| 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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| Project Status |
Completed (Fiscal Year 2004)
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| Budget Amount *help |
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2004: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 2003: ¥2,100,000 (Direct Cost: ¥2,100,000)
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| Keywords | 3D image / 3D modeling / Surface model / 3D Image recognition / 3D image generation / Object-based coding / 物体モデル / 物体認識 / 形状合成 / 不変量 / PDEモデル / 領域分割 / オブジェクトベースド符号化 / Hough変換 |
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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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