A Study of Efficient Coding Methods of Three Dimensional Shapes
Project/Area Number  01550260 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
電子通信系統工学

Research Institution  Nagaoka University of Technology 
Principal Investigator 
OHTAKE Kohhei Nagaoka University of Technology, Faculty of Engineering, Professor, 工学部, 教授 (30203813)

CoInvestigator(Kenkyūbuntansha) 
荻原 春生 長岡技術科学大学, 工学部, 助教授 (30185532)

Project Fiscal Year 
1989 – 1990

Project Status 
Completed(Fiscal Year 1991)

Budget Amount *help 
¥1,800,000 (Direct Cost : ¥1,800,000)
Fiscal Year 1990 : ¥800,000 (Direct Cost : ¥800,000)
Fiscal Year 1989 : ¥1,000,000 (Direct Cost : ¥1,000,000)

Keywords  Three Dimensional Shape / Tangential Coordinates / Curvature / Power spectrum / Spherical harmonics / Spherical Fourier Transform / Sampling Theorem / Vector Quantization / 三次元凸形状 / 接平面極座標表示 / 曲率 / 電力スペクトル / 球面調和関数 / 球面フリエ変換 / 標本化定理 / ベクトル量子化 / ガウス曲率 / 支持関数 / 変換符号化 / ガウス像 / 形状のスペクトル 
Research Abstract 
In order to investigate an effective coding method of smooth three dimensional convex shapes, techniques of efficient shape representation, samplingreconstruction and quantization are studied theoretically and by computer simulation. The research results are summarized as follows. 1. An efficient shape representation method by tangential plane coordinates is proposed, which is based on shape curvature. Using the representation, a power spectrum of a shape is introduced and it is shown that the spectrum is invariable to parallel displacement and rotation of the shape and has low pass characteristics. 2. From the above properties, band width of the shape is defined as an invariable independent to coordinates in the space. It is shown such a sampling theorem that the band limited shape is reconstructed completely from a finite number of sample values of the representation function. 3. For the band unlimited shape, the reconstructed shape from a finite number of sample values has some distor
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tion. The optimum sampling points selection method for minimizing the shape distortion power is shown. 4. Since the power spectrum of the shape by this tangential polar coordinates is narrowed than that by conventional polar coordinates, it is shown from S/N characteristics for the shape distortion and computer simulation that the shape is efficiently sampled and reconstructed with the smaller number of sampling points selected by the method. 5. Three kinds of quantization schemes are proposed ; scalar quantization of sample values of the representation function, scalar quantization and gainshape vector quantization of the spectrum of the shape. Quantization errors are theoretically analyzed for these three schemes and it is shown that the shape spectrum scalar quantization scheme is most effective from evaluation of quantization rate vs. S/N characteristics for the reconstructed shape and quantizer realizability. This result is assured by computer simulation of a samplingquantizationreconstruction system of convex shapes. 今後の課題として,一般の三次元形状への本理論の展開が重要である. Less

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Research Output
(4results)