The browser you are using is not supported by this website. All versions of Internet Explorer are no longer supported, either by us or Microsoft (read more here: https://www.microsoft.com/en-us/microsoft-365/windows/end-of-ie-support).

Please use a modern browser to fully experience our website, such as the newest versions of Edge, Chrome, Firefox or Safari etc.

Critical configurations for projective reconstruction from multiple views

På svenska

Author

  • Richard Hartley
  • Fredrik Kahl

Summary, in English

This paper investigates a classical problem in computer vision: Given corresponding points in multiple images, when is there a unique projective reconstruction of the 3D geometry of the scene points and the camera positions? A set of points and cameras is said to be critical when there is more than one way of realizing the resulting image points. For two views, it has been known for almost a century that the critical configurations consist of points and camera lying on a ruled quadric surface. We give a classification of all possible critical configurations for any number of points in three images, and show that in most cases, the ambiguity extends to any number of cameras. The underlying framework for deriving the critical sets is projective geometry. Using a generalization of Pascal's Theorem, we prove that any number of cameras and scene points on an elliptic quartic form a critical set. Another important class of critical configurations consists of cameras and points on rational quartics. The theoretical results are accompanied by many examples and illustrations.

Publishing year

2007

Language

English

Pages

5-47

Publication/Series

International Journal of Computer Vision

Volume

71

Issue

1

Document type

Journal article

Publisher

Springer

Topic

  • Mathematics

Keywords

  • multiple view geometry
  • critical sets
  • degeneracy
  • projective geometry
  • structure from motion
  • geometry 3D reconstruction

Status

Published

ISBN/ISSN/Other

  • ISSN: 1573-1405