Perturbation of polynomials and applications to the Hough transform

Let $f$ and $g$ be complex polynomials of the same degree. We provide a new lower bound on the Euclidean distance of points belonging to their zero-loci in terms of Bombieri's norm. We also present a minimization of the Bombieri's norm of the difference $g-\lambda f$, for $\lambda\in \C^{^*}$. In the real case, we apply the results above in the setting of the Hough transform, a standard technique to detect curves in images, suggesting a Bombieri's norm based recognition algorithm.