Computer algebra algorithms applied to computer vision in a parking management system

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 x 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.