Dual Computation of Projective Shape and Camera Positions from Multiple Images

  • Authors:

  • Stefan Carlsson;Daphna Weinshall

  • Affiliations:

  • Dept. of Numerical Analysis and Computing Science, Royal Institute of Technology, S-100 44 Stockholm, Sweden. E-mail: stefanc@nada.kth.se;Institute of Computer Science, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel. E-mail: daphna@cs.huji.ac.il

  • Venue:
  • International Journal of Computer Vision
  • Year:
  • 1998

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Abstract

Given multiple image data from a set of points in3D, there are two fundamental questions that can beaddressed:What is the structure of the set of points in 3D?What are the positions of the cameras relative to thepoints?In this paper we show that, for projective views and withstructure and position defined projectively, these problems aredual because they can be solved using constraint equations wherespace points and camera positions occur in a reciprocal way. Morespecifically, by using canonical projective reference frames forall points in space and images, the imaging of point sets in spaceby multiple cameras can be captured by constraint relationsinvolving three different kinds of parameters only, coordinates of:(1) space points, (2) camera positions (3) image points. Theduality implies that the problem of computing camera positions fromp points in q views can be solved with the same algorithm asthe problem of directly reconstructing q+4 points in p-4views. This unifies different approaches to projectivereconstruction: methods based on external calibration and directmethods exploiting constraints that exist between shape and imageinvariants.