A fast robust geometric fitting method for parabolic curves. (December 2018)

• Record Type: Journal Article
• Authors: López-Rubio, Ezequiel; Thurnhofer-Hemsi, Karl; Blázquez-Parra, Elidia Beatriz; de Cózar-Macías, Óscar David; Ladrón-de-Guevara-Muñoz, M. Carmen
• Is Part Of: Pattern recognition. Volume 84(2018:Dec.)
• Page Start: 301
• Page End: 316
• Publication Date: 2018-12
• Subjects: Parabolic fitting -- Geometric curve fitting -- Noise -- Minimization of absolute errors -- Robust estimation; Pattern perception -- Periodicals; Perception des structures -- Périodiques; Patroonherkenning; 006.4
• DOI: 10.1016/j.patcog.2018.07.019
• Languages: English
• ISSNs: 0031-3203

Abstract

Highlights: A new method to fit parabolic curves is presented. The method is fast and robust to noisy observations due to the use of absolute error minimization. Stability is further improved by normalization of the directrix vector. Our approach outperforms state of the art competitors in both synthetic and real datasets. Abstract: Fitting discrete data obtained by image acquisition devices to a curve is a common task in many fields of science and engineering. In particular, the parabola is some of the most employed shape features in electrical engineering and telecommunication applications. Standard curve fitting techniques to solve this problem involve the minimization of squared errors. However, most of these procedures are sensitive to noise. Here, we propose an algorithm based on the minimization of absolute errors accompanied by a normalization of the directrix vector that leads to an improved stability of the method. This way, our proposal is substantially resilient to noisy samples in the input dataset. Experimental results demonstrate the good performance of the algorithm in terms of speed and accuracy when compared to previous approaches, both for synthetic and real data.