Least Squares Problems with Absolute Quadratic Constraints

Abstract EN

This paper analyzes linear least squares problems with absolute quadratic constraints.

We develop a generalized theory following Bookstein's conic-fitting and Fitzgibbon's direct ellipse-specific fitting.

Under simple preconditions, it can be shown that a minimum always exists and can be determined by a generalized eigenvalue problem.

This problem is numerically reduced to an eigenvalue problem by multiplications of Givens' rotations.

Finally, four applications of this approach are presented.