Geometric Algebra Applications Vol. I by Eduardo Bayro-Corrochano

Author:Eduardo Bayro-Corrochano
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(12.88)

where is the vector of Plücker coordinates and the matrix contains the and ’s, that is, information about the camera configuration.

When we back-project a point or line l in the image plane, we produce their duals, that is, a line or a plane , respectively. These back-projected lines and planes are given by the following expressions:

(12.89)

(12.90)

12.6.2 Geometry of Two Views

In this and subsequent sections, we will work in projective space , although a return to 3D Euclidean space will be necessary when we discuss invariants in terms of image coordinates; this will be done via the projective split. Figure 12.3 shows a world point projecting onto points and in the two image planes and , respectively.

Fig. 12.3Sketch of binocular projection of a world point

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