Randomized hybrid linear modeling by local best-fit flats

Teng Zhang, Arthur Szlam, Yi Wang, Gilad Lerman

Research output: Chapter in Book/Report/Conference proceedingConference contribution

36 Scopus citations

Abstract

The hybrid linear modeling problem is to identify a set of d-dimensional affine sets in RD. It arises, for example, in object tracking and structure from motion. The hybrid linear model can be considered as the second simplest (behind linear) manifold model of data. In this paper we will present a very simple geometric method for hybrid linear modeling based on selecting a set of local best fit flats that minimize a global l1 error measure. The size of the local neighborhoods is determined automatically by the Jones' β2 numbers; it is proven under certain geometric conditions that good local neighborhoods exist and are found by our method. We also demonstrate how to use this algorithm for fast determination of the number of affine subspaces. We give extensive experimental evidence demonstrating the state of the art accuracy and speed of the algorithm on synthetic and real hybrid linear data.

Original languageEnglish (US)
Title of host publication2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2010
Pages1927-1934
Number of pages8
DOIs
StatePublished - 2010
Event2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2010 - San Francisco, CA, United States
Duration: Jun 13 2010Jun 18 2010

Publication series

NameProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
ISSN (Print)1063-6919

Other

Other2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2010
CountryUnited States
CitySan Francisco, CA
Period6/13/106/18/10

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition

Cite this

Zhang, T., Szlam, A., Wang, Y., & Lerman, G. (2010). Randomized hybrid linear modeling by local best-fit flats. In 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2010 (pp. 1927-1934). [5539866] (Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition). https://doi.org/10.1109/CVPR.2010.5539866