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Machine Learning

, Volume 50, Issue 1–2, pp 45–71 | Cite as

EM, MCMC, and Chain Flipping for Structure from Motion with Unknown Correspondence

  • Frank Dellaert
  • Steven M. Seitz
  • Charles E. Thorpe
  • Sebastian Thrun
Article

Abstract

Learning spatial models from sensor data raises the challenging data association problem of relating model parameters to individual measurements. This paper proposes an EM-based algorithm, which solves the model learning and the data association problem in parallel. The algorithm is developed in the context of the the structure from motion problem, which is the problem of estimating a 3D scene model from a collection of image data. To accommodate the spatial constraints in this domain, we compute virtual measurements as sufficient statistics to be used in the M-step. We develop an efficient Markov chain Monte Carlo sampling method called chain flipping, to calculate these statistics in the E-step. Experimental results show that we can solve hard data association problems when learning models of 3D scenes, and that we can do so efficiently. We conjecture that this approach can be applied to a broad range of model learning problems from sensordata, such as the robot mapping problem.

expectation-maximization Markov chain Monte Carlo data association structure from motion correspondence problem efficient sampling computer vision 

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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Frank Dellaert
    • 1
  • Steven M. Seitz
    • 2
  • Charles E. Thorpe
    • 3
  • Sebastian Thrun
    • 3
  1. 1.College of ComputingGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Department of Computer Science and EngineeringUniversity of WashingtonSeattleUSA
  3. 3.School of Computer ScienceCarnegie Mellon UniversityPittsburghUSA

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