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-?f, for ??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
Perturbation of polynomials and applications to the Hough transform
M Torrente;
2017
Abstract
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-?f, for ??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 algorithmFile in questo prodotto:
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