Optimal Geometric Fitting Under the Truncated L-2-Norm

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceeding


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.


  • Erik Ask
  • Olof Enqvist
  • Fredrik Kahl
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematics
Original languageEnglish
Title of host publication2013 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
PublisherIEEE--Institute of Electrical and Electronics Engineers Inc.
Publication statusPublished - 2013
Publication categoryResearch
Event26th IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2013 - Portland, OR, United States
Duration: 2013 Jun 232013 Jun 28

Publication series

ISSN (Print)1063-6919


Conference26th IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2013
CountryUnited States
CityPortland, OR