Adaptively determining degrees of implicit polynomial curves and surfaces

Authors:
Bo Zheng;Jun Takamatsu;Katsushi Ikeuchi
Affiliations:
Institute of Industrial Science, The University of Tokyo, Tokyo, Japan;Institute of Industrial Science, The University of Tokyo, Tokyo, Japan;Institute of Industrial Science, The University of Tokyo, Tokyo, Japan
Venue:
ACCV'07 Proceedings of the 8th Asian conference on Computer vision - Volume Part II
Year:
2007

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Abstract

Fitting an implicit polynomial (IP) to a data set usually suffers from the difficulty of determining a moderate polynomial degree. An over-low degree leads to inaccuracy than one expects, whereas an overhigh degree leads to global instability. We propose a method based on automatically determining the moderate degree in an incremental fitting process through using QR decomposition. This incremental process is computationally efficient, since by reusing the calculation result from the previous step, the burden of calculation is dramatically reduced at the next step. Simultaneously, the fitting instabilities can be easily checked out by judging the eigenvalues of an upper triangular matrix from QR decomposition, since its diagonal elements are equal to the eigenvalues. Based on this beneficial property and combining it with Tasdizen's ridge regression method, a new technique is also proposed for improving fitting stability.