Person: Valdés Morales, Antonio
Loading...
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
20 results
Search Results
Now showing 1 - 10 of 20
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.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 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 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 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 Camera Autocalibration and the Calibration Pencil(Journal of Mathematical Imaging and Vision, 2005) Valdés Morales, Antonio; Ronda Prieto, José IgnacioWe study the geometric object given by the set of lines incident with the absolute conic. We see that this object is given by a pencil of quadrics of P5, which is characterized. We describe some of its most relevant properties for the camera autocalibration problem. Finally, we illustrate the applicabil- ity of the theory proposing a linear algorithm for the metric upgrading of a projective calibration of a set of ten or more cameras with varying parameters and known skew and aspect ratio.Item Line geometry and camera autocalibration(Journal of Mathematical Imaging and Vision, 2008) Ronda Prieto, José Ignacio; Valdés Morales, Antonio; Gallego Bonet, GuillermoWe provide a completely new rigorous matrix formulation of the absolute quadratic complex (AQC), given by the set of lines intersecting the absolute conic. The new results include closed-form expressions for the camera intrinsic parameters in terms of the AQC, an algorithm to obtain the dual absolute quadric from the AQC using straightforward matrix operations, and an equally direct computation of a Euclidean-upgrading homography from the AQC. We also completely characterize the 6x6 matrices acting on lines which are induced by a spatial homography. Several algorithmic possibilities arising from the AQC are systematically explored and analyzed in terms of efficiency and computational cost. Experiments include 3D reconstruction from real images.Item Autocalibration of a camera pair(2006) Ronda Prieto, José Ignacio; Valdés Morales, AntonioGiven a pair of cameras with identical intrinsic parameters and known pixel shape, there exists a uniparametric set of possible 3D Euclidean reconstructions. We provide for this set a closed-form explicit parameterization. Therefore, given a single piece of data from the scene, the set of solutions can be efficiently searched for the best-fit reconstruction. An experiment with real images, showing the applicability of the method, is included.