A Computational Approach to Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Estimation of a circular arc center and its radius
Computer Vision, Graphics, and Image Processing
Out-of-Roundness Problem Revisited
IEEE Transactions on Pattern Analysis and Machine Intelligence
Circle fitting by linear and nonlinear least squares
Journal of Optimization Theory and Applications
Unbiased least square fitting of circular arcs
CVGIP: Graphical Models and Image Processing
Least-squares fitting by circles
Computing
On the circle closest to a set of points
Computers and Operations Research - Location analysis
Least Squares Fitting of Circles
Journal of Mathematical Imaging and Vision
Pipe eccentricity measurement using laser triangulation
Image and Vision Computing
Fitting circles to data with correlated noise
Computational Statistics & Data Analysis
Approximation of n-dimensional data using spherical and ellipsoidal primitives
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
Fast Circular Arc Segmentation Based on Approximate Circularity and Cuboid Graph
Journal of Mathematical Imaging and Vision
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Geometric fitting is present in different fields of sciences, engineering and astronomy. In particular, circular arc primitives are some of the most commonly employed geometric features in digital image analysis and visual pattern recognition. In this paper, a robust geometric method based on mean absolute error to fit a set of points is proposed. Most geometric and algebraic methods are sensitive to noise and outlier points and so the results are not usually acceptable. It is well known that the least absolute error criterion leads to robust estimations. However, the objective function is non differentiable and thus algorithms based on gradient cannot be applied. We propose an algorithm based on left and right side partial derivatives that is computationally efficient as an alternative to conventional algorithms, and evaluate the sensitivity of circle fits for different types of data.