bv_cvxbook_extra_exercises

This problem concerns a vector eld on rn ie a

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Unformatted text preview: 7.9 Triangulation from multiple camera views. A projective camera can be described by a linearfractional function f : R3 → R2 , f (x) = 1 (Ax + b), +d cT x dom f = {x | cT x + d > 0}, with rank( A cT ) = 3. The domain of f consists of the points in front of the camera. Before stating the problem, we give some background and interpretation, most of which will not be needed for the actual problem. 65 x x′ principal axis camera center principal plane image plane The 3 × 4-matrix P= A cT b d is called the camera matrix and has rank 3. Since f is invariant with respect to a scaling of P , we can normalize the parameters and assume, for example, that c 2 = 1. The numerator cT x + d is then the distance of x to the plane {z | cT z + d = 0}. This plane is called the principal plane. The point −1 A b xc = − cT d lies in the principal plane and is called the camera center. The ray {xc + θc | θ ≥ 0}, which is perpendicular to the principal plane, is the principal axis. We will define the image plane as the plane parallel to the principal plane, at a...
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.

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