Scale-Space Behaviour and Invariance Properties of Differential Singularities

Tony Lindeberg

Technical report ISRN KTH/NA/P--92/26--SE.

Shortened version in: Y. O. Ying, A. Toet, D. Foster, H. Heijmanns and P. Meer (eds.) (1994) Shape in Picture: Mathematical Description of Shape in Grey-Level Images, (Proc. of workshop in Driebergen, Netherlands, Sep. 7--11, 1992). NATO ASI Series F, vol. 126, Springer-Verlag, pp. 591--600.

Abstract

This article describes how a certain way of expressing low-level feature detectors, in terms of singularities of differential expressions defined at multiple scales in scale-space, simplifies the analysis of the effect of smoothing. It is shown how such features can be related across scales, and generally valid expressions for drift velocities are derived with examples concerning edges, junctions, Laplacean zero-crossings, and blobs. A number of invariance properties are pointed out, and a particular representation defined from such singularities, the scale-space primal sketch, is treated in more detail.

Keywords: scale-space, drift velocity, feature detection, primal sketch, singularity, invariance.

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