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研究生:俞有華
研究生(外文):Yu-hua Yu
論文名稱:基於投射模型和仿射模型的立體影像扭正
論文名稱(外文):Stereo Image Rectification Based on Projective and Affine Models
指導教授:吳先晃
指導教授(外文):Hsien-Huang P. Wu
學位類別:博士
校院名稱:國立雲林科技大學
系所名稱:工程科技研究所博士班
學門:工程學門
學類:綜合工程學類
論文種類:學術論文
論文出版年:2006
畢業學年度:94
語文別:英文
論文頁數:152
中文關鍵詞:基本矩陣共軛幾何影像扭正
外文關鍵詞:image rectificationepipolar geometryfundamental matrix
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對於立體視覺的應用,在不需相機校正的情形下,投射幾何是個有用的工具可以解決扭正問題,然而,投射扭正(projective rectification)必須選擇適當的最小限制條件來減少幾何失真,在本論文中,我們提出改進的演算法,結合新發展的投射轉換和剪割轉換(shearing transform)以減少失真,強調低的幾何失真使得本方法不僅適合3D重建而且適用在立體視覺的應用。另外,我們改進上面所提的方法稱為相對修正法,此方法使用更少的參數去完成最小化,能減少運算時間各改進扭正結果,測試數種不同形態的立體影像對,與其它方法比較我們的演算法在視覺和數值上有很好的適用性及可靠程度。
很多研究指出平面鏡在反射立體系統中能使用單一相機取得立體影像,PCS系統不僅提供輻射優點超越雙相機立體系統,而且減少複雜度和立體取像的成本,雖然許多研究已經完成PCS系統的設計,但是較少專注在分析它的共軛幾何(epipolar geometry),也就是基本矩陣(fundamental matrix),本論文認真仔細地研究PCS系統及證明在某種結構能近似仿射共軛幾何,仿射模型可在基本矩陣中使用較少參數的數目,從傳統立體系統七個參數減少到四個參數,實驗結果證實使用較少參數的共軛模型的PCS系統有較多的強�魕囥M精確性以及更容易實現,而且,立體影像的扭正基於仿射基本矩陣表現更完美及顯著降低幾何失真,在PCS系統仿射基本矩陣的使用,這些顯著的優點是被肯定的。
For stereo vision applications, projective geometry has proved to be a useful tool for solving the rectification problem without camera calibration. However, the criterion of minimisation for projective rectification must be chosen properly in order to avoid unduly geometric distortion. In this thesis, we propose an improved algorithm to minimize the distortion by combining a newly developed projective transform with a properly chosen shearing transform. The emphasis on low geometric distortion makes this method not only appropriate for 3-D reconstruction but also for stereoscopic viewing applications. Furthermore, we improve the new method to "relative modification"
method. On the basis of relative modification, this method contains fewer parameters (6 degrees of freedom) for minimisation, which reduces the processing time, and improves the rectification result. Several different types of image pairs were tested to demonstrate the applicability and reliability of the proposed algorithm visually and quantitatively. Comparisions with other methods are also provided to verify the improvement
of this new scheme.
Researches show that planar mirror has been used successfully in catadioptric stereo systems to capture stereo images with a single camera. These planar catadioptric stereo (PCS) systems not only provide radiometric advantages over traditional two camera stereo, but also reduce the complexity and cost of acquiring stereoscopic video. Although much research has been done on the design of the PCS system, little attention has been paid to the analysis of its epipolar geometry, that is, the fundamental matrix. In this paper, we thoroughly investigated features of the PCS system and proved that certain structure can be approximated by affine epipolar geometry. This affine model reduces the number of parameters in the fundamental matrix from seven in the conventional stereo system to only four in the PCS system. Experimental results verify that by using the affine model with fewer parameters, estimation of the fundamental matrix for a PCS system can be more robust, precise, and much easier to implement. Furthermore, rectification of the image pair based on the affine fundamental matrix can achieve better performance with much less geometric distortion. These significant advantages confirm the usefulness of an affine fundamental matrix model for the PCS systems.
Contents
1 Introduction .............................................................1
1.1 Image Rectification.....................................................1
1.2 Thesis Contributions....................................................8
1.3 Thesis Organization.....................................................9
2 Projective Rectification for General Case................................10
2.1 Introduction...........................................................10
2.2 Projective Epipolar Geometry...........................................11
2.2.1 Epipolar Constraint ................................................ 11
2.2.2 Epipolar Geometry After Stereo Image Rectification ..................13
2.3 Review of Projective Rectification.....................................14
2.4 Projective Rectification with Reduced Geometric Distortion for
Stereo Vision and Stereoscopic Video...................................... 17
2.4.1 ProposedMethod and FMatrix Parameterization..........................17
2.4.2 Projection Rectification Based on Least Square Distance..............19
2.4.3 Homography withMinimal Geometric Distortion..........................23
2.4.4 Experimental Results and Discussions.................................27
2.5 Projective Rectification Based on Relative Modification and Size
Extension for Stereo Image Pairs ..........................................40
2.5.1 ProposedMethod and FMatrix Parameterization..........................40
2.5.2 Projection Rectification Based on Least Square Distance..............43
2.5.3 Geometric Distortion Reduction by Shearing Transform................ 44
2.5.4 Determination of Image Extent and Resampling.........................45
2.5.5 Outline of Algorithm.................................................46
2.5.6 Experimental Results and Discussions................................ 47
3 Affine Model and Affine Fundamental Matrix...............................58
3.1 Introduction ..........................................................58
3.2 Review of Epipolar Geometry............................................61
3.2.1 CameraModel .........................................................62
3.2.2 Epipolar Constraint and FundamentalMatrix............................63
3.2.3 Epipolar Equation for General ProjectionModel .......................65
3.3 Epipolar Geometry of Catadioptric Stereo with Two PlanarMirrors........67
3.3.1 Relative Orientation Between Real and Virtual Cameras................68
3.3.2 Relative Orientation and Fundamental matrix of Two Virtual
Cameras....................................................................70
3.4 Epipolar Geometry of PCS with Constraint ............................. 74
3.4.1 Affine Fundamental Matrix ...........................................75
3.4.2 Computation of F Matrix..............................................80
3.4.3 Advantages of Affine Model...........................................82
3.4.4 Maximum Likelihood Estimation of Affine Fundamental Matrix ..........83
3.5 Experimental Results and Discussions.................................. 85
3.5.1 PCS System and Its Reflection Transformation.........................85
3.5.2 Evaluation Criteria .................................................88
3.5.3 Type 1: Image Pair Acquired by Affine Camera ....................... 91
3.5.4 Type 2: Image Pairs Acquired by PCS with TwoMirrors..................96
3.6 Conclusions...........................................................106
4 Affine Rectification....................................................109
4.1 Introduction..........................................................109
4.2 Epipolar Geometry of Catadioptric Stereo with Two PlanarMirrors.......110
4.3 The Proposed Affine Rectification Algorithm ..........................110
4.3.1 Epipolar Geometry after Image Rectification ....................... 111
4.3.2 Parameterization of Homographies................................... 112
4.3.3 Projection Rectification Based on Least Square Distance.............115
4.3.4 Homography with Constrained Geometric Distortion................... 120
4.3.5 Outline of Algorithm .............................................. 123
4.4 Experimental Results and Discussions..................................124
4.4.1 Epipolar Geometry and Homographies of the Selected PCS System....................................................................124
4.4.2 Experimental Results ...............................................129
5 Conclusions ............................................................136
Bibliography............................................................. 138
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