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

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.

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Correspondence to Eric Paquet.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://doi.org/creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Paquet, E. Representation of 3D and 4D Objects Based on an Associated Curved Space and a General Coordinate Transformation Invariant Description. EURASIP J. Adv. Signal Process. 2007, 042505 (2006). https://doi.org/10.1155/2007/42505

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Keywords

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