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Shape and motion from image streams: a factorization method.

C Tomasi1, T Kanade

  • 1School of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15213, USA.

Proceedings of the National Academy of Sciences of the United States of America
|November 1, 1993
PubMed
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This study introduces a novel factorization method for recovering 3D scene geometry and camera motion from image streams. It accurately reconstructs shape and motion without intermediate depth calculations, even with occlusions.

Area of Science:

  • Computer Vision
  • Robotics
  • 3D Reconstruction

Background:

  • Inferring scene geometry and camera motion from image streams is challenging, especially for distant objects.
  • Existing methods often struggle with ill-conditioned problems and require depth as an intermediate step.

Purpose of the Study:

  • To develop a robust factorization method for recovering 3D shape and camera motion from image sequences.
  • To overcome the limitations of existing methods, particularly for distant objects and occluded features.

Main Methods:

  • Representing image streams as a 2F x P measurement matrix of tracked image coordinates.
  • Utilizing the rank-3 property of the measurement matrix under orthographic projection.
  • Employing singular value decomposition (SVD) to factor the measurement matrix into shape and motion components.

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Main Results:

  • The factorization method successfully recovers accurate 3D scene geometry and camera motion.
  • The method handles partially filled measurement matrices, accommodating feature disappearances due to occlusions or tracking failures.
  • No smoothing is introduced in the recovered shape or motion, preserving fine details.

Conclusions:

  • The developed factorization method provides an effective solution for 3D scene geometry and camera motion inference from image streams.
  • It offers accurate and robust results, even in the presence of occlusions and tracking issues.
  • The approach avoids intermediate depth computation, simplifying the reconstruction process.