IEEE Transactions on Pattern Analysis and Machine Intelligence
A buyer's guide to conic fitting
BMVC '95 Proceedings of the 6th British conference on Machine vision (Vol. 2)
Assessing error of fit functions for ellipses
Graphical Models and Image Processing
Matrix computations (3rd ed.)
Direct Least Square Fitting of Ellipses
IEEE Transactions on Pattern Analysis and Machine Intelligence
Statistical Bias of Conic Fitting and Renormalization
IEEE Transactions on Pattern Analysis and Machine Intelligence
Revisiting Hartley's Normalized Eight-Point Algorithm
IEEE Transactions on Pattern Analysis and Machine Intelligence
Direct estimation of homogeneous vectors: an ill-solved problem in computer vision
ICVGIP'06 Proceedings of the 5th Indian conference on Computer Vision, Graphics and Image Processing
Linear pose estimate from corresponding conics
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
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A new method to fit specific types of conics to scattered data points is introduced. Direct, specific fitting of ellipses and hyperbolae is achieved by imposing a quadratic constraint on the conic coefficients, whereby an improved partitioning of the design matrix is devised so as to improve computational efficiency and numerical stability by eliminating redundant aspects of the fitting procedure. Fitting of parabolas is achieved by determining an orthogonal basis vector set in the Grassmannian space of the quadratic terms' coefficients. The linear combination of the basis vectors that fulfills the parabolic condition and has a minimum residual norm is determined using Lagrange multipliers. This is the first known direct solution for parabola specific fitting. Furthermore, the inherent bias of a linear conic fit is addressed. We propose a linear method of correcting this bias, producing better geometric fits which are still constrained to specific conic type.