Scale-Space

Tony Lindeberg

In: Encyclopedia of Computer Science and Engineering (Benjamin Wah, ed), John Wiley and Sons, Volume~IV, pages 2495--2504, Hoboken, New Jersey, Jan 2009. dx.doi.org/10.1002/9780470050118.ecse609 (Sep 2008)

Abstract

Scale-space theory is a framework for multi-scale image representation, which has been developed by the computer vision community with complementary motivations from physics and biological vision. The idea is to handle the multi-scale nature of real-world objects, which implies that objects may be perceived in different ways depending on the scale of observation. If one aims at developing automatic algorithms for interpreting images of unknown scenes, there is no way to know a priori what scales are relevant. Hence, the only reasonable approach is to consider representations at all scales simultaneously. From axiomatic derivations is has been shown that given the requirement that coarse-scale representations should correspond to true simplifications of fine scale structures, convolution with Gaussian kernels and Gaussian derivatives is singled out as a canonical class of image operators for the earliest stages of visual processing. These image operators can be used as basis for solving a large variety of visual tasks, including feature detection, feature classification, stereo matching, motion descriptors, shape cues and image-based recognition. By complementing scale-space representation with a module for automatic scale selection based on the maximization of normalized derivatives over scales, early visual modules can be made scale invariant. In this way, visual modules will be able to automatically adapt to the unknown scale variations that may occur due to objects and substructures of varying physical size as well as objects with varying distances to the camera. An interesting similarity to biological vision is that the scale-space operators closely resemble receptive field profiles registered in neurophysiological studies of the mammalian retina and visual cortex.

Keywords: computer vision; image processing; multi-scale representation; gaussian smoothing; wavelets; feature detection; feature classification; scale selection; scale invariance; image-based recognition

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Earlier overviews of scale-space methods can be found in:

• T. Lindeberg: "Principles for automatic scale selection", Technical report ISRN KTH NA/P--98/14--SE. Revised version in: B. Jähne (et al., eds.), Handbook on Computer Vision and Applications, volume 2, pp 239--274, Academic Press, Boston, USA, 1999.

• T. Lindeberg: "Automatic scale selection as a pre-processing stage to interpreting the visual world", Invited paper in: D. Chetverikov and T. Sziranyi (eds) Proc. Fundamental Structural Properties in Image and Pattern Analysis FSPIPA'99 (Budapest, Hungary), September 6-7, 1999. Schriftenreihen der Österreichischen Computer Gesellschaft, volume 130, pp 9--23.

• T. Lindeberg: "Scale-space: A framework for handling image structures at multiple scales", Proc. CERN School of Computing, Egmond aan Zee, The Netherlands, 8--21 September, 1996.

• Lindeberg: ``Scale-space theory: A basic tool for analysing structures at different scales'', J. of Applied Statistics, 21(2), pp. 224--270, 1994. (Supplement on Advances in Applied Statistics: Statistics and Images: 2).

• T. Lindeberg: Scale-Space Theory in Computer Vision, Kluwer Academic Publishers, Dordrecht, Netherlands, 1994.