Sensitivity analysis of optimized curve fitting to uniform-noise point samples
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2012-05
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Curve reconstruction from noisy point samples is needed for surface reconstruction in many applications (e.g. medical imaging, reverse engineering,etc.) -- Because of the sampling noise, curve reconstruction is conducted by minimizing the fitting error (f), for several degrees of continuity (usually C0, C1 and C2) -- Previous works involving smooth curves lack the formal assessment of the effect on optimized curve reconstruction of several inputs such as number of control points (m), degree of the parametric curve (p), composition of the knot vector (U), and degree of the norm (k) to calculate the penalty function (f) -- In response to these voids, this article presents a sensitivity analysis of the effect of mand k on f -- We found that the geometric goodness of the fitting (f) is much more sensitive to m than to k -- Likewise, the topological faithfulness on the curve fit is strongly dependent on m -- When an exaggerate number of control points is used, the resulting curve presents spurious loops, curls and peaks, not present in the input data -- We introduce in this article the spectral (frequency) analysis of the derivative of the curve fit as a means to reject fitted curves with spurious curls and peaks -- Large spikes in the derivative signal resemble Kronecker or Dirac Delta functions, which flatten the frequency content adinfinitum -- Ongoing work includes the assessment of the effect of curve degree p on f for non-Nyquist point samples
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@inproceedings{oruiz_TMCE2012,
author ={Oscar E. Ruiz and C. Cortes and Diego A. Acosta and M. Aristizabal},
title ={Sensitivity Analysis of Optimized Curve Fitting to Uniform-Noise Point Samples},
booktitle ={Proceedings of the 9th International Symposium on Tools and Methods of Competitive Engineering, TMCE 2012},
year ={2012},
editor ={ I. Horv\'ath and Z. Rus\'ak and A. Albers and M. Behrendt},
month ={May 7-11},
address ={ Karlsruhe, Germany },
keys ={Parametric curve reconstruction, noisy point cloud,
sensitivity analysis, minimization},
organization ={Delft University of Technology and Karlsruhe Institute of Technology},
pages ={ 671--684 },
publisher ={Faculty of Industrial Design Engineering, Delft University of Technology},
abstract ={Curve reconstruction from noisy point samples is needed for surface reconstruction in many applications (e.g. medical imaging, reverse engineering, etc.). Because of the sampling noise, curve reconstruction is conducted by minimizing the fitting error ($f$), for several degrees of continuity (usually $C^0$, $C^1$ and $C^2$). Previous works involving smooth curves lack the formal assessment of the effect on optimized curve reconstruction of several inputs such as number of control points ($m$), degree of the parametric curve ($p$), composition of the knot vector ($U$), and degree of the norm ($k$) to calculate the penalty function ($f$). In response to these voids, this article presents a sensitivity analysis of the effect of $m$ and $k$ on $f$. We found that the geometric goodness of the fitting ($f$) is much more sensitive to $m$ than to $k$. Likewise, the topological faithfulness on the curve fit is strongly dependent on $m$. When an exaggerate number of control points is used, the resulting curve presents spurious loops, curls and peaks, not present in the input data. We introduce in this article the spectral (frequency) analysis of the derivative of the curve fit as a means to reject fitted curves with spurious curls and peaks. Large spikes in the derivative signal resemble Kronecker or Dirac Delta functions, which flatten the frequency content ad-infinitum. Ongoing work includes the assessment of the effect of curve degree $p$ on $f$ for non-Nyquist point samples},
isbn ={978-90-5155-082-5}
}