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Optimal Geometric Fitting Under the Truncated L-2-Norm

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Author

  • Erik Ask
  • Olof Enqvist
  • Fredrik Kahl

Summary, in English

This paper is concerned with model fitting in the presence of noise and outliers. Previously it has been shown that the number of outliers can be minimized with polynomial complexity in the number of measurements. This paper improves on these results in two ways. First, it is shown that for a large class of problems, the statistically more desirable truncated L-2-norm can be optimized with the same complexity. Then, with the same methodology, it is shown how to transform multi-model fitting into a purely combinatorial problem-with worst-case complexity that is polynomial in the number of measurements, though exponential in the number of models. We apply our framework to a series of hard registration and stitching problems demonstrating that the approach is not only of theoretical interest. It gives a practical method for simultaneously dealing with measurement noise and large amounts of outliers for fitting problems with low-dimensional models.

Publishing year

2013

Language

English

Pages

1722-1729

Publication/Series

2013 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)

Document type

Conference paper

Publisher

IEEE - Institute of Electrical and Electronics Engineers Inc.

Topic

  • Mathematics

Conference name

26th IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2013

Conference date

2013-06-23 - 2013-06-28

Conference place

Portland, OR, United States

Status

Published

ISBN/ISSN/Other

  • ISSN: 1063-6919