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Computer Algebra Algorithms Applied to Computer Vision in a Parking Management System

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Authors
López Sastre, Roberto JavierUniversity of Alcalá Author; Gil Jiménez, PedroUniversity of Alcalá Author; Acevedo Rodríguez, Francisco JavierUniversity of Alcalá Author; Maldonado Bascón, SaturninoUniversity of Alcalá Author
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/1270
Publisher
Institute Electrical Electronics Engineering
Date
2007-06
Affiliation
Universidad de Alcalá. Departamento de Teoría de la Señal y Comunicaciones
Bibliographic citation
Lopez Sastre, R.J.; Gil Jimenez, P.; Acevedo, F.J.; Maldonado Bascon. "Computer Algebra Algorithms Applied to Computer Vision in a Parking Management System", IEEE International Symposium on Industrial Electronics, 2007. ISIE 2007, 4-7 June 2007 , p. 1675 - 1680
Keywords
Computer vision
Algebra
Parking management system
Object recognition
Document type
info:eu-repo/semantics/conferenceObject
Access rights
info:eu-repo/semantics/openAccess
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Abstract
From this paper, we propose a novel methodology to compute a 2D Homography applying some algorithms of computer algebra. We consider the classical problem of solving (exactly) a linear system of algebraic equations, and we suggest a new algorithm for computer vision, based on homomorphism methods over Z, to solve a system of equations necessary to achieve a 3 × 3 matrix H which lets us to compute the projective transformation which translates coordinates between points in different planes. From this work, we want to show that it is possible to apply a symbolic approach to some crucial issues of computer vision, moreover of the numerical methodology, in order to reduce the complexity of some algorithms, and to eliminate the problems associated with loss of precision and normalization. We test our technique in a real situation: a parking management system, which creates a pseudo-top-view of a parking area to determine if there are free parking lots or not.
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