The Recognition of Polynomial Position and Orientation through the Finite Polynomial Discrete Radon Transform

Abstract

In this paper, we propose to accurately detect from an image curvilinear features that can be approximated by polynomial curves. Having the a priori knowledge of a polynomial parameters (coefficients and degree), we give the possibility to recognize both the orientation and the position of the polynomial (if it exists) in the given image. For this objective, we present a new approach titled ”The Finite Polynomial Discrete Radon Transform” (FPDRT) that maps the initial image into a Radon space where each point presents the amount of evidence of the existence of a polynomial at the same position. The FPDRT sums the pixels centered on a polynomial and stores the result at the corresponding position in the Radon space. The FPDRT extends the formalism of the Finite Discrete Radon Transform(FRT) which is restricted to project the image along straight lines of equation y = mx + t where m and t are integers. Our method generalizes FRT by projecting the image with respect to polynomials of equation y = mx ⁿ + t where m, n and t are integers. The FPDRT method is exactly invertible, requires only arithmetic operations and is applicable to p×p sized images where p is a prime number. Several applications are allowable by the FPDRT such as fingerprint, palm print biometric applications and multi directional roads recognition.