PT Journal
AU Mohammad Rouhani
   Angel Sappa
TI Implicit Polynomial Representation through a Fast Fitting Error Estimation
SO IEEE Transactions on Image Processing
JI TIP
PY 2012
BP 2089
EP 2098
VL 21
IS 4
DI 10.1109/TIP.2011.2170080
AB 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.
ER