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
5 results
Search Results
Now showing 1 - 5 of 5
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 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 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 3D reconstruction with uncalibrated cameras using the six-line conic variety(2008 IEEE international conference on image processing, proceedings, 2008) Carballeira, Pablo; Ronda Prieto, José Ignacio; Valdés Morales, AntonioWe present new algorithms for the recovery of the Euclidean structure from a projective calibration of a set of cameras with square pixels but otherwise arbitrarily varying intrinsic and extrinsic parameters. Our results, based on a novel geometric approach, include a closed-form solution for the case of three cameras and two known vanishing points and an efficient one-dimensional search algorithm for the case of four cameras and one known vanishing point. In addition, an algorithm for a reliable automatic detection of vanishing points on the images is presented. These techniques fit in a 3D reconstruction scheme oriented to urban scenes reconstruction. The satisfactory performance of the techniques is demonstrated with tests on synthetic and real data.