%0 Journal Article
%T Implicit Polynomial Representation through a Fast Fitting Error Estimation
%A Mohammad Rouhani
%A Angel Sappa
%J IEEE Transactions on Image Processing
%D 2012
%V 21
%N 4
%@ 1057-7149
%F Mohammad Rouhani2012
%O ADAS
%O exported from refbase (http://refbase.cvc.uab.es/show.php?record=1937), last updated on Fri, 23 Jun 2017 10:59:14 +0200
%X Impact FactorThis paper presents a simple distance estimation for implicit polynomial fitting. It is computed as the height of a simplex built between the point and the surface (i.e., a triangle in 2-D or a tetrahedron in 3-D), which is used as a coarse but reliable estimation of the orthogonal distance. The proposed distance can be described as a function of the coefficients of the implicit polynomial. Moreover, it is differentiable and has a smooth behavior . Hence, it can be used in any gradient-based optimization. In this paper, its use in a Levenberg-Marquardt framework is shown, which is particularly devoted for nonlinear least squares problems. The proposed estimation is a generalization of the gradient-based distance estimation, which is widely used in the literature. Experimental results, both in 2-D and 3-D data sets, are provided. Comparisons with state-of-the-art techniques are presented, showing the advantages of the proposed approach.
%U http://refbase.cvc.uab.es/files/RoS2012b.pdf
%U http://dx.doi.org/10.1109/TIP.2011.2170080
%P 2089-2098