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Multilinear Constraints in Two-dimensional Vision and Isogonal Conjugacy

Invariance has become increasingly important in computer vision. One type of invariance is viewpoint invariance, i.e. properties of viewed objects that are invariant under camera motion. Another important concept is object invariance, i.e. properties of the image that only depend on motion and not on the viewed objects. The epipolar constraint in three dimensional vision, is an example of the latter. This paper deals with the generalisation of the epipolar constraint to multilinear constraints, for two-dimensional vision. In particular, the calibrated trilinear tensor is studied. It is shown that each such tensor is associated with two different reconstructions. The ambiguity is closely related to a concept from planar geometry, the so called isogonal conjugacy of two points with respect to a triangle.