多台攝影機之靜態與動態校正技術

Abstract

在本論文中，我們提出兩個新穎且有效的攝影機校正技術。第一個是多台攝影機的靜態校正方法，其以同一平面上的簡單物體之影像，投影回空間為基礎;另一個則是多台攝影機的動態校正技術，其以單一攝影機所拍之畫面在時間軸上的變化，以及多台攝影機之間的相對方位為基礎。我們所採用的系統模型，能普遍適用於大部分配有多台攝影機的監控系統，不論是靜態或動態校正方法，都不需要特別的系統架設或使用特定的校正樣本。值得一提的是，我們的動態校正技術不用作複雜的特徵點對應技術。 此論文所提的多台攝影機之靜態校正，是指尋找攝影機之間的相對位置和方向。一開始我們先推導在攝影機傾斜角度的變化下，三度空間和攝影機影像的座標轉換關係，此對應關係建立之後，再透過攝影機觀察水平面上的簡單物體，來估測此攝影機的擺放高度及其傾斜角度。接著，依據每台攝影機所估測的傾斜角度和高度，我們將各攝影機所觀測到的同一向量，投影回三度空間中，藉著比較此向量的空間座標，各攝影機之間的相對方位即可很容易地被估測出來。就某個方面來看，我們的方法可被視為將homography矩陣的運算，拆解成兩個簡單的校正過程，因此可以減少多台攝影機校正的運算量。除此之外，不需要使用到座標化的校正樣本，而我們的校正結果可以提供較直接的幾何感覺。本論文亦討論關於參數波動和測量誤差的敏感性分析，我們將數學分析的結果和電腦模擬的結果都呈現出來以驗證我們的分析，實際影像的實驗結果也展現此方法的功效和可行性。 至於動態校正的問題，我們推測多台攝影機的左右轉動角度（pan angle）和傾斜角度（tilt angle）的變化情況。在這個部分中，我們將左右轉動角度的因素考慮進來，並且重新建立在攝影機左右轉動、以及上下轉動的情況下，三維空間中水平面和二維影像的對應關係，以此關係為基礎，利用影像特徵點的位移情形，和多台攝影機之間所形成的epipolar平面的約束，來估測各台攝影機左右轉動角度和傾斜角度的變化。此方法不需要複雜的特徵點對應技術，而且也允許移動物體出現在校正場景中，這樣的動態校正過程，對於主動式之視訊監控的相關應用將會非常地有用。此外，我們也從數學上去探討了關於測量誤差和前次估測誤差的敏感性分析，從模擬的結果，證明了左右轉動角度和傾斜角度的變化之估計誤差，在實例中是可被接受的。而此方法的功效和可行性也在實際場景的實驗中展現出來。

In this dissertation, we present two new and efficient camera calibration techniques. The first one is the static calibration for multiple cameras, which is based on the back-projections of simple objects lying on the same plane. The other one is the dynamic calibration for multiple cameras, which is based on the temporal information on a single camera and the relative space information among multiple cameras. We adopt a system model that is general enough to fit for a large class of surveillance systems with multiple cameras. Both our static and dynamic calibration methods do not require particular system setup or specific calibration patterns. It is worthwhile to mention that, for our dynamic calibration, no complicated correspondence of feature points is needed. Hence, our calibration methods can be well applied to a wide-range surveillance system with multiple cameras. In the problem of static calibration for multiple cameras, we infer the relative positioning and orientation among multiple cameras. The 3D-to-2D coordinate transformation in terms of the tilt angle of a camera is deduced first. After having established the 3D-to-2D transformation, the tilt angle and altitude of each camera are estimated based on the observation of some simple objects lying on a horizontal plane. With the estimated tilt angles and altitudes, the relative orientations among multiple cameras can be easily obtained by comparing the back-projected world coordinates of some common vectors in the 3-D space. In some sense, our approach can be thought to have decomposed the computation of homography matrix into two simple calibration processes so that the computational load becomes lighter for the calibration of multiple cameras. Additionally, no coordinated calibration pattern is needed and our calibration results can offer direct geometric sense. In this dissertation, we also discuss the sensitivity analysis with respect to parameter fluctuations and measurement errors. Both mathematical analysis and computer simulation results are shown to verify our analysis. Experiment results over real images have demonstrated the efficiency and feasibility of this approach. In the problem of dynamic calibration, we infer the changes of pan and tilt angles for multiple cameras. In this part of the thesis, we take the pan angle factor into account and re-build the mapping between a horizontal plane in the 3-D space and the 2-D image plane on a panned and tilted camera. Based on this mapping, we utilize the displacement of feature points and the epipolar-plane constraint among multiple cameras to estimate the pan-angle and tilt-angle changes for each camera. This algorithm does not require a complicated correspondence of feature points. It also allows the presence of moving objects in the captured scenes while performing dynamic calibration. This kind of dynamic calibration process can be very useful for applications related to active video surveillance. Besides, the sensitivity analysis of our dynamic calibration algorithm with respect to measurement errors and fluctuations in previous estimations is also discussed mathematically. From the simulation results, the estimation errors of pan and tilt angle changes are proved to be acceptable in real cases. The efficiency and feasibility of this approach has been demonstrated in some experiments over real scenery.