High-Order Differential Geometry of Curves for Multiview Reconstruction and Matching

  • Ricardo Fabbri
  • Benjamin B. Kimia
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3757)


The relationship between the orientation and curvature of projected curves and the orientation and curvature of the underlying space curve has been previously established. This has allowed a disambiguation of correspondences in two views and a transfer of these properties to a third view for confirmation. We propose that a higher-order intrinsic differential geometry attribute, namely, curvature derivative, is necessary to account for the range of variation of space curves and their projections. We derive relationships between curvature derivative in a projected view, and curvature derivative and torsion of the underlying space curve. Regardless of the point, tangent, and curvature, any pair of curvature derivatives are possible correspondences, but most would lead to very high torsion and curvature derivatives. We propose that the minimization of third order derivatives of the reconstruction, which combines torsion and curvature derivative of the space curve, regularizes the process of finding the correct correspondences.


Computer Vision Space Curve Illusory Contour Total Curvature Curvature Derivative 
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 2005

Authors and Affiliations

  • Ricardo Fabbri
    • 1
    • 2
  • Benjamin B. Kimia
    • 1
  1. 1.Division of EngineeringBrown UniversityProvidenceUSA
  2. 2.Funded by CNPqBrazil

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