Trifocal Tensors for Weak Perspective and Paraperspective Projections

Trilinear relationships among the image point coordinates obtained by perspective projection of several feature points over three views have been investigated, and it has been shown that seven point correspondences are sufficient to determine the coefficients involved. We show that analogous trilinear relationships exist for the weak perspective and paraperspective projections, and that only four point correspondences are necessary for the determination of the coefficients. When the trilinear relationships are known, the position of the image of a point in one camera system can be determined from its image in the two other camera systems through linear equations.