| Project/Area Number |
07650075
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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 |
Engineering fundamentals
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| Research Institution | University of Tokyo |
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Principal Investigator |
SUGIHARA Kokichi University of Tokyo, Department of Mathemematical Engineering and Information Physics, Professor, 大学院・工学系研究科, 教授 (40144117)
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| Co-Investigator(Kenkyū-buntansha) |
IMAI Toshiyuki University of Tokyo, Department of Mathemematical Engineering and Information Ph, 大学院・工学系研究科, 助手 (90213214)
HAYAMI Ken University of Tokyo, Department of Mathemematical Engineering and Information Ph, 大学院・工学系研究科, 助教授 (20251358)
OKABE Yasunori University of Tokyo, Department of Mathemematical Engineering and Information Ph, 大学院・工学系研究科, 教授 (30028211)
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| Project Period (FY) |
1995 – 1996
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| Project Status |
Completed (Fiscal Year 1996)
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| Budget Amount *help |
¥2,500,000 (Direct Cost: ¥2,500,000)
Fiscal Year 1996: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 1995: ¥1,000,000 (Direct Cost: ¥1,000,000)
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| Keywords | Image processing / Computational geometry / Distance transformation / Voronoi diagram / Minkowski sum / Spline curve / Robust computation / Triangulation / スプライン曲面 / ディジタル画像 / ミンコフスキー演算 / 多角形ボロノイ図 / 位相優先法 / 記号摂動法 |
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| Research Abstract |
The purpose of this research was to apply our method for robust geometric computation to image processing. Conventionally image processing techniques are based on the pixel structure of the digital images, and consequently require huge space of memory and huge time of computation. This research aims at replacing these techniques by spline-based techniques and thus saving space and time.
In this research period, we obtained the following results. First, a method was constructed for representing digital color images by spline surfaces ; because of the flexibility of spline surfaces, we can expand and shrink image data in any scales. Secondly, the Minkowski algebra was extended to a larger algebra in which any element has its inverse. This extension guarantees the stability of the Minkowski addition and substraction, and therefore we can manipulate figures without worrying about flase elements. Thirdly, robust geometric algorithms were constructed and implemented for Voronoi diagram on the plane, Voronoi diagram on the sphere, Voronoi diagram in the three-dimensional space, Voronoi diagrams for general figures, etc. Fourthly, several efficient methods were found for judging the sign of a large integer by modular arithmetic.
Those results altogether enable us to represent and manipulate image and figure information efficiently from both time and space points of view.
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