Representation of 3D and 4D Objects Based on an Associated Curved Space and a General Coordinate Transformation Invariant Description. (28th November 2006)

• Record Type: Journal Article
• Authors: Paquet Paquet, Eric Eric
• Other Names: Daras Daras Petros Petros Academic Editor.
• Is Part Of: EURASIP journal on advances in signal processing. Volume 2007(2007)
• Publication Date: 2006-11-28
• Subjects: Signal processing -- Periodicals; Traitement du signal; Signal processing; Periodicals; 621.3822
• DOI: 10.1155/2007/42505
• Languages: English
• ISSNs: 1687-6172

Abstract

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.