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標題: 三維離散X射線轉換實現之改良
Improving the Implementation of 3D Discrete X-ray Transform
作者: 何承諭
Ho, Cheng-Yu
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: 電機工程學系所
引用: [1] 石建軒,“三維離散X光轉換之正轉換實現”,國立中興大學碩士論文, 2010。 [2] 劉讓熙,“三維離散X光轉換之反轉換實現”,國立中興大學碩士論文, 2010。 [3] 李懷哲,“極座標之傅立葉體積成像”,國立中興大學碩士論文,2006。 [4] Amir Averbuch, Yoel Shkolnisky,“3D discrete X-ray transform”, Applied and Computational Harmonic Analysis, vol.17, pp.529-276,2004. [5] Aili Li, Klaus Mueller, Thomas Ernst,“Methods for Efficient, High Quality Volume Resampling in the Frequency Domain”, IEEE Visualization, pp.3-10, 2004. [6] Tom Malzbender,“Fourier Volume Rendering”, ACM Transactions on Graphics, vol.12, pp.233-250, 1993. [7] Marc Levoy, “Display of Surfaces from Volume Data”, IEEE Computer Graphics and Applications, vol.8, pp.29-37, 1988. [8] Takashi Totsuka, Marc Levoy, “Frequency Domain Volume Rendering”, 20th Annual Conference on Computer Graphics and Interactive Techniques, 1993. [9] Raoqiong Tong, Robert W. Cox, “Rotation of NMR Images Using the 2D Chirp Z-Transform”, Magnetic Resonance in Medicine, vol.41, pp.253-256, 1999. [10] Lawrence R. Rabiner, Ronald W. Schafer, Charles M. Rader, “The Chirp Z-Transform Algorithm”, IEEE Transactions on Audio and Electroacoustics, vol.17, pp.86-92, 1969. [11] Alan V.Oppenheim, Ronald W. Schafer,“Discrete-Time Singnal Processing ”, Prentice Hall, 1989. [12] Charles L.Phillips, John M.Parr, Eve A.Riskin, “Signals, Systems, and Transforms”, Third Edition, Prentice Hall, 2003. [13] Rafael C. Gonzalez, Richard E. Woods, Steven L. Eddins,“Digital Image Processing Using MATLAB”, Prentice Hall, 2003. [14] “ Fastest Fourier Transform in the West“, [15] “超氧化物歧化
隨著電腦科技的進步與各領域越趨廣泛的應用,高解析度體積成像的需求也日益增加,在體積成像的技術中要如何有效率地處理龐大的體積資料量已成為一個重要的議題。體積成像大致分成兩種技術:直接體積成像(Direct Volume Rendering, DVR)與傅立葉體積成像(Fourier Volume Rendering, FVR),DVR技術直接在空間域計算出體積資料的投影,而FVR則是將體積資料轉換到頻域做前置處理,最後做即時成像轉回空間域得到投影。而三維離散X射線轉換法屬於FVR技術的一種。
原始的三維離散X射線轉換法(3D Discrete X-ray Transform)使用暴力法(Brute Force)將體積資料的頻譜直接乘上一指數項做累加來得到頻譜的切面,這種方式的計算複雜度較高。另外,原始的三維離散X射線轉換法在特定投影角度的成像上會因為相位差導致影像失真。
本論文針對上述的兩個問題提出改良,將演算法使用暴力法的部分,改成以快速傅立葉轉換做Chirp Z-Transform (CZT)來實現,如此能夠有效降低計算複雜度。另外,我們藉由空間域與頻域的兩階段平移來解決特定投影角度的成像失真問題。

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. Volume rendering can roughly be divided into two techniques: direct volume rendering (DVR) and Fourier volume rendering (FVR). DVR directly calculates the projection of the volumetric dataset in spatial domain. FVR first transforms the volumetric dataset to frequency domain in pre-processing. Real-time image rendering is done by extracting a slice in frequency domain and inverse Fourier transforming the slice. 3D discrete X-ray transform (3D DXT) is one of the FVR techniques.
The original 3D DXT uses brute force transform. The frequency transform of the volumetric dataset is calculated by direct multiplication of exponential terms and repetitive summation. This leads to very high computational complexity. Moreover, the images of the original 3D DXT are distorted at specific projection angles.
In this thesis, we improve 3D DXT and solve the two problems. First, the brute force transform is replaced by Chirp Z-transform (CZT) with fast Fourier transform (FFT) implementation. This reduces computational complexity. Moreover, we utilize spatial-domain and frequency-domain shifting to correct the distortion at specific projection angles.
其他識別: U0005-2707201113260700
Appears in Collections:電機工程學系所

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