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標題: 三維離散X光轉換之正轉換實現
Implementation of Forward Transform for 3D discrete X-ray transform
作者: 石建軒
Shih, Chien-Hsuan
關鍵字: Volume Rendering;體積成像;3D Discrete X-Ray Transform;Fourier Slice Theorem;三維離散X射線轉換法;傅立葉切片理論
出版社: 通訊工程研究所
引用: [1] 林新德,“Turbo C 範例教本”,學貫行銷,2001. [2] 李懷哲,“極座標之傅立葉體積成像”,國立中興大學,2006 [3] 張智星,“MATLAB程式設計與應用”,清蔚科技,2000 [4] Alan V.Oppenheim and Ronald W. Schafer,“Discrete-Time Singnal Processing,”Prentice Hall,1989. [5] A.Averbuch,Y. Shkolnisky,“3D Discrete X-ray Transform”,Appl. Comput. Harmon.Anal,vol.17,pp.529-276,2004. [6]“ Fastest Fourier Transform in the West“, [7] L.R. Rabiner, R.W. Schafer, C.M. Rader, The Chirp Z-Transform Algorithm, IEEE Trans. Audio Electroacoustics vol.17,pp.86–92,1969.
高解析度體積成像的需求隨著現代電腦科技的進步而日益增加,要如何有效處理巨大的體積資料在體積成像的技術中成為一個重要的議題。三維離散X射線轉換法(3D Discrete X-ray Transform)相較於傳統的體積成像法,省去了內插法的環節,不僅以更簡化的流程來運算,更可以避免內插法所造成的資料數值遭受破壞,因此有著優越的運算優勢,適合用來快速產生體積資料的投影影像。
三維離散X射線轉換法的概念是先將離散的體積資料經由迪利克雷核(Dirichlet Kernel)的內插法以滿足積分線做疊加投影,而針對不同方向向量的積分線所做的疊加投影可以得到不同角度的投影面,而在實作的部分,因為可以經由平移運算子將迪利克雷核的部分化簡為一指數項,並藉由Chirp Z-Transform來完成運算,所以可以免去在實作上的內插法。

With the development of modern computer technology, the need for high-resolution volume visualization is rapidly increasing. How to visualize large volumetric datasets effectively becomes an important problem. Comparing to traditional volume rendering techniques, 3D discrete X-ray transform (3D DXT) does not need interpolation. This simplifies the implementation of the visualization algorithm and eliminates distortions caused by interpolation. Therefore, 3D DXT has low computational complexity and is suitable for interactive visualization applications.
The derivation of 3D DXT starts with a perfect reconstruction of the input discrete dataset using Dirichlet kernel. After projection along the desired viewing direction, the convolution with Dirichlet kernel can be simplified into multiplication with exponential terms. This simplification eliminates the need for interpolation. In implementation, 3D DXT can be accomplished by first applying a 2D fast Fourier transform and followed by a Chirp Z-transform. All transforms can be implemented using efficient algorithms and ensure optimal speed.
In this thesis, we will explain the theory of 3D DXT in details. We will demonstrate the implementation of 3D DXT. Finally, the results will be presented.
其他識別: U0005-2107201015170500
Appears in Collections:通訊工程研究所

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