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Tractable Algorithms for Robust Model Estimation

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Author

Summary, in English

What is the computational complexity of geometric model estimation in the presence of noise and outliers? We show that the number of outliers can be minimized in polynomial time with respect to the number of measurements, although exponential in the model dimension. Moreover, for a large class of problems, we prove that the statistically more desirable truncated L2-norm can be optimized with the same complexity. In a similar vein, it is also shown how to transform a multi-model estimation problem into a purely combinatorial one—with worst-case complexity that is polynomial in the number of measurements but exponential in the number of models. We apply our framework to a series of hard fitting problems. It gives a practical method for simultaneously dealing with measurement noise and large amounts of outliers in the estimation of low-dimensional models. Experimental results and a comparison to random sampling techniques are presented for the applications rigid registration, triangulation and stitching.

Publishing year

2015

Language

English

Pages

115-129

Publication/Series

International Journal of Computer Vision

Volume

112

Issue

1

Document type

Journal article

Publisher

Springer

Topic

  • Mathematics

Keywords

  • Outliers Geometry Optimization 3D reconstruction Image registration

Status

Published

Research group

  • Mathematical Imaging Group

ISBN/ISSN/Other

  • ISSN: 1573-1405