Representation of 3-D and 4-D Objects based on an Associated Curved Space and a General Coordinate Transformations Invariant Description

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TypeBook Chapter
Subjectabstract graph; general coordinate transformation; invariant representation; Riemannian geometry; transformation générale des coordonnées; représentation invariante; géométrie riemannienne
AbstractThis paper presents a new theoretical approach for the description of multidimensional objects for which 3-D and 4-D 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 a statistical and an abstract graph representation 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.
Publication date
AffiliationNRC Institute for Information Technology; National Research Council Canada
Peer reviewedNo
NRC number48733
NPARC number8913739
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Record identifier202566f6-ebcc-4bd2-94a0-6de5ec79937e
Record created2009-04-22
Record modified2016-05-09
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