Coordinate Rotation Invariance of Image Characteristics
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.
KeywordsIrreducible Representation Optical Flow Principal Curvature Translation Velocity Relative Invariant
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- 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