Two efficient solutions for visual odometry using directional correspondence

Oleg Naroditsky, Xun S. Zhou, Jean Gallier, Stergios I. Roumeliotis, Kostas Daniilidis

Research output: Contribution to journalArticlepeer-review

67 Scopus citations


This paper presents two new, efficient solutions to the two-view, relative pose problem from three image point correspondences and one common reference direction. This three-plus-one problem can be used either as a substitute for the classic five-point algorithm, using a vanishing point for the reference direction, or to make use of an inertial measurement unit commonly available on robots and mobile devices where the gravity vector becomes the reference direction. We provide a simple, closed-form solution and a solution based on algebraic geometry which offers numerical advantages. In addition, we introduce a new method for computing visual odometry with RANSAC and four point correspondences per hypothesis. In a set of real experiments, we demonstrate the power of our approach by comparing it to the five-point method in a hypothesize-and-test visual odometry setting.

Original languageEnglish (US)
Article number6095561
Pages (from-to)818-824
Number of pages7
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Issue number4
StatePublished - 2012

Bibliographical note

Funding Information:
The authors are grateful for support through the following grants: US National Science Foundation (NSF)-IIS-0713260, NSF-IIP-0742304, NSF-IIP-0835714, and ARL MAST-CTA W911NF-08-2-0004.


  • Computer vision
  • Groebner basis
  • minimal problems
  • structure from motion
  • visual odometry


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