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 本文主要利用4×4齊次座標轉換矩陣與幾何光學Snell定理，推導歪斜光線追蹤法，探討立體成像系統的建模與分析。　　文中首先提出以旋轉曲面、齊次座標轉換方法及幾何光學Snell定理，分析光線行經介質邊界時，其折(反)射光線行進方向及入射點(折射點)位置。所得結果適合以數學模式解析下列幾何光學基本現象：(1)折(反)射光線的行進方向。(2)光線行經邊界的靈敏度分析。(3)分析複色光行經光學系統的像差。其次以光線追蹤分析立體角鏡回射器，並由靈敏度分析取得Pechan稜鏡成像方位的變化。　　立體影像常應用於許多量測與影像處理問題上，如3-D座標量測、機器人視覺導引系統及近景攝影量測。以往此類問題的影像處理，均利用簡易針孔模型作為成像的理論基礎，而非依循幾何光學折(反)射定理，所以缺乏嚴謹的影像分析過程，因此高精度立體成像系統較難建立。　　本文將以歪斜光線追蹤法，分析照相機成像過程物點與像點幾何關係，進而建立雙照相機立體成像系統，並應用此立體成像系統作3-D表面座標量測，利用雙照相機影像座標反推物點的3-D世界座標。由數值模擬與實際表面座標量測結果，可知本文建構的光線追蹤立體成像系統，比針孔立體成像系統具有較佳的量測結果與可靠度。
 The purpose of this paper is to analysis and modeling of two-CCD camera stereo vision system by utilizing the skew ray tracing method. This method is derived from a 4×4 homogeneous coordinate transformation matrix and the Snell’s law of the geometrical optics.　　We first apply the revolution geometry, homogeneous coordinate transformation matrix and Snell’s law to develop the mathematical model of the direction of refracted (reflected) ray and the position of incident point of light rays while crossing medium boundary surfaces. Therefore, with this model, we are able to investigate three important topics of the geometrical optics: 1) The direction of a refracted (reflected) ray is determined according to Snell’s law. 2) Sensitivity analysis expresses differential changes of refracted (reflected) rays in terms of differential changes of incident rays. 3) Aberration of polychromatic light is presented analytically. Then the corner-cube retro-reflector is analyzed by the skew ray tracing methodology and the image orientation of Pechan prism is determined by sensitivity analysis.　　An accurate binocular stereo vision system can greatly simplify solutions of many important vision problems such as the 3-D coordinate measurement, the mobile-robot visual guidance problem, and photogrammetry. However, precise modeling of binocular stereo vision systems is difficult because there is no fundamental imaging formation theory, and as a result, only the simplest pinhole model has previously been utilized traditionally. This paper has demonstrated that a binocular stereo vision system can be modeled by the skew ray tracing method to study the geometric relations between the binocular camera images and the 3-D surface. Numerical and experimental verification indicate that the performance of the proposed method is more excellent than the traditional pinhole model.
 中文摘要 I英文摘要 II誌謝 III目錄 IV表目錄 VII圖目錄 VIII符號說明 XII英文符號說明 XV第一章 前言 1第二章 文獻探討 4　　2.1、齊次座標轉換 4　　2.2、幾何光學基本定理 6　　2.3、3-D表面座標量測 9第三章 歪斜光線追蹤 26　　3.1、旋轉曲面參數式 27　　3.2、幾何光學的折射、反射 28　　3.3、平坦邊界歪斜光線追蹤分析 32　　3.4、立體角鏡回射器光線追蹤 34　　3.5、球面邊界歪斜光線追蹤分析 39第四章 光學系統邊界靈敏度分析 55　　4.1、平坦邊界靈敏度分析 55　　4.2、立體角鏡回射器靈敏度分析 58　　4.3、球面邊界靈敏度分析 61　　4.4、複色光色差分析 63第五章 立體成像系統的建模與分析 83　　5.1、針孔成像模型 83　　5.2、照相機針孔立體成像原理 86　　5.3、光線追蹤立體成像系統建模分析 88　　5.4、針孔立體成像系統靈敏度分析 93　　5.5、光線追蹤立體成像系統靈敏度分析 97第六章 立體成像3-D表面座標量測 106　　6.1、數值模擬 106　　6.2、實際3-D表面座標量測 107第七章 結論與建議 118參考文獻 120附 錄 A 130附 錄 B 132附 錄 C 137附 錄 D 139著 作 140自 述 141