling ofthe Gaussian scale-space and the level of blur in the input image are two ofthese sources. This article presents a numerical analysis of their impact onthe extracted keypoints stability. Such an analysis has both methodological andpractical implications, on how to compare feature detectors and on how toimprove SIFT. We show that even with a significantly oversampled scale-spacenumerical errors prevent from achieving perfect stability. Usual strategies tofilter out unstable detections are shown to be inefficient. We also prove thatthe effect of the error in the assumption on the initial blur is asymmetric andthat the method is strongly degraded in presence of aliasing or without acorrect assumption on the camera blur.
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