Ellipses Estimation from their Digitization
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Ellipses in general position, and problems related to their reconstruction from digital data resulting from their digitization, are considered. If the ellipse
$$E:\tilde A\left( {x - p} \right)^2 + 2\tilde B\left( {x - p} \right)\left( {y - q} \right) + \tilde C\left( {y - q} \right)^2 \leqslant 1, \tilde A\tilde C - \tilde B^2 > 0,$$
is presented on digital picture of a given resolution, then the corresponding digital ellipse is:
$$D\left( E \right) = \left\{ {\left( {i,j} \right) | A\left( {i - a} \right)^2 + 2B\left( {i - a} \right)\left( {j - b} \right) + C\left( {j - b} \right)^2 \leqslant r^2 , i,j are integers} \right\},$$
where r denotes the number of pixels per unit and a = pr, b = qr, \(A = \tilde Ar^2 , B = \tilde Br^2 , C = \tilde Cr^2 .\)
[1] M. Huxley. Exponential sums and lattice points III , 2003 .
[2] Alfred M. Bruckstein,et al. Design of Perimeter Estimators for Digitized Planar Shapes , 1989, IEEE Trans. Pattern Anal. Mach. Intell..
[3] Marcel Worring,et al. Digitized Circular Arcs: Characterization and Parameter Estimation , 1995, IEEE Trans. Pattern Anal. Mach. Intell..