摘 要
紋理影像的研究是一個值得探討的議題，但目前在紋理的影像描述上，並無一套固定且廣義的方法，通常描述的方法是依照紋理的屬性以及應用的範圍來決定。本研究中，嘗試針對人造的規則紋理影像作分析，利用紋理基元間堆疊組合的特性，建立出階層式模型。此外，若紋理基元具有對稱的特性，我們可以進一步將階層式模型改良成映射階層式模型，這模型將能更有效率的描述出紋理。
由於規則紋理影像中，基元形式固定且排列具有強烈的週期性，所以很適合利用頻率方式分析。本研究利用傅立葉轉換，對紋理影像作頻域上的分析，根據頻譜圖上能量分佈位置，可以求得方向上的頻率，進而檢測出紋理基元的週期大小及排列的方向性。此外，經由觀察紋理影像位移前後的相位差，可以直接得到紋理影像的位移量。
由實驗的結果可以證明，利用觀測頻譜能量方式所計算出的紋理週期，與實際測量出的紋理週期非常的接近。

Abstract
Textured image research is a topic worth many effort. In this issue, there is generally no widely accepted way to describe a textured image at present. The usual way has to depend on the property of texture and the domain of the application.
In this research, we try to analyze a type of artificially generated texture images. Based on the feature of texture element combination we use hierarchical modeling and further improve the hierarchical modeling using the projective hierarchical modeling. This model could describe the texture more efficiency.
The regular texture image is very suitable to analyze in frequency way since texture element is in fixed placement and shows strong periodicity. We use the Fourier transform to analyze the frequency content of a texture image. We can get the frequency distribution in each direction and get the period of the texture. We can also get the displacement of the texture image by observe the variation of phase.
At the end of the research we show that the period calculated by observing the spectrum is very close to the period of that is actually measured.

目錄
第一章 緒論 1
1.1 研究背景 1
1.1.1紋理定義 1
1.1.2紋理分析與描述 2
1.1.3紋理的研究與應用 4
1.2研究動機 5
1.3論文架構 6
第二章 紋理描述分析 8
2.1統計方法分析 8
2.1.1 一維特徵 8
2.1.2 二維特徵 9
2.2結構方法分析 14
2.3頻率方法分析 18
2.3.1 自相關函數(autocorrelation function) 18
2.3.2 Fourier功率頻譜函數 21
2.4 模型方法分析 24
2.4.1 隨機場模式分析 24
2.4.2 碎形(fractals)模式分析 25
第三章 階層式模型 28
3.1 理想模型建立 28
3.2 結構中心 29
3.3 組織規則描述 31
第四章 傅立葉紋理分析 37
4.1 基本相位分析 37
4.2 規則紋理影像相位分析 40
4.3 規則性紋理振幅分析 45
第五章 實驗結果 50
5.1實驗設備 50
5.2 實驗一：真實紋理影像採頻譜分析方法 50
5.2.1 真實格狀紋理 50
5.2.2 真實圓點狀紋理 54
5.2.3 受光不均格狀紋理 58
5.2.4 討論 62
5.3 實驗二：縮減紋理影像分析頻譜變化 62
第六章 結論與未來研究方向 67
6.1 結論 67
6.2 未來研究方向 67
參考文獻 69

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