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研究生:林士桓
研究生(外文):Shih-Huan Lin
論文名稱:計算視網膜下積液體積的演算法
論文名稱(外文):A Computational Algorithm for Subretinal Fluid Volume
指導教授:施因澤崔大山
指導教授(外文):Yin-Tzer ShihTa-Shan Tsui
口試委員:張嘉仁
口試委員(外文):Chia-Jen Chang
口試日期:2017-07-17
學位類別:碩士
校院名稱:國立中興大學
系所名稱:應用數學系所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2017
畢業學年度:106
語文別:中文
論文頁數:41
中文關鍵詞:視網膜下積液體積氣球蛇行演算法模糊函數組內相關係數光學相干斷層掃描
外文關鍵詞:subretinal fluid volumeballoon snake algorithmfuzzy functionintraclass correlation coefficientoptical coherence tomography
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新的眼科儀器檢測技術帶給醫生更方便及準確診治。例如改良式
的檢眼鏡被發明,或是光學相干斷層掃描被引入眼科學,都使眼科醫
生能更準確診斷眼睛的疾病。所以本文希望能建立眼科OCT 影像的
3D 模型,並計算其視網膜下積液的體積,以利於醫生判斷病人恢復
的情況與更準確預估恢復時間。
視網膜下積液的輪廓線為封閉曲線,因此我們建議以氣球蛇行演
算法為主,來近似積液的輪廓線。先採用高斯濾波器與調整亮度的公
式來做前處理,再用三次樣條插值及模糊函數來建立輪廓線的數學模
型,最後建立視網膜下積液的3D 模型,並計算體積。
本論文在經過20 組病例的實測,並與專業人員描繪輪廓線所推估
的體積比較後,其組內相關係數高達0.9934。在計算視網膜下積液的
體積與建立3D 模型上提供了快速、穩定的演算法。
New detection technology of ophthalmic instrument brings more convenience and accuracy on treatment to doctors. For example, the improved ophthalmoscope was invented, and the optical coherence tomography was introduced in ophthalmology. It all helps the ophthalmologists diagnose the eye disease more accurately. As a result, this article aims at establishing a 3D model for eye OCT images and calculating subretinal fluid volume, in that way, we can help doctors to determine the patient''s recovery condition and estimate the recovery time accurately.

Subretinal fluid contour is a closed curve, so we recommend take Balloon Snake as the main algorithm to detect subretinal fluid contour. We first adopt Gaussian filter and brightness adjustment formula to do preprocessing, using cubic spline interpolation and fuzzy function to build the required contours’ mathematical model, finally establish 3D model of subretinal fluid and calculate the volume.

After 20 medical cases, we make the comparison with the calculated volume and the volume estimated by the contour drawn by professional staff, the posterior intraclass correlation coefficient is up to 0.9934. It provides fast and stable algorithms in the calculation of subretinal fluid’s volume and the establishment of the 3D model.
1 緒論1
1.1 研究背景. . . . . . . . . . . . . . . . . . . . . . 1
1.2 文獻回顧. . . . . . . . . . . . . . . . . . . . . . 2
1.3 研究動機. . . . . . . . . . . . . . . . . . . . . . 2
1.4 論文概要. . . . . . . . . . . . . . . . . . . . . . 3
1.5 符號. . . . . . . . . . . . . . . . . . . . . . . . 3
2 去雜訊與加強對比. . . . . . . . . . . . . . . . . . . 4
2.1 高斯濾波器. . . . . . . . . . . . . . . . . . . . . 4
2.2 對比強化. . . . . . . . . . . . . . . . . . . . . . 5
2.2.1 閥值的選擇. . . . . . . . . . . . . . . . . . . 5
2.2.2 調整亮度. . . . . . . . . . . . . . . . . . . . . 6
3 邊緣偵測. . . . . . . . . . . . . . . . . . . . . . 7
3.1 索貝爾算子. . . . . . . . . . . . . . . . . . . . . 7
3.2 坎尼邊緣偵測. . . . . . . . . . . . . . . . . . . . 9
3.3 蛇行演算法. . . . . . . . . . . . . . . . . . . . . 10
3.4 氣球蛇行演算法. . . . . . . . . . . . . . . . . . . 12
4 視網膜下積液體積的計算與比較的方法 . . . . . . . . . . 13
4.1 函數化. . . . . . . . . . . . . . . . . . . . . . 13
4.1.1 三次樣條插值. . . . . . . . . . . . . . . . . . 13
4.1.2 模糊函數. . . . . . . . . . . . . . . . . . . . . 15
4.1.3 三次樣條函數的模糊插值. . . . . . . . . . . . . 16
4.2 視網膜下積液曲面模型的建立. . . . . . . . . . . . . 19
4.3 體積真正值的推估. . . . . . . . . . . . . . . . . . 20
4.3.1 斷層掃描中視網膜下積液面積的計算. . . . . . . 20
4.3.2 辛普森法. . . . . . . . . . . . . . . . . . . . . 21
4.4 統計分析. . . . . . . . . . . . . . . . . . . . . . 22
4.5 演算法. . . . . . . . . . . . . . . . . . . . . . 23
5 測試與實驗結果 . . . . . . . . . . . . . . . . . . . 25
5.1 對比強化中的參數選擇. . . . . . . . . . . . . . . . 25
5.2 插分實驗. . . . . . . . . . . . . . . . . . . . . . 27
5.3 邊緣偵測. . . . . . . . . . . . . . . . . . . . . . 28
5.4 實際病例. . . . . . . . . . . . . . . . . . . . . . 30
6 結論與未來展望 . . . . . . . . . . . . . . . . . . . 37
參考文獻. . . . . . . . . . . . . . . . . . . . . . 38
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