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

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 Zopf, to solve a system of equations necessary to achieve a 3 times 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.