使用平面校正物進行折射反射式攝影機的校正

Abstract

折射反射式攝影機憑藉著廣大視角的優點，近來被廣泛的應用在視訊監控及自動車導航等許多的電腦視覺的應用當中。然而，折射反射式攝影機的相機結構比傳統透視投影攝影機較為複雜，因此其校正問題也比傳統透視投影攝影機更為困難。根據是否具有單一視點的性質，折射反射式攝影機可以分為置中式與非置中式兩種。置中式折射反射式攝影機具備單一視點的性質，因此我們可以利用epipolar geometry，以及空間中幾何形狀在影像中的幾何不變性來估測其相機參數。但是在實際的應用上，置中式折射反射式攝影機體積相當龐大，且精準的將傳統攝影機與反射鏡放置在正確的位置是個非常困難的問題，因此大部分的折射反射式攝影機皆屬於非置中式折射反射式攝影機。因為非置中式折射反射式攝影機沒有單一視點的性質，而且我們還必須估測傳統攝影機與反射鏡的相對位置，所以其校正問題就更為困難了。因此非置中式折射反射式攝影機的校正法皆是利用空間中特徵點與其在影像的成像點的對應關係，再透過一個最佳化流程來估測出精準的相機參數。 在此論文中，我們提出了新的校正法來估測置中式以及非置中式折射反射式攝影機的相機參數。在所提出的方法中，我們利用平面校正物來進行相機的校正，且利用此平面校正物，我們就可以透過簡單的校正流程來估測出精準的相機參數。對於置中式折射反射式攝影機，我們可以利用觀視球模型來描述三維空間中的座標點與其在影像的成像點之間的對應關係。在我們的校正流程中，我們只需從一些不同角度來拍攝此校正版數張影像。利用觀視球模型及其相關參數，我們可以透過設定一台虛擬的透視投影攝影機，從原始環場影像計算出其反扭曲影像。我們證明了環繞著環場攝影機拍攝一個平面校正物，會等同於一個靜態虛擬的透視投影攝影機從許多不同角度拍攝同一個校正物。接下來我們就可以利用所計算出的這組反扭曲影像，計算出虛擬相機與校正物之間的相對姿勢，且再利用homography方法我們可以計算出校正版上每個特徵點的校正誤差。最後再透過一個非線性的最佳化過程，我們即可估測出準確的觀視球模型參數。 對於非置中式折射反射式攝影機，由於該攝影機不遵守單一視點的限制，因此我們不能使用觀視球模型來描述其成像。也因如此，校正非置中式折射反射式攝影機為一個更困難的問題。在我們所提出的方法中，我們利用一個已校正完成的置中式折射反射式攝影機來當作我們校正的媒介。首先，我們擺放一組位置固定的液晶螢幕，該螢幕會顯示一連串的特殊樣式讓置中式折射反射式攝影機來拍攝影像。因為置中式折射反射式攝影機已經校正完成，因此我們可以自動的估測 出螢幕上所有特徵點的三維空間座標。接下來我們讓所要校正的非置中式折射反射式攝影機拍攝相同位置的液晶螢幕。對於每個螢幕上的特徵點，我們得到其在非置中式攝影機的影像上的對應點。且所有特徵點其三維座標在先前已被估測出來，因此我們可以利用照相測量術來估測出其相機參數。在所提出的方法中，我們利用Mashita的方法來估測出相機參數的起始值，接下來再透過一個最佳化過程來估測出一組精準的相機參數。 模擬及實體的實驗皆證明了我們所提出的校正法的準確性及穩定性。在模擬實驗中，我們加入了不同程度的高斯雜訊在模擬資料中來驗證我們方法的效能。其結果顯示我們的方法的確是穩定且準確的。我們也實作了Ying的校正法，與我們所提出的方法比較效能，其結果也顯示我們所提出的方法效能較好。在實體實驗部份，我們校正了由Marlin 1394以及一個雙曲面鏡所組成的置中式環場攝影機。非置中式方面，我們也校正了由宜昇科技公司所生產的MAPCAM。此外，我們也實作了一個整合式的監控系統，在此系統中，我們會利用一個已校正好的非置中式折射反射式攝影機來對自動車進行導航。

Catadioptric camera has been widely used in the applications of video surveillance and robot navigation due to its advantage of large field of view. However, it is more difficult to calibrate this kind of cameras than to calibrate perspective cameras because the camera structure is more complicated and there are more camera parameters to be determined. Catadioptric camera can be either central or non-central, depending on whether it keeps the single viewpoint constraint. The central catadioptric camera has a single center of projection, hence the epipolar geometry can be applied to calibrate the camera parameters. Considering the practical issues, such as the large size of central catadioptric camera and the difficulty of precise alignment between the camera and the mirror, most off-the-shelf catadioptric cameras are non-central ones without obeying the single viewpoint constraint. A non-central catadioptric camera can be calibrated by photogrammetric methods requiring the correspondence of 3-D world coordinate and 2-D image coordinate. In this thesis, we propose novel calibration methods for determining camera parameters of both central and non-central catadioptric cameras. Our methods utilize planar objects and can achieve very accurate results while keeping the calibration procedures simple. For central catadioptric camera, 2-D projection point in image for a 3-D projection ray can be determined by the viewing sphere model. In the proposed calibration procedure, we place a planar calibration plate several times surrounding the camera and capture an image for each pose of the calibration plate. With the viewing sphere model and the associated parameters, we can unwarp the captured catadioptric image into the image captured by a virtual perspective camera with known intrinsic parameters as well as extrinsic parameters relative to the viewing sphere. We show that moving a calibration plate around the catadioptric camera is equivalent to placing the same calibration plate at different poses relative to a static, virtual, perspective camera. We can then use this set of unwarped perspective images to calculate the relative poses of the calibration plate as well as the projection error of the feature points on the calibration plate by using the homography method. The associated parameters of the viewing sphere model can be obtained by minimizing the projection error in a nonlinear optimization procedure. For non-central catadioptric camera, the single viewpoint constraint does not hold and the viewing sphere model cannot be applied. Thus it is even more difficult to calibrate a non-central catadioptric camera. In this work we determine the projection model of the non-central catadioptric camera through a calibrated central catadioptric camera as an intermediate. First, we use a set of LCD panels with fixed positions to present feature patterns to the central catadioptric camera. Image coordinates of these feature patterns in the captured images are automatically determined and the corresponding 3-D coordinates can be calculated since the camera is calibrated. The same set of LCD panels are then presented to the non-central catadioptric camera. For each feature point, we can obtain its 2-D coordinate in the image captured by the non-central catadioptric camera. Since the 3-D coordinates of the feature points are determined beforehand, camera parameters of the non-central catadioptric camera can then be obtained photogrammetrically. In the proposed method, we use Mashita’s method to determine the initial values of the parameters in the reflected ray model and then optimize the values of the parameters by minimizing the projection error. Experiments with simulation and real data clearly demonstrate the robustness and accuracy of the proposed calibration methods. In the simulation data, we add gaussian noise with zero-mean and standard deviation ( = 0.0 ? 2.0) to evaluate the performance of proposed methods. The results show that our methods are indeed robust and accurate. We also implement calibration method using geometric invariants for the purpose of comparison. The results show that our methods are indeed robust and accuracy, and have better performance than one using geometric invariants. Moreover, we also present an integrated surveillance system in which the calibrated non-central catadioptric camera is used to navigate a mobile robot for patrolling.