本研究提出一個新的方法用以量化糖尿病的嚴重程度之指標。由視網膜顯示，患有嚴重糖尿病之患者，其視網膜血管分布之幾何複雜度遠較正常者高，而經由研究發現，患有嚴重糖尿病之患者，其視網膜血管分布與正常者相較之下，前者之碎形維度值較後者高。
　　然而，如欲求得正確的碎形維度值必須仰賴高品質的影像，要想獲得良好的影像處理結果，則必須依靠適當的影像處理技術才行。
　　除了碎形維度值之外， 本研究並且提出另外一個碎形特徵值— 間隙性(Lacunarity)，有些幾何圖形儘管有著相同的碎形維度值，然而其外觀卻不盡相同，例如有些血管分布圖其碎形維度值可能相同，此時便可由間隙性此一特徵值來做進一步的分類。
　　本研究不只探討影像處理技術，同時也探討如何決定適當的影像解析度。本文提出影像解析度對於計算碎形維度值之正確性有何影響，經由研究發現，過低的影像解析度將無法計算出正確之碎形維度值，因此，本研究將建議如何找到影像解析度之最低限制，以利計算正確之碎形維度值。
　　除了碎形維度值與間隙性，第三個量化指標就是慣性矩。本研究發現慣性矩的計算複雜度是低於碎形維度值的計算複雜度，如此一來，利用慣性矩取代碎形維度值作為特徵值得話，可節省其計算時間卻又不影響其正確率。
　　至於針對疾病之嚴重程度之分類，本研究提出四種分類方法做比較並試圖達到更高的正確率，並且成功地驗證碎形維度值、間隙性以及慣性矩等特徵值是可以作為糖尿病嚴重程度之分類指標。
　　倘若影像檔案大小增加，其所需耗費之計算時間亦隨之增加，幸而本研究所提出之特徵值之計算方法可以將影像分段處理，使得計算過程能夠在平行處理系統計算，用以節省計算時間。另外，本研究並提出網格計算之概念，倘若一個診斷系統能夠分享其影像資料庫，並且有良好的演算法能從資料中找出人眼不易察覺之細節，就能對早期偵測出疾病之徵兆有所助。

　　A novel diagnostic scheme to develop quantitative indexes of diabetes is introduced in this dissertation. It is shown that the geometry complexity of a severe diabetic patient's retinal vascular distribution appears greater than that of a normal human’s. The fractal dimension of the vascular distribution is estimated because we discovered that the fractal dimension of a severe diabetic patient's retinal vascular distribution appears greater than that of a normal human's.
　　The issue of how to yield an accurate fractal dimension is to use high quality of images. To achieve a better image-processing result, an appropriate image-processing algorithm is adopted in this work.
　　Another important fractal feature introduced in this dissertation is the measure of lacunarity, which describes the characteristics of fractals that have the same fractal dimension but different appearances. For those vascular distributions in the same fractal dimension, further classification can be made using the degree of lacunarity.
　　Besides the image-processing technique, the resolution of original image is also discussed here. In this dissertation, the influence of the image resolution upon the fractal dimension is explored. We found that a low-resolution image cannot yield an accurate fractal dimension. Therefore, an approach for examining lower bound of image resolution is also proposed in this dissertation.
　　In addition to fractal dimension and lacunarity, the third quantitative index, moment of inertia, is introduced in this study. It is found that the complexity of computation time of moment of inertia is less than that of fractal dimension. The correctness remains the same but the computation effort is spared.
　　As for the classification of diagnosis results, four different approaches are compared to achieve higher accuracy. In this study, fractal dimension, the measure of lacunarity and the moment of inertia have shown their significance in the classification of diabetes and are adequate for use as quantitative indexes.
　　The computation time increases as the image size grows. Fortunately, the image can be partitioned into a number of independent segments, each of which can be further processed in parallel due to the independent iterations of the computation. Also, the grid computing topology is illustrated in this study. If a diagnosis system is capable of sharing every image in the database, using algorithms to detect abnormalities that would be missed by the human eye, it may help doctors to detect diseases in early stages.

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