電腦斷層掃描(CT)是檢測肺結節(lung nodule)相當有效之影像學檢查方法。然而，由於其取得之影像數量相當龐大，故有不少研究人員致力於開發電腦輔助診斷／檢測(computer-aided diagnosis/detection, CAD)系統，以降低放射科醫師之負擔，並提出「第二意見」(second opinion)供其參考。在肺結節檢測CAD系統中，會利用強化濾波器(enhancement filter)來進行前置處理，以減少在候選結節識別上之誤判情形。在各種強化濾波器中，選擇性強化濾波器(selective enhancement filter)兼具有良好之靈敏度(sensitivity)與專一性(specificity)，可有效地降低候選結節識別上之誤判情形。然而，由於選擇性強化濾波器需要耗費龐大之計算量來計算矩陣之特徵值(eigenvalue)，以得到其輸出值，故其處理速度相當緩慢。本論文之主要目的，即在藉由減輕由計算矩陣特徵值所引起之計算負擔，來提升選擇性強化濾波器之處理速度。藉由矩陣特徵多項式係數之性質，以及控制工程領域中廣為人知之Routh-Hurwitz判準(Routh-Hurwitz criterion)，在某些特定條件下，無須計算矩陣之特徵值，即可得到選擇性強化濾波器之輸出值，因而得以減輕其計算負擔。實例測試結果顯示，本論文所提出之演算法，可顯著地提升選擇性強化濾波器之處理速度。

Computed tomography (CT) is a very effective imaging modality for the detection of lung nodules. However, the number of images obtained is large. Therefore, many researchers are devoted to the development of computer-aided diagnosis/detection (CAD) systems to mitigate the workload of radiologists and provide computer output as a “second opinion”. In a CAD system for lung nodule detection, an enhancement filter can be employed as a pre-processing step to reduce the erroneous detection of nodule candidates. Among various enhancement filters, the selective enhancement filters possess good sensitivity and specificity and can effectively reduce the erroneous detection of nodule candidates. However, the processing speeds of selective enhancement filters are slow since they require much computational effort to compute eigenvalues of matrices to obtain output values. The purpose of this master thesis is to increase the processing speeds of selective enhancement filters by reducing the computation burden caused by the computation of eigenvalues of matrices. By using the property of the coefficients of the characteristic polynomial of a matrix and the well-known Routh-Hurwitz criterion in the field of control engineering, under certain conditions, the output values of selective enhancement filters can be obtained without having to compute the eigenvalues of matrices. The computational burden thus can be reduced. Experimental results show that the algorithms proposed in this master thesis can significantly increase the processing speeds of selective enhancement filters.

中文摘要 --------------------------------------------------------------------- i
英文摘要 -------------------------------------------------------------------- ii
誌謝 ----------------------------------------------------------------------- iii
目錄 ------------------------------------------------------------------------ iv
表目錄 ---------------------------------------------------------------------- vi
圖目錄 --------------------------------------------------------------------- vii
一、 緒論--------------------------------------------------------------------- 1
1.1 問題描述------------------------------------------------------------------ 1
1.2 研究目的------------------------------------------------------------------ 3
二、 文獻回顧----------------------------------------------------------------- 4
三、 相關理論與資料來源------------------------------------------------------- 6
3.1 選擇性強化濾波器---------------------------------------------------------- 6
3.2 Routh-Hurwitz 判準------------------------------------------------------- 10
3.3 矩陣之特徵值------------------------------------------------------------- 13
3.4 2*2與3*3對稱矩陣特徵值之計算--------------------------------------------- 13
3.5 有限差分近似------------------------------------------------------------- 15
3.6 LIDC-IDRI 資料庫--------------------------------------------------------- 16
四、 研究方法---------------------------------------------------------------- 18
4.1 2D 影像選擇性強化濾波器之改良-------------------------------------------- 18
4.1.1 2D 影像點狀物體選擇性強化濾波器之改良---------------------------------- 18
4.1.2 2D 影像線狀物體選擇性強化濾波器之改良---------------------------------- 20
4.2 3D 影像選擇性強化濾波器之改良-------------------------------------------- 21
4.2.1 3D 影像點狀物體選擇性強化濾波器之改良---------------------------------- 21
4.2.2 3D 影像線狀物體選擇性強化濾波器之改良---------------------------------- 23
4.2.3 3D 影像面狀物體選擇性強化濾波器之改良---------------------------------- 25
五、 實例測試結果------------------------------------------------------------ 28
5.1 2D影像選擇性強化濾波器實例測試結果----------------------------------------28
5.2 3D影像選擇性強化濾波器實例測試結果----------------------------------------32
六、結論與未來展望------------------------------------------------------------36
6.1 結論----------------------------------------------------------------------36
6.2 未來展望------------------------------------------------------------------36
參考文獻----------------------------------------------------------------------37

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行政院衛生署(民101)。100年國人主要死因統計。取自http://www.doh.gov.tw/CHT2006/DM/DM2_p01.aspx?class_no=25&;level_no=1&;doc_no=84788