Abstract
In Chap. 2, we studied invariance properties of image characteristics under image coordinate rotation. In this chapter, we study invariance properties under the camera rotation we introduced in Chap. 1. Just as invariants for the image coordinate rotation are obtained by irreducibly reducing representations of SO(2), invariants for the camera rotation are obtained by irreducibly reducing representations of SO(3). However, direct analysis is very difficult due to the fact that SO(3) is not Abelian. Fortunately, a powerful tool is available: we only need to analyze “infinitesimal transformations”. This is because the structure of a compact Lie group is completely determined by its Lie algebra. To demonstrate our technique, we analyze the transformation of optical flow under camera rotation.
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