2004 Fiscal Year Final Research Report Summary
Representation, recognition and synthesis of 3D images using Lie algebra surace model
| Project/Area Number |
15560335
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Communication/Network engineering
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| Research Institution | CHUO UNIVERSITY |
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Principal Investigator |
CHAO Jinhui Chuo University, Faculty of Science and Engineering, Professor, 理工学部, 教授 (60227345)
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| Co-Investigator(Kenkyū-buntansha) |
MAKINO Mitsunori Chuo University, Faculty of Science and Engineering, Professor, 理工学部, 教授 (90238890)
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| Project Period (FY) |
2003 – 2004
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| Keywords | 3D image / 3D modeling / Surface model / 3D Image recognition / 3D image generation / Object-based coding |
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| Research Abstract |
Recently, 3D images and 3D computer graphics are playing an important rule in virtual environment, multimedia communications and digital contents. Therefore, it is highly desirable to have powerful and efficient model for 3D free surfaces for efficient representation, coding, recognition and synthesis of 3D objects.
This research presents a global method to represent surface models of 3D objects invariantly under Euclidean or Affine motions using their tangential and normal Lie algebras. The global shapes as Lie groups are completely described by purelylocal information in these Lie algebra. Particularly, we focus on linear Lie algebras and Hamiltonian Lie algebras, which can represent algebraic shapes and a much wider class of non-algebraic shapes as well. We obtain the complete sets of invariants under Euclidean motions which uniquely, determines and reproduces the objects.
Algorithms are also proposed to extract these invariants easily and robustly from local data on the surfaces by solving a system of linear equations. These invariants can then be used in segmentation and recognition of the objects.
We also propose a novel surface model called fibre-bundle model for free surfaces, which represents an arbitrary surface as a local product between a base curve and a fibre curve. In particular, this model using fibres as 1-parameter group of linear Lie algebra or Hamilton Lie algebra is very efficient in the sense that the surface can be represented by a base curve and six invariants or 15 parameters, in the linear Lie algebraic case. The surface can be synthesised fastly without numerical error.
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