傅立葉立體資料描繪法之研究與轉換函數之設計

Abstract

立體資料描繪法在醫學診療及生物科技上是很常用的科學視覺化技術，但是傳統的立體資料描繪法所需的時間複雜度太大以致無法達成即時的顯像。傅立葉立體資料描繪法具有快速的繪圖時間，它對立體資料的大小為 的時間複雜度是 ，可以滿足即時顯像的需求。但是它會有頻域空間再取樣的問題，導致重疊影像的失真現象，因此濾波器的設計對傅立葉立體資料描繪法是非常重要的研究主題。另外，如何讓傅立葉立體資料描繪法達成分類顯像的效果也是本論文的重點，我們利用了傅立葉轉換具有線性組合之特性，設計了兩種分類顯像的方式，一是預先影像處理，另一是貝茲曲線轉換函數。這兩種方式可以準確地進行資料分類，而且可以很容易的實作在目前一般個人電腦上使用的顯示卡上。

Volume rendering are common visualization methods for medical science and biological science. Traditional methods are not real-time rendering because their high complexity rendering time. The Fourier Volume Rendering that is a real-time method has computational complexity of O(N^2logN) for a volume of size N^3 . But resampling in the frequency domain will causes replicas occur in the spatial domain if we do not use any reconstruction filter. Therefore, the design of an efficient filter is an important study issue in this paper. The classification for Fourier Volume Rendering is the main subject in this paper, too. We used the linear combination property of the Fourier transform to design two classification methods, the image preprocessing and the Bézier curve transfer function, both are accurate classification methods on rendering stage and easy to implement using graphics card in general PC.