照相機校正即以物體二維影像來重建其三維形貌的首要步驟，它是用以定義世界座標系與影像座標系間幾何關係的重要技術。然而幾乎所有的校正法皆以針孔成像理論來對照相機的成像進行建模，意即忽略了鏡頭中的所有光學元件，而僅理想地以透視投影法做為照相機成像上的假設。雖然傳統針孔成像模型照相機校正法的數學模型較為簡單且易於使用，但僅能對照相機的5個內部參數和6個外部參數完成校正，且在視覺量測的應用上精度與範圍皆因此而受限。本論文介紹了兩種新的照相機校正方法：

1) 歪斜光線成像模型照相機校正法：以Snell’s Law為基礎，嚴僅地描述歪斜光線在照相機系統中的光線路徑，因此避免了針孔成像模型所引起的成像誤差。其數學模型雖較為複雜，但也因此提高了照相機參數(內、外部參數及各透鏡位姿參數)在視覺量測應用上的精度與範圍。

2) 近軸光線成像模型照相機校正法：將歪斜光線追蹤法的推導結果，實施一階泰勒級數展開運算，以近軸光線與軸光線間的光線差，完成照相機成像上的建模。此方法不同於傳統必須對校正點聚焦與取像，而使用可決定初始光線位置與方向的光源系統對照相機參數進行校正。但由於假設各透鏡皆正確地延著光軸整齊排列，相較於歪斜光線成像模型照相機校正法而言，除了對照相機的內、外部參數進行校正外，僅各透鏡在光軸上的位置參數完成校正。

由於立體視覺量測的精度與待測區和校正區兩者間的位置有關，本研究則針對以上三種照相機校正法所獲得的照相機參數進行光線追蹤實驗。實驗結果顯示，平均讀值誤差將隨量測點與校正區間的距離而增加，即當待測區離開校正區時，則平均讀值誤差將明顯偏高，且由觀察中發現傳統針孔成像模型照相機校正法的平均讀值誤差量最大。更進一步發現，針孔成像模型照相機校正法提供了不合理的參數校正值，且照相機參數的校正結果對校正點的使用亦十分敏感。

Three-dimensional (3D) model construction from two-dimensional (2D) images is an effective method of 3D modeling. To determine the 3D objects, camera calibration is a crucial step to resolve the relationship between the 3D world coordinates and their corresponding image coordinates. Nearly all camera calibration method uses the pinhole model, which is a perspective projection algorithm using geometrical approximations for the multiple optical elements in a camera system. Therefore, the traditional pinhole model camera calibration method is methodologically easy to use and can only calibrate five intrinsic parameters and six extrinsic parameters but suffers from accuracy problems. We introduce two novel methods for camera calibration in this dissertation:

1) Snell model camera calibration method: Based on an analytic geometrical version of Snell’s law, this model rigorously describes the behavior of a skew ray crossing the camera system, hence avoids many of the errors inherent in the pinhole model. Although this model is mathematically most complex, it promotes the camera parameters (five intrinsic parameters, six extrinsic parameters and six lens position parameters) to the higher accuracy levels on the vision measurement, and to be usable for the wider range of conditions theoretically.

2) Paraxial model camera calibration method: We use the first order Taylor series expansion of Snell’s laws to acquire the differential ray (between the axis ray and paraxial ray) for modeling the imaging of a camera and then apply it to the camera calibration. A laser/pinhole assembly is used to experiment with this method. In contrast to the original camera calibration device, it is unnecessary for the laser/pinhole assembly to focus and image the calibration point. This allows allow quick determination of originating at point and traveling along unit directional vector of the source ray. In contrast to the Snell model, the paraxial model offers analytical governing equations, but can only calibrate one position parameter since it assumes that all elements are located without tilt along the optical axis.

However, the accuracy of such calibration is known in general to be sensitive to the distance from camera to observed object. Thus, we apply these three methods respectively on the camera calibration experiment by ray-tracing. Experimentation exhibited the average error increases for ranges away from the calibrated range, and the error increases more rapidly when the distance of calibrated range and the measured range increases. Consequently, the average error by pinhole method is greatest. Moreover, the pinhole model provided the unreasonable calibration values and calibration values are very sensitive to calibration points.

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