Subspace projection and QR decomposition applied to ellipse fitting

Subspace projection is a very effective technique extensively applied to various fields of modern signal processing. But, how to apply it to ellipse fitting is still a problem to be answered. In traditional ellipse fitting algorithms, the tightly couplings between 3 subspaces of ellipse data matrix with greatly different energies can significantly increase the condition number so as to greatly degrade its numerical performance. By means of twice of subspace projections, the couplings are thoroughly eliminated and 3 components of the ellipse parameter vector are optimally estimated or directly computed progressively. Therefore, after combined QR decomposition, it obviously improves the practical performance. It is proved that the suggested technique is essentially a constrained global optimization procedure that minimizes the norm of an orthogonal component of fitting error vector under constrains that the other two orthogonal components of fitting error vector are equal to zero. The theoretical analysis and experimental demonstration have proved that the new algorithm is fast and exact, its anti-noise ability is strong and its fitting success rate is high