On Projection Matrices {\cal P}^k\,{\rightarrow}\, {\cal P}^2,k\,{=}\,3,\ldots, 6, and their Applications in Computer Vision

  • Authors:

  • Lior Wolf;Amnon Shashua

  • Affiliations:

  • School of Computer Science and Engineering, The Hebrew University, Jerusalem 91904, Israel.;School of Computer Science and Engineering, The Hebrew University, Jerusalem 91904, Israel.

  • Venue:
  • International Journal of Computer Vision - Marr Prize Special Issue
  • Year:
  • 2002

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Abstract

Projection matrices from projective spaces {\cal P}^3 to {\cal P}^2 have long been used in multiple-view geometry to model the perspective projection created by the pin-hole camera. In this work we introduce higher-dimensional mappings {\cal P}^k\,{\rightarrow}\, {\cal P}^2,k\,{=}\,3,4,5,6 for the representation of various applications in which the world we view is no longer rigid. We also describe the multi-view constraints from these new projection matrices (where k 3) and methods for extracting the (non-rigid) structure and motion for each application.