Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Representation of 3D and 4D Objects Based on an Associated Curved Space and a General Coordinate Transformation Invariant Description | Hindawi Publishing Corporation EURASIP Journal on Advances in Signal Processing Volume 2007 Article ID 42505 10 pages doi 2007 42505 Research Article Representation of 3D and 4D Objects Based on an Associated Curved Space and a General Coordinate Transformation Invariant Description Eric Paquet Visual Information Technology Group National Research Council M-50 Montreal Road Ottawa ON Canada K1A 0R6 Received 25 January 2006 Revised 24 July 2006 Accepted 26 August 2006 Recommended by Petros Daras 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. Copyright 2007 Eric Paquet. 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. 1. INTRODUCTION Content-based description plays a prominent role in indexing and retrieval 1-4 . It is therefore important to develop invariant representations for 3D objects. An excellent review about indexing and retrieval of 3D objects can be found in 1-3 . As can be seen from this review most of the proposed techniques are invariant under a very limited class of transformations for example translations scaling and rotations. Relatively less attention has been devoted to the development of representations that are invariant under .
