Elliptic fit of objects in two and three dimensions by moment of inertia optimization
Pattern Recognition Letters
Ellipse detection and matching with uncertainty
Image and Vision Computing - Special issue: BMVC 1991
Geometric invariants and object recognition
International Journal of Computer Vision
A note on the least squares fitting of ellipses
Pattern Recognition Letters
Statistical Bias of Conic Fitting and Renormalization
IEEE Transactions on Pattern Analysis and Machine Intelligence
A fast automatic extraction algorithm of elliptic object groups from remote sensing images
Pattern Recognition Letters - Special issue: Pattern recognition for remote sensing (PRRS 2002)
Least Squares Fitting of Circles
Journal of Mathematical Imaging and Vision
A multi-population genetic algorithm for robust and fast ellipse detection
Pattern Analysis & Applications
Least-squares-based fitting of paraboloids
Pattern Recognition
A simple method for fitting of bounding rectangle to closed regions
Pattern Recognition
A hierarchical approach for fast and robust ellipse extraction
Pattern Recognition
Edge curvature and convexity based ellipse detection method
Pattern Recognition
A precise ellipse fitting method for noisy data
ICIAR'12 Proceedings of the 9th international conference on Image Analysis and Recognition - Volume Part I
Expert Systems with Applications: An International Journal
Journal of Visual Communication and Image Representation
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Fitting circles and ellipses of an object is a problem that arises in many application areas, e.g. target detection, shape analysis and biomedical image analysis. In the past, algorithms have been proposed, which fit circles and ellipses in some least squares sense without minimizing the geometric distance to the given points. In this paper, the problem of fitting circle or ellipse to an object in 2-D as well as the problem of fitting sphere, spheroid or ellipsoid to an object in 3-D have been considered. The proposed algorithm depends on the border points of the object. Here, assume that the center of the ellipse or circle coincides with the centroid of all border points of the object. The major and minor axes of the ellipse are presented by least sum perpendicular distance of all border points of the object. The main concept is that the border points satisfy the equation of conic. On the basis of this concept, all the border points of the object will generate an error function (algebraic function) and the other parameters of the conic are estimated by minimizing this error function. The extension of this idea in 3-D for fitting sphere, spheroid and ellipsoid are proposed.