Measurement uncertainty is a recurrent concern in visual reconstruction. Image formation and 3D structure recovery are essentially projective processes that do not quite fit into the classical framework of affine least squares, so intrinsically projective error models must be developed. This paper describes initial theoretical work on a fully projective generalization of affine least squares. T...

Martin Urban, Tomáš Pajdla, Václav Hlaváč Abstract Projective reconstruction recovers 3-D points in projective space P3 from their several projections to 2-D images. Applications of projective reconstruction include algorithms for selecting point correspondences, algorithms for camera self-calibration, and algorithms for 3D shape recovery. We introduce a method for the projective reconstruction...

Let A be a hyperplane arrangement, and k a field of arbitrary characteristic. We show that the projective degree-one resonance variety R(A, k) of A over k is ruled by lines, and identify the underlying algebraic line complex L(A, k) in the Grassmannian G(2, kn), n = |A|. L(A, k) is a union of linear line complexes corresponding to the neighborly partitions of subarrangements of A. Each linear l...

Denote by S the projective special linear group PSL2(q) over the field of q elements. We determine, for all values of q > 3, the degrees of the irreducible complex characters of every group H such that S 6 H 6 Aut(S). We also determine the character degrees of certain extensions of the special linear group SL2(q). Explicit knowledge of the character tables of SL2(q), GL2(q), PSL2(q), and PGL2(q...

We show that for a special class of geometric quantizations with “small” quantum errors, the classical correspondence gives rise to an asymptotic projective unitary representation group Hamiltonian diffeomorphisms. As application, we get obstruction actions finitely presented groups.

Let X be a smooth projective surface such that linear and numerical equivalence of divisors on X coincide and let σ ⊆ |D| be a linear pencil on X with integral general fibers. A fiber of σ will be called special if either it is not integral or it has non-generic multiplicity at some of the base points (including the infinitely near ones) of the pencil. In this note we provide an algorithm to co...