臺灣博碩士論文加值系統

本研究針對以空間頻率(spatial frequency)為基礎之三維空間重建(three dimensional space reconstruction)系統，提出新的數學演算法以改善計算效率、運算能力與精準度。
由於先前研究並未對深度量測(depth measurement)的演算效率進行探討，本研究提出新的空間頻率演算法是利用不同空間頻率的影像有不同頻譜圖的特性，藉由分析主要頻率與相鄰頻率間的振幅比值來進行空間頻率的反向計算，進而將單維度的深度計算擴展至三維空間重建。
根據理想之空間頻率建立完美週期影像並計算對應的頻譜圖。紀錄頻譜圖中的主要頻率與相鄰頻率間的振幅比值數據，可以產生一份空間頻率與頻譜組成的清單，以比較理想頻譜圖與實際頻譜圖來進行空間頻率計算。
實際量測與分析結果顯示，在1公尺之量測範圍中，深度解析度約為5mm且x-y平面之平面解析度小於1cm，運算時間最短可在0.5秒內完成單張影像的三維空間重建運算。

Based on the spatial frequency, this study proposes a new mathematical algorithm for improving the calculation efficiency, operation capability, and precision of the three dimensional (3-D) space reconstruction system.
Since the previous study did not discuss the efficiency of depth measurement, we propose a new spatial frequency algorithm which uses the feature of different spectrums for images with different spatial frequencies in the study. By analyzing the amplitude ratio between the main frequency and adjacent one, the spatial frequency can be reversely calculated. Furthermore, the one-dimensional (1-D) depth measurement can be extended to the 3-D space reconstruction.
According to ideal spatial frequencies, the perfect periodic images and corresponding spectrums can be created. By recording the amplitude ratio between the main spatial frequency and adjacent one, a list of spatial frequencies and spectrum compositions can be generated. It is used for calculating the spatial frequency by comparing the ideal spectrum with the actual one.
The practical measurements and analytical results show that the depth resolution is about 5 mm and x-y plane resolution is less than 1 cm in the measuring range of one meter. The shortest operation time of a single shot for the 3-D space reconstruction could be less than 0.5 seconds.

摘 要 i
Abstract ii
目錄 iii
圖目錄 v
表目錄 vii
第一章 緒論 1
1.1 研究背景與目的 1
1.2 文獻回顧 5
1.2.1取樣次數 5
1.2.2影像特徵 6
1.2.3編碼形式 7
1.3 論文架構 8
第二章 相關理論介紹 9
2.1 三維空間重建技術 9
2.1.1 雷射測距法 10
2.1.2 立體機器視覺法 12
2.2 電腦全像元件演算法 14
2.2.1 全像術(holography) 14
2.2.2 電腦全像元件(computer generated hologram, CGH) 15
2.3 空間頻率 17
2.3.1 概念 17
2.3.2 理想影像之快速傅立葉計算 18
2.3.3 實際拍攝影像之計算 19
2.3.4 頻譜解析 20
2.4 影像函數之頻譜 22
2.5 三維空間重建理論 23
第三章 空間頻率計算演算法 25
3.1 主架構 25
3.2 擷取影像範圍對空間解析度的影響 27
3.2.1 第一類計算法 29
3.2.2 第二類計算法 30
3.2.3 設定擷取計算影像範圍 31
3.3 三線篩選法(簡稱：三線法) 35
3.3.1 三線法的設計邏輯 36
3.3.2 三線法的篩選流程 37
3.4 根據數值轉變計算影像空間頻率 38
3.4.1 擷取影像的頻譜變化分析 38
3.4.2 擷取影像的相位影響 40
3.5 空間頻率資料庫比對法 42
第四章 量測系統 45
4.1 實驗設備與系統參數 46
4.1.1 相機 46
4.1.2 投影機 49
4.2 系統設計與校正 51
第五章 實際量測與分析 53
5.1 平面空間頻率計算 54
5.2 立體物件三維空間重建 56
5.3 計算時間比較 58
第六章 結果討論與未來展望 59
6.1 結論 59
6.2 未來展望 60
參考文獻 61

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