Person: Valdés Morales, Antonio
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First Name
Antonio
Last Name
Valdés Morales
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Matemáticas
Department
Álgebra, Geometría y Topología
Area
Geometría y Topología
Identifiers
25 results
Search Results
Now showing 1 - 10 of 25
Item Autocalibration of Cameras with Known Pixel Shape(2005) Ronda Prieto, José Ignacio; Valdés Morales, Antonio; Gallego Bonet, GuillermoWe present new algorithms for the recovery of the Euclidean structure from a projective calibration of a set of cameras of known pixel shape but otherwise arbitrarily varying intrinsic and extrinsic parameters. The algorithms have a geometrical motivation based on the properties of the set of lines intersecting the absolute conic. The theoretical part of the paper contributes with theoretical results that establish the relationship between the geometrical object corresponding to this set of lines and other equivalent objects as the absolute quadric. Finally, the satisfactory performance of the techniques is demonstrated with synthetic and real data.Item Autocalibration with the Minimum Number of Cameras with Known Pixel Shape(International Journal of Computer Vision, 2011) Ronda Prieto, José Ignacio; Valdés Morales, Antonio; Gallego Bonet, GuillermoWe address the problem of the Euclidean upgrading of a projective calibration of a minimal set of cameras with known pixel shape and otherwise arbitrarily varying intrinsic and extrinsic parameters. To this purpose, we introduce as our basic geometric tool the six-line conic variety (SLCV), consisting in the set of planes intersecting six given lines of 3D space in points of a conic. We show that the set of solutions of the Euclidean upgrading problem for three cameras with known pixel shape can be parameterized in a computationally efficient. As a consequence, we propose an algorithm that performs a Euclidean upgrading with 5 ({theoretical minimum}) or more cameras with the knowledge of the pixel shape as the only constraint. We provide experiments with real images showing the good performance of the technique.Item Recursive camera autocalibration with the Kalman filter(2007 IEEE international conference on image processing, 2007) Gallego Bonet, Guillermo; Ronda Prieto, José Ignacio; Valdés Morales, Antonio; García, NarcisoGiven a projective reconstruction of a 3D scene, we address the problem of recovering the Euclidean structure of the scene in a recursive way. This leads to the application of Kalman filtering to the problem of camera autocalibration and to new algorithms for the autocalibration of cameras with varying parameters. This has benefits in saving memory and computational effort, and obtaining faster updates of the 3D Euclidean structure of the scene under consideration.Item Camera autocalibration using Plucker coordinates(2005 international conference on image processing (ICIP), 2005) Ronda Prieto, José Ignacio; Gallego Bonet, Guillermo; Valdés Morales, AntonioWe present new results on the Absolute Line Quadric (ALQ), the geometric object representing the set of lines that intersect the absolute conic. We include new techniques for the obtainment of the Euclidean structure that lead to an efficient algorithm for the autocalibration of cameras with varying parameters.Item The number of functionally independent invariants of a pseudo-Riemannian metric(Journal of physics A: Mathematical and theoretical, 1994) Muñoz Masqué, Jaime; Valdés Morales, AntonioThe number of functionally independent scalar invariants of arbitrary order of a generic pseudo-Riemannian metric on an n-dimensional manifold is determined.Item A report on functorial connections and differential invariants(Rendiconti di Matematica e delle sue Applicazioni. Serie VII, 1997) Muñoz Masqué, Jaime; Valdés Morales, AntonioLet M be an n -dimensional manifold, π:F(M)→M the linear frame bundle, and G a closed subgroup of GL(n,R) . As is known, there is a one-to-one correspondence between the G -structures on M and the sections of the bundle π ¯ :F(M)/G→M . A functorial connection is an assignment of a linear connection ∇(σ) on M to each section σ of the bundle π ¯ which satisfies the following properties: ∇(σ) is reducible to the subbundle P σ ⊂FM corresponding to σ , depends continuously on σ , and for every diffeomorphism f:M→M there holds ∇(f⋅σ)=f⋅∇(σ) . The article is a survey of the authors' recent results concerning functorial connections and their use in constructing differential invariants of G -structures. The most attention is concentrated on the problem of existence of a functorial connection for a given subgroup G⊂GL(n,R) and on the calculation of the number of functionally independent differential invariants of a given order. Special consideration is devoted to the G -structures determined by linear and projective parallelisms and by pseudo-Riemannian metrics.Item A canonical connection associated with certain G -structures.(Czechoslovak Mathematical Journal, 1997) Sierra, José M.; Valdés Morales, AntonioLet P be a G-structure on a manifold M and AdP be the adjoint bundle of P. The authors deduce the following main result: there exists a unique connection r adapted to P such that trace(S iX Tor(r)) = 0 for every section S of AdP and every vector field X on M, provided Tor(r) stands for the torsion tensor field of r. Two examples, namely almost Hermitian structures and almost contact metric structures, are discussed in more detail. Another interesting result reads: for a given structure group G, if it is possible to attach a connection to each G-structure in a functorial way with the additional assumption that the connection depends on first order contact only, then the first prolongation of the Lie algebra of G vanishesItem Real and complex projectively parallelizable manifolds(Revue roumaine de mathematiques pures et appliquees, 1999) Durán Díaz , R.; Muñoz Masqué, Jaime; Valdés Morales, AntonioThe notion of a projective parallelism either on a differentiable or on a complex analytic manifold $M$ is introduced and its topological invariants and cohomological obstructions are studied. In the complex case a canonical linear connection is introduced and the topological consequences of the existence of such a connection are deduced.Item Conic geometry and autocalibration from two images(Journal of Mathematical Imaging and Vision, 2007) Ronda Prieto, José Ignacio; Valdés Morales, AntonioWe show how the classical theory of projective conics provides new insights and results on the problem of 3D reconstruction from two images taken with uncalibrated cameras. The close relationship between Kruppa equations and Poncelet's Porism is investigated, leading, in particular, to a closed-form geometrically meaningful parameterization of the set of Euclidean reconstructions compatible with two images taken with cameras with constant intrinsic parameters and known pixel shape. An experiment with real images, showing the applicability of the method, is included.Item Differential invariants of R ∗-structures(Mathematical Proceedings of the Cambridge Philosophical Society, 1996) Valdés Morales, AntonioA differential invariant of a G-structure is a function which depends on the r-jet of the G-structure and such that it is invariant under the natural action of the pseudogroup of diffeomorphisms of the base manifold. The importance of these objects is clear, since they seem to be the natural obstructions for the equivalence of G-structures. Hopefully, if all the differential invariants coincide over two r–jets of G-structure then they are equivalent under the action of the pseudogroup. If all the differential invariants coincide for every r it is hoped that the G-structures are formally equivalent, and so equivalent in the analytic case. This is the equivalence problem of E. Cartan. In this paper we deal with the problem of finding differential invariants on the bundles of *-structures, following the program pointed out in [3]. There are several reasons that justify the study of this type of G-structures. The first one is that it is a non-complicated example that helps to understand the G-structures with the property for the group G of having a vanishing first prolongation (i.e. of type 1). The simplicity comes from the fact that the algebraic invariants of * are very simple. The differential geometry of this type of structure, however, has much in common with general G-structures of type 1. Also, *-structures are objects of geometrical interest. They can be interpreted as ‘projective parallelisms’ of the base manifold and they can also be interpreted as a generalization of Blaschke's notion of a web.
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