Standard Article


  1. Tony Lindeberg

Published Online: 15 SEP 2008

DOI: 10.1002/9780470050118.ecse609

Wiley Encyclopedia of Computer Science and Engineering

Wiley Encyclopedia of Computer Science and Engineering

How to Cite

Lindeberg, T. 2008. Scale-Space. Wiley Encyclopedia of Computer Science and Engineering. 2495–2504.

Author Information

  1. KTH (Royal Institute of Technology), Stockholm, Sweden

Publication History

  1. Published Online: 15 SEP 2008


Scale-space theory is a framework for multiscale image representation, which has been developed by the computer vision community with complementary motivations from physics and biologic vision. The idea is to handle the multiscale nature of real-world objects, which implies that object may be perceived in different ways depending on the scale of observation. If one aims to develop automatic algorithms for interpreting images of unknown scenes, no way exists 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 forthe earliest stages of visual processing. These image operators can be used as basis to solve 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 canadapt automatically to the unknown scale variations that may occur because of objects and substructures of varying physical size as well as objects with varying distances to the camera. An interesting similarity to biologic vision is that the scale-space operators resemble closely receptive field profiles registered in neurophysiologic studies of the mammalian retina and visual cortex.


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