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Coordinate Rotation Invariance of Image Characteristics

  • Kenichi Kanatani
Chapter
Part of the Springer Series in Information Sciences book series (SSINF, volume 20)

Abstract

In this chapter, we present a powerful mathematical tool for analyzing 3D recovery equations. The underlying principle is that the image coordinate system plays only an auxiliary role because no coordinate system is inherent to the image; any coordinate systems obtained by rotations around the image origin can be used equivalently. Based on this observation, we rearrange observed image characteristics into “invariants”. Invoking a general discipline which we call “Weyl’s thesis”, we show that the geometrical meanings of involved quantities become clear if the 3D recovery equations are written in terms of invariants. We also see that analytical solutions often emerge themselves. To illustrate this, we apply our method to optical flow analysis and the shape-from-texture problem.

Keywords

Irreducible Representation Optical Flow Principal Curvature Translation Velocity Relative Invariant 
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Bibliography

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  4. K. Kanatani: Structure and motion from optical flow under orthographic projection. Comput. Vision, Graphics Image Process. 35, 181–199 (1986)CrossRefGoogle Scholar
  5. K. Kanatani: Coordinate rotation invariance of image characteristics for 3D shape and motion recovery, in Proc. 1st Intl. Conf. Comput. Vision, June 1987, London, pp. 55–64Google Scholar
  6. K. Kanatani, T.-C. Chou: Shape from texture: General principle. Artif. Intell. 38 (1), 1–48 (1989)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Kenichi Kanatani
    • 1
  1. 1.Department of Computer ScienceGunma University KiryuJapan

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