臺灣博碩士論文加值系統

早期海岸線量測結果長短不一的問題，反而成為了碎形理論發展與突破的重要推手。如今半世紀以來，碎形理論已被廣泛應用於各項領域。在碎形理論如此蓬勃發展之下，原先根本的海岸線量測問題到了現代是否有明確的結果？測量海岸線碎形維度如圓規法、盒計數法都是主流計算碎形維度的方式，但各類研究測量結果並不盡相同。
而本論文的目的在於以計盒數維度為測量基礎下建立一套計算海岸線的碎形維度流程與分析，以向量地圖的Google Maps為圖資測量依據，放入影像處理的邊界偵測法來得到海岸線的邊界，藉由在螢幕上呈現方正的像素點來作為計盒數維度中的網格來作計算。得到的結果進一步討論量測方法差異，並討論相同海岸線的碎形維度得到的結果差異問題。

The problem of different lengths of early coastline measurements has become an important driving force for the development and breakthrough of fractal theory. Nowadays, fractal theory has been widely used in various fields for half a century. In the measurement of coastline fractal dimensions such as compass and box counting methods are the main ways to calculate the fractal dimension, but the results of various research measurements are not the same. Under the soaring theory of fractals, did the original fundamental shoreline measurement problem have a clear result in modern times?
The purpose of this research is to establish a set of fractal dimension process and analysis for calculating the coastline based on the measurement of Box-counting Dimension. The Google Maps of the vector graphic map is used as the basis for the measurement of the image. Image data is placed into the boundary detection method of image processing to obtain the boundary of the coastline. The boundary of the coastline is obtained, which is calculated by presenting a square pixel on the screen as a grid in the box count dimension. Use the results to discuss the differences between measurement methods.

摘要 I
EXTENDED ABSTRACT II
誌謝 VI
目錄 VII
表目錄 X
圖目錄 XII
符號表 XX
第一章 緒論 1
1.1 關於海岸線的長度計算 1
1.2 碎形維度理論的背景與發展 2
1.3 研究動機與目的 5
1.4 論文架構說明 6
第二章 碎形維度的計算 8
2.1 碎形維度的定義 8
2.2 複雜幾何圖形的表現 8
2.3 冪次律的應用 11
2.4 自我相似維度 13
2.5 圓規維度 16
2.6 計盒數維度 16
第三章 MATLAB影像處理程序與圖資收集 20
3.1 影像處理對於計盒數維度之應用 20
3.2 數位影像處理的基礎概念 21
3.3 GOOGLE地圖的應用程式介面（GOOGLE MAPS API） 22
3.4 MATLAB影像處理與操作程序 27
3.5 提升獲取圖資效率的解決方法 43
第四章 測量台灣海岸線長度與碎形維度 50
4.1 有關海岸線的定義 50
4.2 使用圓規法量測海岸線 54
4.3 使用盒計數法與影像處理測量海岸線（手動截圖） 61
4.4 使用盒計數法與影像處理測量海岸線（MAPCAPT自動截圖） 64
4.5 台灣海岸線的碎形維度結果與討論 66
第五章 測量國外海岸線長度與碎形維度 73
5.1 挪威海岸線量測 73
5.2 英國海岸線量測 76
5.3 台灣、挪威與英國海岸線的碎形維度結果與討論 78
第六章 測量全世界海岸線碎形維度 84
6.1 全世界海岸線的碎形維度 84
6.2 世界局部區域海岸線的碎形維度 86
6.3 世界區域海岸線測量結果討論 94
6.4 以碎形維度驗證板塊構造學說 97
第七章 結論與未來工作 101
參考文獻 103
附錄 109
附錄A 109
附錄B 112
附錄C 113

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