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標題: 三維離散X光轉換之反轉換實現
Implementation of Inverse Transform for 3D discrete X-ray transform
作者: 劉讓熙
Liu, Jang-Hsi
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;傅立葉切片理論
出版社: 電機工程學系所
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。
本篇論文將會先對三維離散X射線轉換法的概念與理論作詳細的說明與介紹,在體積資料的投影面,我們在論文中介紹如何選取投影面所對應的視角,三維離散X射線轉換法將可以在實做的即時運算部分有著最少的運算流程,將只需要做兩次的一維離散反傅立葉轉換(1D Discrete Inverse Fourier Transform),在速度上是大幅度的縮短即時運算的時間,最後我們會呈現出實作後的投影圖像與運算時間,並對我們的實驗結果做進一步的討論。

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.
This thesis first introduces the concepts of 3D DXT. The implementation of the inverse transform of 3D DXT involves two steps. The first step is to derive the relationship of the viewing angle and the discrete slopes in 3D DXT projection. The second step is to apply 2D inverse fast Fourier transform (FFT) to the 2D plane extracted from 3D DXT. Since the inverse transform of 3D DXT needs only 2D FFT, it can be easily implemented and its speed is very fast. Finally, we will show the results of the implementation.
其他識別: U0005-2107201015333100
Appears in Collections:電機工程學系所

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