Estimating 3D positions and velocities of projectiles from monocular views

Evan Ribnick, Stefan Atev, Nikolaos P. Papanikolopoulos

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


In this paper, we consider the problem of localizing a projectile in 3D based on its apparent motion in a stationary monocular view. A thorough theoretical analysis is developed, from which we establish the minimum conditions for the existence of a unique solution. The theoretical results obtained have important implications for applications involving projectile motion. A robust, nonlinear optimization-based formulation is proposed, and the use of a local optimization method is justified by detailed examination of the local convexity structure of the cost function. The potential of this approach is validated by experimental results.

Original languageEnglish (US)
Pages (from-to)938-944
Number of pages7
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Issue number5
StatePublished - 2009

Bibliographical note

Funding Information:
This work has been supported by the US Department of Homeland Security, the ITS Institute at the University of Minnesota, and the US National Science Foundation (through grants IIS-0219863, CNS-0324864, CNS-0420836, IIP-0443945, IIP-0726109, and CNS-0708344).


  • 3D localization
  • Optimization
  • Projectile motion


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