射影幾何於攝影測量之應用

Projective Geometry in Photogrammetry

鄭傑文(Chieh-Wen Cheng)

指導教授 ： 趙鍵哲

國立臺灣大學/工學院/土木工程學研究所/碩士(2007年)

https://doi.org/10.6342/NTU.2007.02742

摘要

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。

關鍵字

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

並列摘要

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.

並列關鍵字

Projective geometry ； Epipolar geometry ； Essential matrix ； Fundamental matrix ； Direct linear transform ； Collinarity equation ； Coplanarity equation

參考文獻

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