The Scale space theory is a framework for multi-scale signal representation. It is a formal theory of how to describe image structures at different scales.

Image representations can be made invariant to scales, i.e. to various distances, by blob-detection (finding local minima in gray level) at different convolutions of the Gaussian kernel (in analogy to a watershed). The scale space of an image is defined as a function

that is produced from the convolution of the Gaussian,

with an input image

:

,

where '*' is the convolution operation in x and y, and

.

Operations like feature detection, feature classification, and shape computation can be based upon scale space representations in terms of combinations of Gaussian derivatives at multiple scales.

Since the early 1990s Tony Lindeberg published and researched scale space at the Royal Institute of Technology (KTH), Stockholm, Sweden.

selected references

• Lindeberg, Tony, Scale-Space Theory in Computer Vision, Kluwer Academic Publishers, 1994, ISBN 0-7923-9418-6
• Lindeberg, Tony, "Scale-space: A framework for handling image structures at multiple scales", In: Proc. CERN School of Computing, Egmond aan Zee, The Netherlands, 8-21 September, 1996
• Lowe, D. G., “Distinctive Image Features from Scale-Invariant Keypoints”, International Journal of Computer Vision, 60, 2 (2004), pp. 91-110

see also

• pyramids (image processing)
• wavelets
• multi-grid methods

external links

• Lecture on scale-space at the University of Massachusetts (pdf)