IEEE Trans Image Process - Implicit polynomial representation through a fast fitting error estimation.

Tópicos

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Resumo

This 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.

Resumo Limpo

paper present simpl distanc estim implicit polynomi fit comput height simplex built point surfac ie triangl d tetrahedron d use coars reliabl estim orthogon distanc propos distanc can describ function coeffici implicit polynomi moreov differenti smooth behavior henc can use gradientbas optim paper use levenbergmarquardt framework shown particular devot nonlinear least squar problem propos estim general gradientbas distanc estim wide use literatur experiment result d d data set provid comparison stateoftheart techniqu present show advantag propos approach

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