趙鍵哲臺灣大學：土木工程學研究所鄭傑文Cheng, Chieh-WenChieh-WenCheng2007-11-252018-07-092007-11-252018-07-092007http://ntur.lib.ntu.edu.tw//handle/246246/50339　　一般常見的攝影測量方法在解算影像方位參數上常使用共線式來取得最佳參數估值，雖然此種演算模式嚴謹，但因屬非線性方程，解算時須提供近似值以及進行漸進計算直至獲得收斂解，而射影幾何法提供不同於傳統幾何運算及座標系統轉換等方法，可透過線性解算模式直接取得待求解參數，或者可進一步供作非線性嚴密模式平差解算的參數起始近似值。除此之外，透過射影幾何法本身的嚴密模式，亦可得到近似於一般常用之攝影測量解算方法成果，提供求解方位參數及重建核線影像一個不同的途徑，將射影幾何法引入攝影測量計算中，可使攝影測量的解算不侷限於一般常用的共線式及共面式解法，取而代之的是一個快速自動的射影幾何解算模式，或兩者融合為兼具解算自動化及嚴密解雙效的運算工具。 　　本研究主要探討的應用可以分成兩個部份，一為共線式與射影幾何法於空間後方交會解算方位參數及空間前方交會地面點成果之比較，二為共面式與射影幾何法解算核線影像幾何之比較。前者利用模擬實驗測試各種變因，包含控制點精度、觀測量精度、控制點數量及分佈等，對攝影測量方位解算以及三維物點座標解算的影響。另外，並以實際影像，包含航照及近景影像，執行後交、前交及核線影像解算。經由上述資料之測試與分析，驗證射影幾何法於攝影測量上之應用可行性。　　The collinearity equation is commonly used to estimate the best result when determining orientation parameters. This method is rigorous, but because it belongs to systems of non-linear equations, it is necessary to use parameter approximations and the iteration process to get convergent results. Projective geometry provides an alternative method for representing and transforming geometric entities, and transfers the complicated non-linear problems in photogrammetry into simple linear cases. The results can then be treated as the approximations for the rigorous non-linear system. Projective geometry also produces estimates of orientation parameters and epipolar images that are of similar quality as the results yielded by using the common collinearity and coplanarity methods. It is a possible substitute procedure, which supports automated calculation, to the collinearity and coplanarity methods for photogrammetry issues. 　　This study consists of two parts. The first part is a comparative study between using the collinearity method and the projective geometry method to determine orientation parameters and intersecting ground points. The second part is a comparative study between using the coplanarity method and the projective geometry method to solve epipolar geometry. The first part tested, via simulated experiments, several factors that would affect the results in determining the orientation parameters and the coordinates of ground points, such as the accuracy of control points, the accuracy of observations, the number of control points, and the distribution of control points. Actual aerial and close-range photos were used to execute the resection, intersection and epipolar image solving process. After analyzing the data, the feasibility of the projective geometry in photogrammetry was verified.口試委員審定書…………………………………………………………....i 誌謝………………………………………………………………………..iii 中文摘要…………………………………………………………………...v 英文摘要…………………………………………………………………..vi 目錄……………………………………………………………………….vii 表目錄.........................................................................................................xii 圖目錄........................................................................................................xiv 第一章 前言.............................................................................................1 1-1 研究動機與目的..........................................................................................2 1-2 相關文獻回顧..............................................................................................2 1-3 研究方法與流程..........................................................................................5 1-4 論文架構......................................................................................................6 第二章 射影幾何法基本定理.................................................................9 2-1 射影概念及源起..........................................................................................9 2-2 齊次座標系統介紹....................................................................................11 2-2-1 二維點…………...............................................................................11 2-2-2 二維線…………...............................................................................11 2-2-3 三維點…………...............................................................................12 2-2-4 三維面…………...............................................................................13 2-2-5 三維線…………...............................................................................13 2-3 射影幾何法幾何運算模式介紹................................................................15 2-3-1 二維空間中之幾何運算模式...........................................................15 2-3-1-1 關聯………….......................................................................15 2-3-1-2 相交……………...................................................................16 2-3-1-3 連結……..............................................................................16 2-3-1-4 距離………….......................................................................16 2-3-2 三維空間中之幾何運算模式...........................................................18 2-3-2-1 連結與相交…………………............................................18 2-3-2-2 關聯………….......................................................................19 2-3-2-3 距離………….......................................................................19 2-3-3 射影幾何法之座標轉換...................................................................21 2-3-3-1 二維點座標轉換...................................................................21 2-3-3-2 三維點座標轉換...................................................................22 2-3-3-3 二維線及面座標轉換...........................................................23 2-3-3-4 三維線座標轉換...................................................................23 2-3-3-5 二維點及三維點間之座標投影轉換...................................24 2-4 射影幾何法及共面式與核線幾何之關聯................................................26 2-4-1 核線幾何基本構成...........................................................................27 2-4-2 射影幾何法與核線幾何之關聯.......................................................28 2-4-3 共面式與核線幾何之關聯...............................................................30 第三章 射影幾何法於空間後方交會及前方交會上之應用.................33 3-1 DLT參數與內、外方位參數間之轉換......................................................33 3-2 由DLT參數誤差傳播至外方位參數精度介紹........................................35 3-3 DLT法空間後方交會及前方交會模式....................................................36 3-3-1 DLT法空間後方交會模式...............................................................37 3-3-2 DLT法空間前方交會模式...............................................................38 3-4 共線式空間後方交會及前方交會模式....................................................38 3-4-1 共線式空間後方交會模式...............................................................39 3-4-2 共線式空間前方交會模式...............................................................40 第四章 射影幾何法於核線影像重建之應用.......................................43 4-1 Essential Matrix及對應核線之解算.........................................................43 4-1-1 Essential Matrix之解算模式.............................................................43 4-1-2 Essential Matrix實驗精度計算方法.................................................46 4-1-3 Essential Matrix理論精度計算方法.................................................46 4-1-3-1 平差後參數的方差矩陣.......................................................47 4-1-3-2 核線計算的方差矩陣...........................................................47 4-1-3-3 檢核點到對應核線之距離理論精度...................................47 4-1-4 Essential Matrix與相對方位參數間的轉換....................................48 4-2 Fundamental Matrix及對應核線之解算...................................................49 4-2-1 Fundamental Matrix之解算模式......................................................50 4-2-2 Fundamental Matrix實驗精度計算方法..........................................51 4-2-3 Fundamental Matrix理論精度計算方法..........................................51 4-3 共面式相對方位參數及對應核線之解算................................................52 4-3-1 共面式相對方位參數之解算模式...................................................52 4-3-2 共面式實驗精度計算方法...............................................................53 4-3-3 共面式理論精度計算方法...............................................................53 4-4 核線影像之重建模式及流程圖................................................................53 4-4-1 射影幾何法重建核線影像...............................................................53 4-4-2 共面式解法重建核線影像...............................................................58 4-4-3 射影幾何法及共面式解法核線影像重建流程圖...........................62 第五章 模擬資料實驗測試及成果分析...............................................63 5-1 模擬實驗場配置情形................................................................................63 5-2 DLT法與共線式之空間後方交會及前方交會模擬實驗........................64 5-2-1 DLT法與共線式外方位參數解算精度比較...................................65 5-2-2 地面控制點精度的影響分析...........................................................65 5-2-3 像片觀測量精度的影響分析...........................................................67 5-2-4 地面控制點數量及分布的影響分析...............................................68 5-2-5 地面控制點高程對解算成果的影響分析.......................................69 5-2-6 台灣都會地區航攝影像於DLT解算易遭遇之問題探討...............72 5-2-7 DLT法與共線式之空間後交及前交模擬資料測試結論...............77 5-3 Essential Matrix解算成果分析.................................................................78 5-3-1 Essential Matrix解算約制條件比較分析........................................78 5-3-2 Essential Matrix與共面式方位參數間的轉換實驗成果分析........80 5-4 核線解算及核線影像重建模擬實驗........................................................80 5-4-1 像片觀測量精度的影響分析...........................................................81 5-4-2 像片觀測量數量的影響分析...........................................................82 5-4-3 絕對方位與相對方位解算模式之差別...........................................84 5-4-4 核線解算及核影像重建模擬資料測試結論...................................85 第六章 實際資料實驗測試及成果分析...............................................87 6-1 航攝影像實際資料實驗測試及成果分析................................................87 6-1-1 航攝影像實驗場配置情形...............................................................87 6-1-2 DLT法與共線式之空間後方交會及前方交會實驗測試...............89 6-1-2-1 DLT法與共線式外方位參數解算精度比較.......................89 6-1-2-2 地面控制點數量及分布的影響分析...................................91 6-1-3 核線解算及核線影像重建實驗測試...............................................93 6-1-3-1 Essential Matrix與共面式相對方位參數間的轉換............93 6-1-3-2 像片觀測量數量的影響分析...............................................94 6-1-3-3 絕對方位與相對方位解算模式之差別...............................96 6-1-3-4 核線影像重建成果展示.......................................................97 6-1-4 航攝影像實際資料實驗測試結論.................................................100 6-2 近景影像實際資料實驗測試及成果分析..............................................101 6-2-1 近景影像實驗場配置情形.............................................................101 6-2-2 DLT法與共線式之空間後方交會及前方交會實驗測試.............105 6-2-2-1 DLT法與共線式外方位參數解算精度比較.....................105 6-2-2-2 地面控制點數量及分布的影響分析.................................107 6-2-3 核線解算及核線影像重建實驗測試.............................................109 6-2-3-1 Essential Matrix與共面式相對方位參數間的轉換..........109 6-2-3-2 像片觀測量數量的影響分析.............................................110 6-2-3-3 絕對方位與相對方位解算模式之差別.............................113 6-2-3-4 核線影像重建成果展示.....................................................114 6-2-4 近景影像實際資料實驗測試結論.................................................117 第七章 結論與建議.............................................................................119 7-1 結論..........................................................................................................119 7-2 建議..........................................................................................................120 參考文獻...................................................................................................123 附錄...........................................................................................................127 作者簡歷...................................................................................................1574508641 bytesapplication/pdfen-US射影幾何核線幾何基本矩陣基礎矩陣直接線性轉換共線式共面式Projective geometryEpipolar geometryEssential matrixFundamental matrixDirect linear transformCollinarity equationCoplanarity equationthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/50339/1/ntu-96-R93521122-1.pdf