@Article{MohammadRouhani2012,
author="Mohammad Rouhani
and Angel Sappa",
title="Implicit Polynomial Representation through a Fast Fitting Error Estimation",
journal="IEEE Transactions on Image Processing",
year="2012",
volume="21",
number="4",
pages="2089--2098",
abstract="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.",
optnote="ADAS",
optnote="exported from refbase (http://refbase.cvc.uab.es/show.php?record=1937), last updated on Fri, 23 Jun 2017 10:59:14 +0200",
issn="1057-7149",
doi="10.1109/TIP.2011.2170080",
file=":http://refbase.cvc.uab.es/files/RoS2012b.pdf:PDF"
}