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Critical curves and surfaces for euclidean reconstruction

In English

Författare

  • Fredrik Kahl
  • Richard Hartley

Summary, in English

The problem of recovering scene structure and camera motion from images has a number of inherent ambiguities. In this paper, configurations of points and cameras are analyzed for which the image points alone are insufficient to recover the scene geometry uniquely. Such configurations are said to be critical. For two views, it is well-known that a configuration is critical only if the two camera centres and all points lie on a ruled quadric. However, this is only a necessary condition. We give a complete characterization of the critical surfaces for two calibrated cameras and any number of points. Both algebraic and geometric characterizations of such surfaces are given. The existence of critical sets for n-view projective reconstruction has recently been reported in the literature. We show that there are critical sets for n-view Euclidean reconstruction as well. For example, it is shown that for any placement of three calibrated cameras, there always exists a critical set consisting of any number of points on a fourth-degree curve.

Avdelning/ar

Publiceringsår

2002

Språk

Engelska

Sidor

447-462

Publikation/Tidskrift/Serie

Computer Vision - ECCV 2002, PT II

Volym

2351

Dokumenttyp

Konferensbidrag

Förlag

Springer

Ämne

  • Mathematics

Nyckelord

  • Euclidean reconstruction
  • critical surfaces
  • critical curves
  • scene structure
  • fourth-degree curve
  • n-view projective reconstruction
  • calibrated cameras
  • scene geometry
  • camera motion

Conference name

Computer Vision - ECCV 2002. 7th European Conference on Computer Vision.

Conference date

2002-05-28 - 2002-05-31

Conference place

Copenhagen, Denmark

Status

Published

ISBN/ISSN/Övrigt

  • ISSN: 0302-9743
  • ISSN: 1611-3349
  • ISBN: 3-540-43744-4