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# Real-time scale selection in hybrid multi-scale representations

## Tony Lindeberg and Lars Bretzner

Technical report CVAP279, ISRN KTH NA/P--03/07--SE. Department of Numerical Analysis and Computer Science, KTH (Royal Institute of Technology), SE-100 44 Stockholm, Sweden, June 2003.

Shortened version in Proc. Scale-Space'03, Isle of Skye, Scotland, Springer Lecture Notes in Computer Science, volume 2695, pages 148-163

## Abstract

Local scale information extracted from visual data in a bottom-up manner constitutes an important cue for a large number of visual tasks. This article presents a framework for how the computation of such scale descriptors can be performed in real time on a standard computer.

The proposed scale selection framework is expressed within a novel type of multi-scale representation, referred to as hybrid multi-scale representation, which aims at integrating and providing variable trade-offs between the relative advantages of pyramids and scale-space representation, in terms of computational efficiency and computational accuracy. Starting from binomial scale-space kernels of different widths, we describe a family pyramid representations, in which the regular pyramid concept and the regular scale-space representation constitute limiting cases. In particular, the steepness of the pyramid as well as the sampling density in the scale direction can be varied.

It is shown how the definition of $\gamma$-normalized derivative operators underlying the automatic scale selection mechanism can be transferred from a regular scale-space to a hybrid pyramid, and two alternative definitions are studied in detail, referred to as variance normalization and $l_p$-normalization. The computational accuracy of these two schemes is evaluated, and it is shown how the choice of sub-sampling rate provides a trade-off between the computational efficiency and the accuracy of the scale descriptors. Experimental evaluations are presented for both synthetic and real data. In a simplified form, this scale selection mechanism has been running for two years, in a real-time computer vision system.

PostScript: (TR 482 kb) (Shortened 393 kb)