Rank Classification of Linear Line Structure in Determining Trifocal Tensor

  • Ming Zhao
  • Ronald Chung
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5303)


The problem we address is: given line correspondences over three views, what is the condition of the line correspondences for the spatial relation of the three associated camera positions to be uniquely recoverable? We tackle the problem from the perspective of trifocal tensor, a quantity that captures the relative positions of the cameras in relation to the three views. We show that the rank of the matrix that leads to the estimation of the tensor reduces to 7, 11, 15 respectively for line pencil, point star, and ruled plane, which are structures that belong to linear line space; and 12, 19, 23 for general ruled surface, general linear congruence, and general linear line complex. These critical structures are quite typical in reality, and thus the findings are important to the validity and stability of practically all algorithms related to structure from motion and projective reconstruction using line correspondences.


Motion Estimation Camera Motion Line Structure Estimation Matrix Linear Line 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Ming Zhao
    • 1
  • Ronald Chung
    • 1
  1. 1.Department of Mechanical & Automation EngineeringThe Chinese University of Hong KongHong Kong

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