Person:
Valdés Morales, Antonio

First Name

Antonio

Last Name

Valdés Morales

URI

https://hdl.handle.net/20.500.14352/75621

Affiliation

Universidad Complutense de Madrid

Faculty / Institute

Ciencias Matemáticas

Department

Álgebra, Geometría y Topología

Area

Geometría y Topología

Identifiers

Full item page

Search Results

Now showing 1 - 10 of 12

Conic geometry and autocalibration from two images
(Journal of Mathematical Imaging and Vision, 2007) Ronda Prieto, José Ignacio; Valdés Morales, Antonio
We 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.
Autocalibration of Cameras with Known Pixel Shape
(2005) Ronda Prieto, José Ignacio; Valdés Morales, Antonio; Gallego Bonet, Guillermo
We 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.
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, Narciso
Given 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.
Camera autocalibration using Plucker coordinates
(2005 international conference on image processing (ICIP), 2005) Ronda Prieto, José Ignacio; Gallego Bonet, Guillermo; Valdés Morales, Antonio
We 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.
Camera Autocalibration and the Calibration Pencil
(Journal of Mathematical Imaging and Vision, 2005) Valdés Morales, Antonio; Ronda Prieto, José Ignacio
We 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.
Line geometry and camera autocalibration
(Journal of Mathematical Imaging and Vision, 2008) Ronda Prieto, José Ignacio; Valdés Morales, Antonio; Gallego Bonet, Guillermo
We 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.
Autocalibration of a camera pair
(2006) Ronda Prieto, José Ignacio; Valdés Morales, Antonio
Given 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.
The Absolute Line Quadric and Camera Autocalibration
(International Journal of Computer Vision, 2004) Valdés Morales, Antonio; Ronda Prieto, José Ignacio; Gallego Bonet, Guillermo
We introduce a geometrical object providing the same information as the absolute conic: the absolute line quadric (ALQ). After the introduction of the necessary exterior algebra and Grassmannian geometry tools, we analyze the Grassmannian of lines of P3 from both the projective and Euclidean points of view. The exterior algebra setting allows then to introduce the ALQ as a quadric arising very naturally from the dual absolute quadric. We fully characterize the ALQ and provide clean relationships to solve the inverse problem, i.e., recovering the Euclidean structure of space from the ALQ. Finally we show how the ALQ turns out to be particularly suitable to address the Euclidean autocalibration of a set of cameras with square pixels and otherwise varying intrinsic parameters, providing new linear and non-linear algorithms for this problem. We also provide experimental results showing the good performance of the techniques.
Projective Evolution of Plane Curves
(International Journal of Computer Vision, 2001) Castrillón López, Marco; Valdés Morales, Antonio
We show that projectively invariant evolution operators have unavoidable singularities. In particular, we see that there exists no non-singular projective evolution operator well-defined over straight lines nor conics.
Camera Autocalibration and Horopter Curves
(International Journal of Computer Vision, 2004) Ronda Prieto, José Ignacio; Valdés Morales, Antonio; Jaureguizar Núñez, Fernando
We describe a new algorithm for the obtainment of the affine and Euclidean calibration of a camera under general motion. The algorithm exploit the relationships of the horopter curves associated to each pair of cameras with the plane at infinity and the absolute conic. Using these properties we define cost functions whose minimization by means of general purpose techniques provides the required calibration. The experiments show the good convergence properties, computational efficiency and robust performance of the new techniques.