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20 February 2007 Subpixel evaluation of distorted circle characteristics
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The subject of this paper is the improvement of measures on imperfect circular forms. Indeed, simple geometric forms have been well studied in image processing. Thus, articles describing circles on a discrete framework are numerous but the case of imperfect geometric forms, in return, is hardly ever deepen. However, it is a classical problem in industrial vision control process to not have a perfect, or perfectly discretized, geometric object due to, notably, manufacturing process, industrial environment (dust, vibrations, objects displacement, etc.), interferences on acquisition chain (electronic noise, lenses imperfections, etc. ). The authors present a comparison of measurement methods of circles characteristics subpixel estimation (center's coordinates and radius) for several distortions (geometric or not). The estimators proposed are classic least mean squares, 3D Hough algorithms and a method combining a Radon transform based estimator and a FitzHugh-Nagumo partial differential equation based active region algorithm. The originality of the method is to furnish a set of geometric envelopes in a single pass from a roughest to a full detailed representation. Moreover, this multiple active region principle also offers interesting electronic implementation possibilities for real time image processing for metrology on production chains.
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Fabrice Mairesse, Tadeusz M. Sliwa, Yvon Voisin, and Stéphane Binczak "Subpixel evaluation of distorted circle characteristics", Proc. SPIE 6503, Machine Vision Applications in Industrial Inspection XV, 65030G (20 February 2007); doi: 10.1117/12.704143;

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