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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

https://doi.org/10.1155/2007/42505

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

Abstract

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.

Keywords

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

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Authors’ Affiliations

(1)
Visual Information Technology Group, National Research Council, M-50 Montreal Road, Ottawa, ON K1A 0R6, Canada

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