臺灣博碩士論文加值系統

相機校正是在電腦視覺中重建三維模型的一個很重要的步驟。我們必須要有正確的相機資訊，才能夠精確地重建出三維模型。相機校正一直是這一個領域很重要的研究主題，其方法大致可以分為照相測量術和自我校正兩類。在本篇論文中，將探討適用於家用機器人的相機校正方法。主要採用的方法是藉由在不同角度觀察一個平面的圖形，來推算相機的各個內部參數。在實驗中，虛擬影像和真實影像皆被使用，都能得到很好的結果，而且這個方法忍受雜訊的能力相當高。但因所需時間稍嫌緩慢，故考慮另一種利用Homography的方法快速地計算相機的焦距，並由結果的對應來獲得更精確的相機內部參數。

Camera calibration is a crucial step in the reconstruction of a 3D model and has been an important research topic in computer vision. We can classify calibration techniques roughly into two categories: photogrammetric calibration and self-calibration. In this paper, we will study different algorithms to calibrate a camera. The major method is based on images of a planar pattern obtained from different viewing angles, as proposed in [30]. Both synthetic data and real images have been tested and results with satisfactory accuracy have been obtained. The method deals with noise well but is time consuming. To improve the efficiency of the calibration, a second method which uses homography to quickly compute the focal length is adopted. Proper mapping between the results obtained by these two methods can then be used to derive the correct camera parameters.

摘 要 I
ABSTRACT II
致謝 III
目錄 IV
表目錄 VI
圖目錄 VII
第一章 簡介 1
1.1 以三維物體為基礎的校正 2
1.2 自我校正 2
第二章 基本投影幾何 5
2.1 齊次座標表示法 5
2.2 三維幾何 6
2.2.1 相似轉換 7
2.2.2 歐幾里德轉換 8
2.2.3 總結 8
2.3 Homography 11
2.3.1 Homography的算法 11
2.4 極線幾何 13
2.5 基本矩陣與極線限制 15
2.5.1 基本矩陣的算法 17
第三章 相機模型與相機校正 21
3.1 照相機模型 21
3.2 從投影幾何到歐氏空間的相機校正 26
3.3 觀察平面圖形做相機校正 29
3.3.1 相機模型 29
3.3.2 求算Homography 30
3.3.3 內部參數的限制 31
3.3.4 相機校正 32
3.3.5 處理因透鏡的扭曲變形 34
3.3.6 微調每一個參數 36
3.3.7 總結 36
3.4 利用Homography求相機焦距 37
第四章 實驗結果 41
4.1 從投影幾何到歐氏空間的相機校正 41
4.1.1 虛擬的非平面三度空間點 41
4.1.2 虛擬的平面三度空間點 43
4.1.3 真實的非平面影像 44
4.2 觀察平面圖形做相機校正 46
4.2.1 多張影像與準確性之比較 47
4.2.2 雜訊程度和準確性之比較 49
4.2.3 穩定性測試 51
4.2.4 相機變焦的校正 54
4.3 利用Homography算焦距 55
4.3.1 虛擬影像點的實驗 56
4.3.2 真實影像的實驗 57
第五章 結論 62
參考文獻 63

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