本研究探討如何利用心臟超音波，來評估心臟功能正常與否之相關議題。使用心臟超音波做心臟切面的檢查，可以對心臟血管的各部份構造提供相當詳細的資料，並達到相當的準確性。許多研究指出，罹患心臟疾病患者的左心室收縮舒張機能相對正常人差，因此對病患研究其收縮與舒張功能是當前的課題。本論文中之數據取自左心室超音波靜態影像的灰階值，由心臟收縮與舒張間灰階值的改變，來評估是否罹患某些類型心臟相關疾病。在此使用因素分析方法簡化並保留重要因素。最後，使用線性及二次區別分析區分受檢之人員心臟正常與否。

This study investigates use of echocardiography to assess the related issues about whether the heart function of a subject examined is normal or not. Two-dimensional echocardiography can make the heart inspection, and provide very detailed informations for each part of the cardiovascular structures with a high degree of accuracy. Many studies indicated that the systolic and diastolic function with left ventricle of heart disease in patients was poorer than those of normal patients. Therefore it is of interest to study the systolic and diastolic function for examining whether there are heart problems. In this work, the data is the gray-scale values of left ventricular static ultrasound images. The gray-scale differences between systolic and diastolic period, are used to assess whether the patient suffers from the heart diseases or not. Here, we use factor analysis to simplify and select the crucial factors, namely the function in different area of the left ventricle. Finally, linear and quadratic discriminant analyses are used to distinguish the normal and the abnormal subjects.

論文審定書 i
誌謝 ii
摘要 iii
Abstract iv
1 背景簡介 1
1.1 研究動機與目的 1
1.2 左心室與心臟超音波 1
1.2.1 左心室 1
1.2.2 心臟超音波 1
2 資料描述 2
2.1 資料搜集方式 2
2.2 資料處理 4
2.2.1 差值比較 5
2.2.2 圖像縮放比較 6
2.2.3 校正 6
2.2.4 資料縮減 7
3 研究方法 8
3.1 因素分析 8
3.1.1 因素分析模型 8
3.1.2 因素模型參數估計-主成分估計法 9
3.1.3 主子空間(Principal subspace) 10
3.1.4 因素轉軸 13
3.2 因素分數 13
3.3 區別分析 14
3.3.1 費雪線性區別分析 14
3.3.2 二次區別分析 15
3.3.3 評斷與驗證 16
3.3.4 因素縮減 16
4 研究結果 18
4.1 因素分析結果 18
4.2 區別分析結果 18
4.3 變數縮減後之區別分析結果 22
5 討論與結語 26
參考文獻 27

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