- 學位論文
使用近軸光學分析估測球面透鏡方位
Estimation of the Position and Orientation of a Spherical Lens Based on Paraxial Optics
摘要
視線追蹤大致上可分為侵入式技術與影像分析技術兩大類， 其中以影像分析技術中的基於眼睛模型的 方法校正方面相對簡單較受歡迎。 但是此類的視線追蹤較不適用於配戴眼鏡的使用者， 因為透鏡折 射會導致觀察到的視線有較大的偏差。 要解決透鏡折射造成的問題， 需要先估測出透鏡方位。 在許家愷的研究當中， 透過光線追蹤的雙折射模型， 分別使用校正板與足標點， 估測出透鏡的方位，但是計算量較大。 本論文主要目的是探討可否使用近軸光模型 (Paraxial Model) 取代雙折射模型， 估測透鏡方位與計算折射補償。 在研究中發展出使用近軸光模型的透鏡 折射補償與使用校正板的透鏡方位估測方法， 並擴展至使用足標點的透鏡方位估測， 最後以電腦模 擬與實際實驗檢驗所發展的方法。 由實驗結果得出使用近軸光模型加上校正板估測透鏡方位時， 方 位會有較大的偏離值， 但是折射補償的精確度， 與雙折射模型相當。 但是在使用近軸光模型加上足 標點估測透鏡方位時， 分為校正與估測兩階段。 在校正階段， 我們使用校正板估測透鏡方位， 並 計算足標點在透鏡座標系中的 3-D 座標值。 在估測階段， 我們使用立體視覺技術， 量測足標點在 攝影機座標系中的 3-D 座標值， 並用以估測透鏡坐標系至攝影機座標系的轉換矩陣。 在這樣的計算過程中， 透鏡方位受足標點限制， 方位偏離值為固定， 導致近軸光模型的的整體誤差 在透鏡屈光度為-1與-3時，比雙折射模型大五倍。 因為當人配戴上眼鏡時， 只能透過眼鏡上方的足 標點估測方位， 所以由這個研究可知近軸光模型並不適用於基於眼睛模型的視線追蹤方法。
並列摘要
Existing gaze tracking methods can be classified into two categories: intrusive methods and video analysis methods. Among the methods in the two categories, the model-based methods in the latter category are popular due to their relatively simplified calibration process. However, because the model-based gaze tracking methods do not consider the effects of lens refraction, the gaze tracking results will be severely degraded for users wearing eyeglasses. To compensate for the lens refraction, we have to estimate the lens orientation first. In Cha-Kai Hsu's research, he proposed two methods based on the double-refraction lens model to estimate the orientation of the lens using a calibration board and fiducial marks, respectively. However, the double-refraction model is unstable (unable to obtain a ray tracing result in some lens orientations) and its computation cost is high. Therefore, the main goal of this theis is to study wheter we can replace the double-refraction model with the paraxial lens model in both lens pose estimation and refraction compensation. We develop a method for refraction compensation with paraxial optics and then apply the compensation method to estimate the lens pose using a calibration board. Furthermore, we extend the fiducial-mark-based lens orientation estimation method developed by Hsu to include the paraxial lens model. The developed methods are tested using both computer simulations and real experiments. According to the experimental results, when using a calibration baord to estimate the pose of the paraxial lens model, the estimated results are heavily biased. However, with the biased paraxial lens pose, accuracy of refraction compensation is about the same order of that computed with the double-refraction model. On the other hand, when using fiducial marks to estimate the lens orientation, it involves a calibration stage and an estimation stage. In a calibration stage, we use a calibration board to estimate the lens orientation and calculate the 3-D coordinates of the fiducial marks in the lens coordinate system (LCS). In the estimation stage, we use the stereo vision technique to estimate the 3-D coordinates of the fiducial marks in the camera coordinate system (CCS), and use them to estimate the transformation matrix from the LCS to the CCS. In this way, lens pose estimation are constrained by the fiducial marks and it is not possible to reduce refraction error by adjusting the lens pose. Therefore, real experimental results so that the resulting overall error of the paraxial lens model is five times worse than that of the double-refraction model when the diopter is -1 or -3. Notably, for users wearing eyeglasses, the orientation can only be estimated using the fiducial marks. Since the overall error of the paraxial lens model is much worse than that of the double-refraction mdoel, we conclude that the paraxial lens model is not suitable for gaze tracking of the model-based method.