# SIMULTANEOUS ROBUST FITTING OF MULTIPLE CURVES

### Jean-Philippe Tarel, Pierre Charbonnier, Sio-Song Ieng

#### Abstract

In this paper, we address the problem of robustly recovering several instances of a curve model from a single noisy data set with outliers. Using M-estimators revisited in a Lagrangian formalism, we derive an algorithm that we call SMRF, which extends the classical Iterative Reweighted Least Squares algorithm (IRLS). Compared to the IRLS, it features an extra probability ratio, which is classical in clustering algorithms, in the expression of the weights. Potential numerical issues are tackled by banning zero probabilities in the computation of the weights and by introducing a Gaussian prior on curves coefficients. Applications to camera calibration and lane-markings tracking show the effectiveness of the SMRF algorithm, which outperforms classical Gaussian mixture model algorithms in the presence of outliers.

Download#### Paper Citation

#### in Harvard Style

Tarel J., Charbonnier P. and Ieng S. (2007). **SIMULTANEOUS ROBUST FITTING OF MULTIPLE CURVES** . In *Proceedings of the Second International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP,* ISBN 978-972-8865-73-3, pages 175-182. DOI: 10.5220/0002040801750182

#### in Bibtex Style

@conference{visapp07,

author={Jean-Philippe Tarel and Pierre Charbonnier and Sio-Song Ieng},

title={SIMULTANEOUS ROBUST FITTING OF MULTIPLE CURVES},

booktitle={Proceedings of the Second International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP,},

year={2007},

pages={175-182},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0002040801750182},

isbn={978-972-8865-73-3},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the Second International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP,

TI - SIMULTANEOUS ROBUST FITTING OF MULTIPLE CURVES

SN - 978-972-8865-73-3

AU - Tarel J.

AU - Charbonnier P.

AU - Ieng S.

PY - 2007

SP - 175

EP - 182

DO - 10.5220/0002040801750182