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  • Research Article
  • Open Access

Representation of 3D and 4D Objects Based on an Associated Curved Space and a General Coordinate Transformation Invariant Description

EURASIP Journal on Advances in Signal Processing20062007:042505

  • Received: 25 January 2006
  • Accepted: 26 August 2006
  • Published:


This paper presents a new theoretical approach for the description of multidimensional objects for which 3D and 4D are particular cases. The approach is based on a curved space which is associated to each object. This curved space is characterised by Riemannian tensors from which invariant quantities are defined. A descriptor or index is constructed from those invariants for which statistical and abstract graph representations are associated. The obtained representations are invariant under general coordinate transformations. The statistical representation allows a compact description of the object while the abstract graph allows describing the relations in between the parts as well as the structure.


  • Information Technology
  • Graph Representation
  • Statistical Representation
  • Theoretical Approach
  • Quantum Information

Authors’ Affiliations

Visual Information Technology Group, National Research Council, M-50 Montreal Road, Ottawa, ON K1A 0R6, Canada


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© Eric Paquet 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.