Reconstruction of general curves, using factorization and bundle adjustment

Rikard Berthilsson, Kalle Åström, Anders Heyden

Research output: Contribution to journalArticlepeer-review

27 Citations (SciVal)


In this paper, we extend the notion of affine shape, introduced by Sparr, from finite point sets to curves. The extension makes it possible to reconstruct 3D-curves up to projective transformations, from a number of their 2D-projections. We also extend the bundle adjustment technique from point features to curves. The first step of the curve reconstruction algorithm is based on affine shape. It is independent of choice of coordinates, is robust, does not rely on any preselected parameters and works for an arbitrary number of images. In particular this means that, except for a small set of curves (e.g. a moving line), a solution is given to the aperture problem of finding point correspondences between curves. The second step takes advantage of any knowledge of measurement errors in the images. This is possible by extending the bundle adjustment technique to curves. Finally, experiments are performed on both synthetic and real data to show the performance and applicability of the algorithm.

Original languageEnglish
Pages (from-to)171-182
Number of pages12
JournalInternational Journal of Computer Vision
Issue number3
Publication statusPublished - 2001 Feb

Subject classification (UKÄ)

  • Mathematics
  • Computer Vision and Robotics (Autonomous Systems)


  • 3D
  • Affine shape
  • Bundle adjustment
  • Curves
  • Error analysis
  • Proximity measure
  • Structure from motion


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