研發一三維封閉不可壓縮黏性流體模型從事立體醫學影像套合

Abstract

影像套合(Image registration)對於醫學工程的研究與醫療診斷是相當重要的，其目的是將兩張或多張醫學影像疊合，以呈現相同生理組織之程序。現存影像套合的方法相當多樣化，本論文敘述物理模型類中的黏性流體方法。我們提出一以處理腦部磁振影像為主的影像套合系統，並推導出三維封閉不可壓縮之黏性流場及研發其數值方法，發展成一立體影像套合架構。黏性流體模型的數值方法包含不易求解的非線性偏微分方程式，但三維偏微分方程式若用一般方法以離散二階微分近似，再利用Cholesky演算法解其線性方程組，相當耗時且記憶體需求極大，其時間複雜度為 ，其中N為像素點的數量。我們提出Alternating-direction implicit (ADI)及Hopscotch等兩種不同的數值方法，求解黏性流體方法中的偏微分方程式，解決傳統數值方法耗時及記憶體使用量大的問題，並將這個方法延伸至三維。另外，二維方法若碰到模板影像及基準影像有垂直方向形變就無法成功套合，發展成三維方法相較於二維方法可以處理有垂直方向形變的影像。我們使用了大量不同的模擬影像及臨床核磁共振影像來評估並比較此兩種方法。從實驗結果中得知，本論文所提出的兩種方法皆可有效解決影像套合的問題，且計算時間及記憶體使用量都達到可行的範圍，其套合結果也相當的準確。

Image registration is very important for a wide variety of image processing applications in engineering and medicine. It provides lots of precious information for further analysis in many fields. Image registration is the process of transforming different images into one coordinate system. We propose a three-dimensional closed incompressible viscous fluid image registration algorithm and develop its numerical methods. The core component of solving the viscous fluid model is the partial differential equations (PDEs). The common way to solve the PDF is approximating it using the finite second order differential followed by the Cholesky algorithm to solve the linear formulas. However, the computation complexity will be tremendous and the memory usage will be unbearable. In addition, if the template image has vertical-direction deformation, the two-dimensional method will not be able to handle this situation. We employ the alternating-direction implicit (ADI) and Hopscotch as the numerical methods to solve the PDE of the three-dimensional viscous fluid model. A wide variety of magnetic resonance images were used to evaluate this new method. Experimental results indicated that the proposed method not only successfully performed registration but also provided excellent accuracy. The computation time and the memory usage have been dramatically reduced as well.