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