José Ignacio Burgos Gil

Generic Self-calibration of Central Cameras from Two Rotational Flows

We address the self-calibration of a smooth generic central camera from only two dense rotational flows produced by rotations of the camera about two unknown linearly independent axes passing through the camera centre. We give a closed-form theoretical solution to this problem, and we prove that it can be solved exactly up to a linear orthogonal transformation ambiguity. Using the theoretical results, we propose an algorithm for the self-calibration of a generic central camera from two rotational flows.In order to solve the self-calibration problem using real images, we also study the computation of dense optical flows from image sequences acquired by the rotation of a smooth generic central camera. We propose a method for the computation of dense smooth generic flows from rotational camera motions using splines. The proposed methods are validated using both simulated and real image sequences.

When do the Recession Cones of a Polyhedral Complex Form a Fan

We study the problem of when the collection of the recession cones of a polyhedral complex also forms a complex. We exhibit an example showing that this is no always the case. We also show that if the support of the given polyhedral complex satisfies a Minkowski–Weyl-type condition, then the answer is positive. As a consequence, we obtain a classification theorem for proper toric schemes over a discrete valuation ring in terms of complete strongly convex rational polyhedral complexes.

Higher arithmetic Chow groups

We give a new construction of higher arithmetic Chow groups for quasi- projective arithmetic varieties over a eld. Our denition agrees with the higher arith- metic Chow groups dened by Goncharov for projective arithmetic varieties over a eld. These groups are the analogue, in the Arakelov context, of the higher algebraic Chow groups dened by Bloch. The degree zero group agrees, for projective varieties, with the arithmetic Chow groups dened by Gillet and Soul e and in general, with the arithmetic Chow groups of Burgos. Our new construction is shown to be a contravariant functor and is endowed with a product structure, which is commutative and associative.

Camera self-calibration with parallel screw axis motion by intersecting imaged horopters

We present a closed-form method for the self-calibration of a camera (intrinsic and extrinsic parameters) from at least three images acquired with parallel screw axis motion, i.e. the camera rotates about parallel axes while performing general translations. The considered camera motion is more general than pure rotation and planar motion, which are not always easy to produce. The proposed solution is nearly as simple as the existing for those motions, and it has been evaluated by using both synthetic and real data from acquired images.

Positivity of the Height Jump Divisor

We study the degeneration of semipositive smooth hermitian line bundles on open complex manifolds, assuming that the metric extends well away from a codimension two analytic subset of the boundary. Using terminology introduced by R. Hain, we show that under these assumptions the so-called height jump divisors are always effective. This result is of particular interest in the context of biextension line bundles on Griffiths intermediate jacobian fibrations of polarized variations of Hodge structure of weight -1, pulled back along normal function sections. In the case of the normal function on M_g associated to the Ceresa cycle, our result proves a conjecture of Hain. As an application of our result we obtain that the Moriwaki divisor on \bar M_g has non-negative degree on all complete curves in \bar M_g not entirely contained in the locus of irreducible singular curves.

Hecke and Sturm bounds for Hilbert modular forms over real quadratic fields

In this article we give an analogue of Hecke and Sturm bounds for Hilbert modular forms over real quadratic fields. Let

Height of varieties over finitely generated fields

K

Heights of Toric Varieties, Entropy and Integration over Polytopes

be a real quadratic field and

Some recent results on generalized analytic torsion classes

\Om_K

Arithmetic geometry of toric varieties. metrics, measures and heights

its ring of integers. Let