Scale-Space Behaviour of Local Extrema and Blobs

Tony Lindeberg

Technical report ISRN KTH/NA/P--92/19--SE.

Published in J. of Mathematical Imaging and Vision, 1(1), pp. 65--99, 1992.

Abstract

We apply elementary techniques from real analysis, singularity theory and statistics to derive analytical results for the behaviour in scale-space of critical points and related entities. The main results of the treatment comprise:

• a description of the general nature of trajectories of critical points in scale-space,
• an estimation of the drift velocity of critical points and straight edges,
• an analysis of the qualitative behaviour of critical points in bifurcation situations, and
• a classification of what types of blob events are possible (annihilation, merge, split, creation).

Keywords scale-space, critical point, bifurcation, singularity, blob, extremum region, blob event, classification, drift velocity, multi-scale representation, computer vision, digital signal processing

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Related work: (Monograph on scale-space theory) (The scale-space primal sketch involving explicit linking of image structures over scales and registration of bifurcation events)