Scale-Space Diagram

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A Scale-Space Diagram is a Multiscale Signal Representation that can handle image structure at different scales.



References

2020a

  • (Wikipedia, 2020) ⇒ https://en.wikipedia.org/wiki/Scale_space Retrieved:2020-1-21.
    • Scale-space theory is a framework for multi-scale signal representation developed by the computer vision, image processing and signal processing communities with complementary motivations from physics and biological vision. It is a formal theory for handling image structures at different scales, by representing an image as a one-parameter family of smoothed images, the scale-space representation, parametrized by the size of the smoothing kernel used for suppressing fine-scale structures[1][2][3][4][5][6][7] The parameter [math]\displaystyle{ t }[/math] in this family is referred to as the scale parameter, with the interpretation that image structures of spatial size smaller than about [math]\displaystyle{ \sqrt{t} }[/math] have largely been smoothed away in the scale-space level at scale [math]\displaystyle{ t }[/math] .

      The main type of scale space is the linear (Gaussian) scale space, which has wide applicability as well as the attractive property of being possible to derive from a small set of scale-space axioms. The corresponding scale-space framework encompasses a theory for Gaussian derivative operators, which can be used as a basis for expressing a large class of visual operations for computerized systems that process visual information. This framework also allows visual operations to be made scale invariant, which is necessary for dealing with the size variations that may occur in image data, because real-world objects may be of different sizes and in addition the distance between the object and the camera may be unknown and may vary depending on the circumstances.[8][9]

  1. Witkin, A. P. “Scale-space filtering", Proc. 8th Int. Joint Conf. Art. Intell., Karlsruhe, Germany,1019–1022, 1983.
  2. Koenderink, Jan "The structure of images", Biological Cybernetics, 50:363–370, 1984
  3. Lindeberg, T., Scale-Space Theory in Computer Vision, Kluwer Academic Publishers, 1994, ISBN 0-7923-9418-6
  4. T. Lindeberg (1994). “Scale-space theory: A basic tool for analysing structures at different scales". Journal of Applied Statistics (Supplement on Advances in Applied Statistics: Statistics and Images: 2). 21 (2). pp. 224–270. doi:10.1080/757582976.
  5. Florack, Luc, Image Structure, Kluwer Academic Publishers, 1997.
  6. Sporring, Jon et al. (Eds), Gaussian Scale-Space Theory, Kluwer Academic Publishers, 1997.
  7. ter Haar Romeny, Bart M. (2008). Front-End Vision and Multi-Scale Image Analysis: Multi-scale Computer Vision Theory and Applications, written in Mathematica. Springer Science & Business Media. ISBN 978-1-4020-8840-7.
  8. Lindeberg, Tony (2008). “Scale-space". Encyclopedia of Computer Science and Engineering (Benjamin Wah, Ed), John Wiley and Sons. IV: 2495–2504. doi:10.1002/9780470050118.ecse609. ISBN 978-0470050118.
  9. T. Lindeberg (2014) "Scale selection", Computer Vision: A Reference Guide, (K. Ikeuchi, Editor), Springer, pages 701–713.

2020b

Figure 9: A one dimensional space-scale diagram of six points as the view zooms in from (a) to (b) to (c) around the point q.

2013

1995

1995 SpaceScaleDiagramsUnderstanding Fig1.png
Figure 1. The basic construction of a Space-Scale diagram from a 2D picture.

1986