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Geometric Modeling in Computer Vision: An Introduction to Projective Geometry

  1. Rimon Elias

Published Online: 16 MAR 2009

DOI: 10.1002/9780470050118.ecse585

Wiley Encyclopedia of Computer Science and Engineering

Wiley Encyclopedia of Computer Science and Engineering

How to Cite

Elias, R. 2009. Geometric Modeling in Computer Vision: An Introduction to Projective Geometry. Wiley Encyclopedia of Computer Science and Engineering. 1400–1416.

Author Information

  1. The German University in Cairo, New Cairo City, Egypt

Publication History

  1. Published Online: 16 MAR 2009

Abstract

This article surveys many fundamental aspects of projective geometry that have been used extensively in computer vision literature. Geometrical relationships are investigated when one, two, or more cameras are observing the scene. Camera parameters in terms of locations and orientations with respect to three dimensional (3D) space and with respect to other cameras create relationships that can be expressed mathematically. Expressing these relationships is the main focus of this article.

Keywords:

  • projective geometry;
  • single view geometry;
  • pinhole camera;
  • perspective projection matrix;
  • intrinsic parameters;
  • extinsic parameters;
  • rotation system;
  • stero vision;
  • binocular vision;
  • epipolar geometry;
  • fundamental matrix;
  • essential matrix;
  • homography matrix;
  • plane homography;
  • three-view geometry;
  • trifocal tensor;
  • 3-d reconstruction