Computational Cross Ratio for Computer Vision

A new "computational" formulation of cross ratio is presented with a view to applications to computer vision problems by extending the framework of "computational projective geometry" of Kanatani (Image Understand. 54, 1991, 333-348). As typical examples, we construct procedures for computing the 3-D orientation of a planar shape from its 2-D projection image and the focus of expansion from an image trajectory of a single point by taking advantage of the perspective invariance of cross ratio and "projective coordinates," and the resulting 3-D interpretation of "harmonic range."