Shape and mutual cross-ratios with applications to exterior, interior and relative orientation
An affine concept of shape is introduced, which is independent of the coordinate description. By comparing the shapes of corresponding object and image configurations, it is possible to draw information about the projective mapping that associates them. This is done by means of mutual cross-ratios, which generalize the classical cross-ratio on the line. The geometric machinery is applied to the various orientation problems (exterior, interior and relative). It makes it possible to construct computational schemes, involving only the solutions of systems of linear equations and polynomial equations in one variable.
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