Abstract
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. © 2011 IEEE.
Original language | English |
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Article number | 6031920 |
Pages (from-to) | 2089-2098 |
Journal | IEEE Transactions on Image Processing |
Volume | 21 |
Issue number | 4 |
DOIs | |
Publication status | Published - 1 Apr 2012 |
Keywords
- Curve/surface fitting
- geometric distance estimation
- implicit polynomial (IP)
- residual error minimization