The Mathematica Book
A Survey of Content Based 3D Shape Retrieval Methods
SMI '04 Proceedings of the Shape Modeling International 2004
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Determining Characteristic Views of a 3D Object by Visual Hulls and Hausdorff Distance
3DIM '05 Proceedings of the Fifth International Conference on 3-D Digital Imaging and Modeling
Three-dimensional shape searching: state-of-the-art review and future trends
Computer-Aided Design
3D object retrieval using the 3D shape impact descriptor
Pattern Recognition
SHREC'09 track: generic shape retrieval
EG 3DOR'09 Proceedings of the 2nd Eurographics conference on 3D Object Retrieval
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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.