TY  - JOUR
AU  - Mohammad Rouhani
AU  - Angel Sappa
PY  - 2012//
TI  - Implicit Polynomial Representation through a Fast Fitting Error Estimation
T2  - TIP
JO  - IEEE Transactions on Image Processing
SP  - 2089
EP  - 2098
VL  - 21
IS  - 4
N2  - 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.
SN  - 1057-7149
L1  - http://refbase.cvc.uab.es/files/RoS2012b.pdf
UR  - http://dx.doi.org/10.1109/TIP.2011.2170080
N1  - ADAS
ID  - Mohammad Rouhani2012
ER  -