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研究生:高吉毅
研究生(外文):Chi-Yi Kao
論文名稱:利用相對長度做相機校正以恢復3D結構
論文名稱(外文):Using relative lengths to camera calibration for 3D structure recovery
指導教授:許文星
指導教授(外文):Wen-Hsing Hsu
學位類別:碩士
校院名稱:國立清華大學
系所名稱:電機工程學系
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:英文
論文頁數:58
中文關鍵詞:3D 重建相機校正
外文關鍵詞:camera calibration3D reconstruction
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早期,3D重建的研究,最常應用於機器人導引的領域,及地形量測領域。隨著IC設計產業的蓬勃發展,使得原本相當費時的3D視覺處理,可以透過硬體來加快處理速度。如今,3D視覺效果,幾乎已成為個人電腦的標準配備,無論是大型電玩,或是電腦遊戲,都強調以3D視覺呈現為其賣點,甚至醫學影像,也朝往3D的領域邁進,以增加診斷的準確性。這都一再顯示3D視覺的重要性,及大幅度提升其未來的價值。有了後段應用層面的需求,則前段建立3D模型的研究,自然引起各界高度的興趣。如何用最普遍的方法,建出最逼真的3D模型,想必是炙手可熱的問題。
利用相機擷取影像,建立物體3D模型,是最普遍的一種方式。現今,相機自我校正的方法,已有不錯的重建效果,但是假如我們可以從真實世界裡,獲取,得到一些欲重建物的資訊,就可以來幫助我們,更提升重建效果,獲得更逼真的3D結構。
在這篇論文裡,我們對於相機自我校正,以及獲得物體3D結構,提出一套完整的演算法。我們的方法,假設已知欲建3D模型物體相對長度的資訊。相對長度,即是兩線段長度的比例關係。在這個方面,我們不限定任一特定的圖形或物體,所以從影像中獲取相對長度的資訊是比較普遍性的。因為相對長度,是存在於公制階層下的一個不變的特性,我們的方法是利用已知的相對長度,透過恆等式,求出一個唯一的轉換矩陣。經由此轉換矩陣,我們將能提升初步由投影階層重建,轉換到的公制階層重建,再進一步的得到更精確的公制階層重建。在公制階層重建下,和真實物體只存在一個尺寸的差異。這也是在不知道實際物體的絕對長度的情況下,可以做到的最高的層級。由實驗結果可以證實,我們提出的方法的確可以提升由Bougnoux的重建方法,獲得更真實的3D結構。
Some calibration methods can estimate the relative positions of cameras and their intrinsic parameters using 3D coordinates of points on a known calibration target. However, it is nearly impossible to use the same calibration target for the wide range of vision tasks that require cameras with long focal length for magnification as well as short one for a larger field of view. Furthermore, many robotic applications demand cameras to be calibrated on-line, which makes it impossible to put a specific calibration target for different camera setups. Now some methods of self-calibration are reported, these methods have not bad effect [31]. If we know some information from the scene, we can exploit the information to improve reconstruction from the methods of self-calibration. By deeply exploring 3D projective geometry we can know that relative lengths are a very beneficial constraint to metric 3D reconstruction. Relative lengths can be easily acquired from geometrical shape such as circle and cubic.
In this thesis, we presented a camera self-calibration and 3D structure recovery algorithm by using the relative lengths which is an invariant property under the similarity transformation. From the studying of 3D geometry and camera model, it can be shown that there exists a homography matrix with its elements partly depending on the intrinsic parameters to be able to upgrade the projective reconstruction to the metric one. Based on the particular form of homography matrix, we can formulate an error function according to the invariance of relative lengths under the similarity transformation and hence camera calibration and 3D structure recovery can be achieved by minimizing this error function. In this way, the recovered structure will automatically satisfy the invariance constraint of metric stratum. Thus, a metric reconstruction of the scene is also achieved. In addition, the proposed method can effectively deal with the case with varying intrinsic parameters of camera for the homography matrix is uniquely determined for every views of the scene.
In this thesis, we have tested the proposed method on some synthetic and real data. The results are encouraging. The reconstructed 3D structures are visually perfect.
1. Introduction p1
1.1 Motivation and Objective...………..………………………………………..p1
1.2 The Overview of 3D Reconstruction…..…………………………………...p2
1.3 The Stratification of 3D geometry…………………………………….p4
1.3.1 Projective Stratum……………………………………………….p5
1.3.2 Affine Stratum…………………………………………………...p6
1.3.3 Metric Stratum…………………………………………………...p6
1.3.4 Euclidean Stratum………………………..……………………...p8
1.4 Organization of the Thesis…………………………………………………..p8

2. Camera Model and the Projective Reconstruction p10
2.1 Camera Model……………………………………………………………...p10
2.2 Camera Calibration…………...……………………………………………p14
2.3 Two View Geometry……….……………………………………………….p15
2.4 The fundamental matrix……………………………………………………p18
1.3.1 Linear Method………………………………………………………p18
1.3.2 Robust Method…………….………………………………………..p21
2.5 Projective Reconstruction of Multiple Views……………………………...p22
3. Self-Calibration p26
3.1 Stratified Self-Calibration……………...………………………………….p26
1.3.1 Modulus Constraint…………………………………………………..p26
1.3.2 Stratified Self-Calibration from Constant Intrinsic Parameters…...…p27
3.2 Self-Calibration from the Constraints of Intrinsic Parameters……..…p28
1.3.1 Looking for the Homography Matrix...…….……......……………..p30
1.3.2 Looking for the Focal Length………………………………………...p31
1.3.3 Looking for the q………………………………………………..……p32

4. Proposed Algorithm-
Self-Calibration Using Relative Lengths p33
4.1 Metric Reconstruction Using the Homography Matrix…….……...………p33
4.2 Camera Calibration……………………………………….…..…………...p34
4.3 The Complete Algorithm….……………………………………………….p36

5. Experimental Results p39
5.1 Synthetic Data……………...………...………...……………………….…p39
5.2 Real Images……………………..…………………………………………p45

6. Conclusion p53
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