Efficient computation of the Gauss-Newton direction when fitting NURBS using ODR

Publication: Research - peer-reviewJournal article

We consider a subproblem in parameter estimation using the Gauss-Newton algorithm with regularization for NURBS curve fitting. The NURBS curve is fitted to a set of data points in least-squares sense, where the sum of squared orthogonal distances is minimized. Control-points and weights are estimated. The knot-vector and the degree of the NURBS curve are kept constant. In the Gauss-Newton algorithm, a search direction is obtained from a linear overdetermined system with a Jacobian and a residual vector. Because of the properties of our problem, the Jacobian has a particular sparse structure which is suitable for performing a splitting of variables. We are handling the computational problems and report the obtained accuracy using different methods, and the elapsed real computational time. The splitting of variables is a two times faster method than using plain normal equations.
Original languageEnglish
JournalBit (Lisse)
Publication date2012
Volume52
Journal number3
Pages571-588
Number of pages18
ISSN0006-3835
DOIs
StatePublished

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