Likelihood functions and confidence bounds for total-least-squares problems

Oscar Nestares, David J. Fleet, David J. Heeger

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

Abstract

This paper addresses the derivation of likelihood functions and confidence bounds for problems involving over-determined linear systems with noise in all measurements, often referred to as total-least-squares (TLS). It has been shown previously that TLS provides maximum likelihood estimates. But rather than being a function solely of the variables of interest, the associated likelihood functions increase in dimensionality with the number of equations. This has made it difficult to derive suitable confidence bounds, and impractical to use these probability functions with Bayesian belief propagation or Bayesian tracking. This paper derives likelihood functions that are defined only on the parameters of interest. This has two main advantages: first, the likelihood functions are much easier to use within a Bayesian framework; and second it is straightforward to obtain a reliable confidence bound on the estimates. We demonstrate the accuracy of our confidence bound in relation to others that have been proposed. Also, we use our theoretical results to obtain likelihood functions for estimating the direction of 3d camera translation.

Original languageEnglish (US)
Title of host publicationProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
PublisherIEEE
Pages523-530
Number of pages8
Volume1
StatePublished - 2000
EventCVPR '2000: IEEE Conference on Computer Vision and Pattern Recognition - Hilton Head Island, SC, USA
Duration: Jun 13 2000Jun 15 2000

Other

OtherCVPR '2000: IEEE Conference on Computer Vision and Pattern Recognition
CityHilton Head Island, SC, USA
Period6/13/006/15/00

Fingerprint

Maximum likelihood
Linear systems
Cameras

ASJC Scopus subject areas

  • Computer Vision and Pattern Recognition
  • Software
  • Control and Systems Engineering
  • Electrical and Electronic Engineering

Cite this

Nestares, O., Fleet, D. J., & Heeger, D. J. (2000). Likelihood functions and confidence bounds for total-least-squares problems. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Vol. 1, pp. 523-530). IEEE.

Likelihood functions and confidence bounds for total-least-squares problems. / Nestares, Oscar; Fleet, David J.; Heeger, David J.

Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. Vol. 1 IEEE, 2000. p. 523-530.

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

Nestares, O, Fleet, DJ & Heeger, DJ 2000, Likelihood functions and confidence bounds for total-least-squares problems. in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. vol. 1, IEEE, pp. 523-530, CVPR '2000: IEEE Conference on Computer Vision and Pattern Recognition, Hilton Head Island, SC, USA, 6/13/00.
Nestares O, Fleet DJ, Heeger DJ. Likelihood functions and confidence bounds for total-least-squares problems. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. Vol. 1. IEEE. 2000. p. 523-530
Nestares, Oscar ; Fleet, David J. ; Heeger, David J. / Likelihood functions and confidence bounds for total-least-squares problems. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. Vol. 1 IEEE, 2000. pp. 523-530
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