You get the empty set in both cases, because nothing in \ Psi ( V ) eliminates every projection function . talk ) 18 : 07, 11 October 2010 ( UTC)
12.
In order to solve this problem it is necessary to know the parameters of the camera projection function from 3D to 2D for the cameras involved, in the simplest case represented by the camera matrices.
13.
That is, a lower elementary recursive function must be a zero, successor, or projection function, a composition of other lower elementary recursive functions, or the bounded sum of another lower elementary recursive function.
14.
Without knowing the depth of the component an inverse projection function can only return a set of possible 3D points, that form a line emanating from the nodal point of the camera lens and passing through the projected 2D point.
15.
:I don't think your W ^ 0 \ cap \ Psi ( V ) can distinguish between the entire V * and the subspace spanned by the projection functions ( that is, elements of V * with finitely many nonzero coefficients ).
16.
This fragment is of great interest because it suffices for Peano arithmetic and most axiomatic set theory, including the canonical ZFC . They also prove that first-order logic with a primitive ordered pair is equivalent to a relation algebra with two ordered pair projection functions.
17.
The projection function " P " takes as its input a camera vector ( denoted " camera " ) and another vector the position of a 3D point in space ( denoted " xyz " ) and returns a 2D point that has been projected onto a plane in front of the camera ( denoted " XY " ).
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