旋转视图的三维重构
|
摘要
近年来,随着3D模型在工程设计、建筑设计、文化遗产的保存和游戏娱乐等领域的广泛应用,为了满足对3D模型日益增长的需求,开发低成本的3D模型获取系统就具有了重要的实际意义和理论研究价值。计算机视觉为解决低成本的获取3D模型这一问题提供了一条路径,计算机视觉的基本任务是根据世界景物的图像去理解景物的结构,其中一个最突出的成就是根据多幅未标定的图像计算摄像机的内参数、摄像机的运动及恢复景物的三维形状。
基于图像的三维重构一直是计算机视觉领域研究的热点问题之一,常用的三维重构方法有多视图几何方法、由阴影恢复形状方法、水平集方法和基于散焦图像的方法等。本论文从计算机视觉的几何理论出发,研究了单幅未标定旋转曲面图像的三维度量重构和多幅未标定的单轴旋转运动图像序列的三维度量重构。在旋转过程中,物体上任意一点的运动轨迹是一个圆,所以整个物体在旋转过程中会形成一个“虚的旋转曲面”,因此本文把这两种情况结合起来进行研究。本论文的主要研究内容和研究成果如下：
(1)摄像机标定是指根据图像计算摄像机的内参数,是实现未标定图像三维度量重构必不可少的一步,因为在摄像机未标定情况下,只能实现射影重构,无法实现度量重构。本文重点研究了基于同轴圆的摄像机标定方法,该方法利用绝对二次曲线的像仅与摄像机内参数有关的性质,对绝对二次曲线的像进行Cholesky分解得到摄像机的内参数。本文在Colombo等人的研究基础上,推导出了新的计算绝对二次曲线的像的公式,实现了摄像机的标定。
(2)如果没有任何先验知识,由单幅未标定图像恢复景物的三维结构几乎是不可能的,本文研究了由单幅未标定旋转曲面的像的三维度量重构,由于旋转曲面的每一个横截面都是圆,其在图像上的投影是椭圆,这一性质为单幅未标定旋转曲面的像的三维度量重构提供了足够的先验知识。本文根据这个性质,从平面透射公式出发,推导出了计算这些椭圆的公式,并推导出了椭圆的反向投影公式,从而实现了旋转曲面的三维重构。
(3)基于未标定的单轴旋转运动图像序列的三维度量重构主要分为两步,即摄像机的标定和三维点的获取。本文发现了旋转曲面与单轴旋转运动之间的共同之处,将改进后的基于旋转曲面的摄像机标定算法引入到了单轴旋转运动的摄像机标定方法中,实现了单轴旋转运动图像序列的摄像机标定。本文引入了由运动求结构的方法来计算物体的三维点,即先SIFT算法计算每一幅图像的特征点,再利用最近邻算法计算相邻图像间的匹配点,最后使用线性三角形法计算物体的三维点。
In the last few years, three-dimensional models have become more and more application fields, which range from engineering and architecture, to preservation of cultural heritage and entertainment. Following the growing demand of 3D models, the development of low cost acquisition systems has also become of key practical and theoretical value. Computer vision has provided important solutions to the low cost acquisition of 3D models, whose important task is to understand the structure of the object from views and one of outstanding achievements is to compute camera internal parameters, camera motion and recover 3D structure of object from multiple uncalibrated views.
3D reconstruction from views has been one of the most popular research subjects in the field of computer vision, common approaches to 3D reconstruction are multiple views geometry, shape from shading, level sets methods and defocus images methods. The paper researches 3D reconstruction of both single uncalibrated view of surface of revolution and multiple uncalibrated views of single axes rotation motion. In the process of rotation, the trajectory of any one of points in the object is a circle, so the whole object will form a'virtual surface of revolution', therefore the paper research the two types. The main research works and achievements are outlined as follows:
(1) Camera calibration is to compute camera internal parameters from views of object, and is one of the essential steps to 3D reconstruction from uncalibrated views, because projective reconstruction can be achieved and metric reconstruction can not be achieved if camera is uncalibrated. The paper focuses on camera calibration method based on coaxial circle, which method make use of the property of the image of absolute conic related to camera internal parameters, and cholesky decomposition of the image of absolute conic can obtain camera internal parameters. On the study of Colombo and others, a new formula to compute the image of absolute conic is derived and camera calibration is finished.
(2) It's impossible to recover 3D structure of object from single uncalibrated view without any priori knowledge. The paper research 3D metric reconstruction from single uncalibrated view of surface of revolution, as the each cross section of surface of revolution is a circle, whose projection is a conic, and the nature provide enough priori knowledge for 3D metric reconstruction from single uncalibrated view of surface of revolution. The formula of conic computation is derived from planar homology and then the formula of conic back-projection is derived, finally 3D metric reconstruction of surface of revolution is achieved.
(3) Three-dimensional reconstruction based on uncalibrated single-axis rotation image sequences is divided into two steps:camera calibration and 3D points acquisition. The similarity between the single-axis rotation and surface of revolution is found, and then camera calibration algorithm based on coaxial circle is introduced to camera calibration method of a single-axis rotation motion. Algorithm of structure from motion is introduced to compute 3D points coordinates, such that SIFT algorithm is used to compute feature points in each view and then nearest-neighbor algorithm is used to compute the matching points between adjacent images, finally linear triangle method is used to compute three-dimensional points of the object.
基于图像的三维重构一直是计算机视觉领域研究的热点问题之一,常用的三维重构方法有多视图几何方法、由阴影恢复形状方法、水平集方法和基于散焦图像的方法等。本论文从计算机视觉的几何理论出发,研究了单幅未标定旋转曲面图像的三维度量重构和多幅未标定的单轴旋转运动图像序列的三维度量重构。在旋转过程中,物体上任意一点的运动轨迹是一个圆,所以整个物体在旋转过程中会形成一个“虚的旋转曲面”,因此本文把这两种情况结合起来进行研究。本论文的主要研究内容和研究成果如下：
(1)摄像机标定是指根据图像计算摄像机的内参数,是实现未标定图像三维度量重构必不可少的一步,因为在摄像机未标定情况下,只能实现射影重构,无法实现度量重构。本文重点研究了基于同轴圆的摄像机标定方法,该方法利用绝对二次曲线的像仅与摄像机内参数有关的性质,对绝对二次曲线的像进行Cholesky分解得到摄像机的内参数。本文在Colombo等人的研究基础上,推导出了新的计算绝对二次曲线的像的公式,实现了摄像机的标定。
(2)如果没有任何先验知识,由单幅未标定图像恢复景物的三维结构几乎是不可能的,本文研究了由单幅未标定旋转曲面的像的三维度量重构,由于旋转曲面的每一个横截面都是圆,其在图像上的投影是椭圆,这一性质为单幅未标定旋转曲面的像的三维度量重构提供了足够的先验知识。本文根据这个性质,从平面透射公式出发,推导出了计算这些椭圆的公式,并推导出了椭圆的反向投影公式,从而实现了旋转曲面的三维重构。
(3)基于未标定的单轴旋转运动图像序列的三维度量重构主要分为两步,即摄像机的标定和三维点的获取。本文发现了旋转曲面与单轴旋转运动之间的共同之处,将改进后的基于旋转曲面的摄像机标定算法引入到了单轴旋转运动的摄像机标定方法中,实现了单轴旋转运动图像序列的摄像机标定。本文引入了由运动求结构的方法来计算物体的三维点,即先SIFT算法计算每一幅图像的特征点,再利用最近邻算法计算相邻图像间的匹配点,最后使用线性三角形法计算物体的三维点。
In the last few years, three-dimensional models have become more and more application fields, which range from engineering and architecture, to preservation of cultural heritage and entertainment. Following the growing demand of 3D models, the development of low cost acquisition systems has also become of key practical and theoretical value. Computer vision has provided important solutions to the low cost acquisition of 3D models, whose important task is to understand the structure of the object from views and one of outstanding achievements is to compute camera internal parameters, camera motion and recover 3D structure of object from multiple uncalibrated views.
3D reconstruction from views has been one of the most popular research subjects in the field of computer vision, common approaches to 3D reconstruction are multiple views geometry, shape from shading, level sets methods and defocus images methods. The paper researches 3D reconstruction of both single uncalibrated view of surface of revolution and multiple uncalibrated views of single axes rotation motion. In the process of rotation, the trajectory of any one of points in the object is a circle, so the whole object will form a'virtual surface of revolution', therefore the paper research the two types. The main research works and achievements are outlined as follows:
(1) Camera calibration is to compute camera internal parameters from views of object, and is one of the essential steps to 3D reconstruction from uncalibrated views, because projective reconstruction can be achieved and metric reconstruction can not be achieved if camera is uncalibrated. The paper focuses on camera calibration method based on coaxial circle, which method make use of the property of the image of absolute conic related to camera internal parameters, and cholesky decomposition of the image of absolute conic can obtain camera internal parameters. On the study of Colombo and others, a new formula to compute the image of absolute conic is derived and camera calibration is finished.
(2) It's impossible to recover 3D structure of object from single uncalibrated view without any priori knowledge. The paper research 3D metric reconstruction from single uncalibrated view of surface of revolution, as the each cross section of surface of revolution is a circle, whose projection is a conic, and the nature provide enough priori knowledge for 3D metric reconstruction from single uncalibrated view of surface of revolution. The formula of conic computation is derived from planar homology and then the formula of conic back-projection is derived, finally 3D metric reconstruction of surface of revolution is achieved.
(3) Three-dimensional reconstruction based on uncalibrated single-axis rotation image sequences is divided into two steps:camera calibration and 3D points acquisition. The similarity between the single-axis rotation and surface of revolution is found, and then camera calibration algorithm based on coaxial circle is introduced to camera calibration method of a single-axis rotation motion. Algorithm of structure from motion is introduced to compute 3D points coordinates, such that SIFT algorithm is used to compute feature points in each view and then nearest-neighbor algorithm is used to compute the matching points between adjacent images, finally linear triangle method is used to compute three-dimensional points of the object.
引文
[1]韦穗,杨尚俊,章权兵,胡茂林译,计算机视觉中的多视图几何.安徽：安徽大学出版社,2002
[2]R. Zhang, P. S. Tsai, J. E. Creyer and M. Shah, Shape from Shading:A Survey. IEEE Transaction on PAMI,1999,21(8):690-706
[3]A. Laurentini, The Visual Hull Concept for Silhouette Based Image Understanding,. IEEE PAMI,1994,16(2):150-162
[4]A. Laureniini, The Visual Hull:A new tool fore Contour-based image understanding. Proceedings 7th Scandinavian Conference, Image Analysis, 2002:1991-993
[5]余峰,陈越,一种可视外壳的快速拓扑生成算法.中国图象图形学报,2004,9(5)：604-610
[6]B. Garcia and P. Brunet,3D reconstruction withn Projective Octrees and Epipolar Geometry, Proceedings of the IEEE International Conference on Computer Vision,1998,4(7):1067-1072
[7]Q. Chen and G. Medioni, A Volumetric Stereo Matching Method:Application to Image-Based Modeling. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition,1999:29-34
[8]G. G. Slabaugh, W. B. Culbetson, T. Malzbender etc, Methods for Volumetric Reconstruction of Visual Scenes. International Journal of Computer Vision, 2004,57(3):179-199
[9]K. N. Kutulakos and S.M.Seitz, A Theory of Shape by Space Carving. International Journal on Computer Vision,1999,38(3):199-218
[10]Slabaugh, T, Malzbender and W. B. Culbertson, Volumetric Warping for Voxel Coloring on an Infinite Domain.3D Structure from Multiple Images for Large Scale Environments(SMILE),2000:41-50
[11]G. G. Slabaugh, W.B,Culbertson, T. Malzbender and R. Schafer, A survey of volumetric scene reconstruction methods from photographs. International Workshop on Volume Graphics,2001:81-100
[12]G. G. Slabaugh, R.Schafer, and M. Hans, Image-based photo Hulls.1st International Symposium on 3D Processing. Visualization and Transmission, 2002:704-708
[13]G. G. Slabaugh, Novel Volumetric Scene Reconstruction Methods for New View Synthesis. Ph.D. Thesis, Georgia Institute of Technology,2002
[14]O. Faugeras, What Can be Seen in Three Dimension with an Uncalibrated Stereo Rig? Computer Vision ECCV'92,1992:563-578
[15]O. Faugeras, Stratification of three-dimensional Vision:Projective, Affine, and Metric Representations,. J. Opt. Soc. Am,1995,12(3):465-484
[16]http://www.cim.mcgill.ca/-dparks/CornerDetector/index.htm
[17]M. Pilu, Uncalibrated Stereo Correspondence by Singular Value Decomposition. Technical Report HPL-97-96,1999
[18]B. Triggs, Joint Feature Distributions for Image Corrospondence. Proceedings of International Conference on Computer Vision,2001,201-208
[19]Z. Zhang, R. Deriche, O. Faugeras and Q. T. Luong, A Robust Technique for Matching Two Uncalibrated Images Through the Recovery of the Unknown Epipolar Geometry. Artificial Intelligence Journal,1995,78:87-119
[20]A.W. Fitzgibbon, Robust Registration of 2D and 3D Point Sets. Image and Vision Computing,2003,21:1145-1153
[21]S. Arya, D. M. Mount, M. S. Netanyahu, R. Silverman and A. Y. Wu, An Optional Algorithm for Approximate nearest Neighbor Searching Fixed Dimensions. Journal of ACM,1998,45(6):891-923
[22]D. Liebowitz and A. Zisserman, Metric Rectification for Perspective Images of Planes. In Proceeding of the Conference on Computer Vision and Pattern Recognition,1998:482-488
[23]M. Polleyfeys, Self-Calibration and Metric 3D Reconstruction from Uncalibrated Image Sequences. PhD thesis,1999
[24]Y. I. Abdel-Aziz and H. M. Karara, Direct Linear Transformation from Comparator Coordinates into Object Space Coordinates. ASP Symposium on Colse-Range Photogrammetry,1971:1-18
[25]R. Tsai, R. Lenz, A Technique for Fully Automomous and Efficient 3D Robotics Hand/Eye Calibration. IEEE Trans. Robotics and Automation,1989, 5(3):345-358
[26]R. Tsai, An Efficient and Accurate Camera Calibration Technique for 3D Machine Vision. Proc. CVPR'86,1986:364-374
[27]Z.Y. Zhang, Flexible Camera Calibration by Viewing a Plane from Unknown Orientations. Proc. ICCV'99,1999:666-673
[28]X. Q. Meng and Z. Y. Hu, A New Easy Camera Calibration Technique Based on Circular Points. Pattern Recognition,2003,36(5):1155-1164
[29]Y. Wu, H. Zhu, Z. Hu, and F. Wu, Camera Calibration from the Quasi-Affine Invariance of Two Parallel Circles. The 8th European Conference on Computer Vision (ECCV),2004:190-202
[30]P. Gurdjos, P. Sturm, and Y. Wu, Euclidean Structure from N>=2 Parallel Circles:Theory and Algorithms. The 10th European Conference on Computer Vision (ECCV),2006:238-252
[31]Y. Wu, X. Li, F. Wu, and Z. Hu. Coplanar Circles, Quasi-Affine Invariance and Calibration. Image and Vision Computing,2006,24(4):319-326
[32]马颂德,张正友,计算机视觉——计算理论与算法基础,科学出版社,1998.
[33]胡占义,吴福朝,基于主动视觉摄像机标定方法.计算机学报,2002,25(11)：1149-1156
[34]吴福朝,李华,胡占义,基于主动视觉的摄像机自标定方法研究,自动化学报,2001,27(6)：752-762
[35]S. Utcke and A. Zisserman, Projective Reconstruction of Surfaces of Revolution. Pattern Recognition,25th DAGM Symposium,2003:265-272
[36]K. Y, K. Wong and P. R. S. Mendonca, Reconstruction of Surfaces of Revolution from Single Uncalibrated Views. Image and Vision Computing,2004,22(10): 829-836
[37]K.Y. K. Wong, Structure and Motion from Silhouttes. PhD thesis, University of Cambrige,2001
[38]K. Y, K. Wong, P. R. S Mendonca and R. Cipolla, Camera Calibration from symmetry, Proceedings Ninth IMA Conference,2001:217-222
[39]K. Y, K. Wong, P. R. S Mendonca and R. Cipolla, Reconstruction of Surfaces of Recvolution from Single Uncalibrated Views, Proceedings British Machine Vision Conference,2002:93-102
[40]K. Y, K. Wong, P. R. S Mendonca and R. Cipolla, Camera Calibration from Surfaces of Recvolution. IEEE Transactions Pattern Analysis and Machine Intelligence,2003,25(2):147-161
[41]C.Colombo, A. D. Bimbo and F. Pernici, Uncalibrated 3D Metric Reconstruction and Flattened Texture Acquisition from a single View of a Surface of Revolution. Proceedings 1 st International Symposium on 3D Data Processing Visualization and Transmission,2002:277-284
[42]C. Colombo, A. D. Bimbo and F. Pernici, Metric 3D Reconstruction and Texture Acquisition of a Surface of Revolution from a Single Uncalibrated View. IEEE Transactions on Pattern Analysis and Machine Intelligence,2005,27(1):99-114
[43]C. Colombo, D. Comanducci and A. D. Bimbo, Camera Calibration with Two Arbitrary Coaxial Circles. Proceedings 9th European Conference on Computer Vision,2006:265-276
[44]C. Colombo, A. D. Bimbo and F. Pernici, Image Mosaicing from Uncalibrated Views of a Surface of Revolution. Proceedings 15th British Machine Vision Conference,2004:407-416
[45]Y. H Wu, G. H. Wang and F. C. Wu, Euclidean Reconstruction of a Circular Truncated Cone only from its Uncalibrated Contours. Image and Vision Computing,2006,24(8):810-818
[46]Y. H Wu, X. J. Li, F. C. Wu and Z. Y. Hu, Coplanar Circles, Quasi-affine Invariance and Calibration, Image and Vision Computing,2006,24:319-326
[47]Y. H Wu, H. Z. Zhu, Z. Y. Hu and F. C. Wu, Camera Calibration from Quasi-affine Invariance of Two Parallel Circles, Compute Vision-ECCV 2004, 2004:190-202
[48]Baungart, Geometric Modeling for Computer Vision. California:Stanford University,1974
[49]S. Sullivan and J. Ponce, Automatic Model Construction, Pose Estimation and Object Recognition from Photographs Using Triangular Splines, IEEE Transactions Pattern Analysis and Machine Intelligence,1998,20(10): 1091-1097
[50]R. Szelisli, Shape from Rotation. Proceedings IEEE Conference Computer and Pattern Recognition,1991:625-631
[51]A. W. Fitzgibbon, G. Cross, and A. Zissman, Automatic 3D Model Construction for Turn-Table Sequences. SMILE,1998:155-170
[52]P. R.S. Mendonca, K. R. K. Wong, and R. Cippolla, Epipolar Geometry from Profiles under Circular Motion, IEEE Transansactions on Pattern Analysis and Machine Intelligence,23(6):604-616 (2001)
[53]G. Jiang, H. T. Tsui, L. Quan and S.Q.Liu, Recovering the Geometry of Single Axis Motion by Fitting Conic. Proc IEEE Conf. Computer Vision and Pattern Recognition,2001:293-298
[54]G. Jiang, H.T.Tsui, L.Quan, and A. Zisserman, Single Axis Motion Geometry by Fitting Conic. Proc European Conf. Computer Vision,2002:537-551
[55]G. Jiang, L. Quan, and H. T. Tsui, Circular Motion Geometry by Minimal 2 Points in 4 Images. Proc. Ninth Int'l Conf. Computer Vision,2003:221-227
[56]G. Jiang, L. Quan, and H.T.Tsui, Circular Motion Geometry by Minimal Data. IEEE. Trans. Pattern Analysis and Machine Intelligence,2004,26(6):721-731
[57]G. Jiang, L. Quan, and H.T.Tsui, Outer-Looking Circular Motion Analysis of Large Image Sequences. IEEE. Trans. Pattern Analysis and Machine Intelligence, 2005,27(2):271-277
[58]David Lowe. Distinctive Image Features From Scale-Invariant Keypoints. International Journal of Computer Vision.2004,60(2):91-110
[59]S. Arya, D. M. Mount, N. S. Netanyahu, R. Silverman and A. Y. Wu. An Optional Algorithm For Approximate Nearest Neighbor Searching Fixed Dimensions. Journal Of the ACM.1998,45(6):891-923
[2]R. Zhang, P. S. Tsai, J. E. Creyer and M. Shah, Shape from Shading:A Survey. IEEE Transaction on PAMI,1999,21(8):690-706
[3]A. Laurentini, The Visual Hull Concept for Silhouette Based Image Understanding,. IEEE PAMI,1994,16(2):150-162
[4]A. Laureniini, The Visual Hull:A new tool fore Contour-based image understanding. Proceedings 7th Scandinavian Conference, Image Analysis, 2002:1991-993
[5]余峰,陈越,一种可视外壳的快速拓扑生成算法.中国图象图形学报,2004,9(5)：604-610
[6]B. Garcia and P. Brunet,3D reconstruction withn Projective Octrees and Epipolar Geometry, Proceedings of the IEEE International Conference on Computer Vision,1998,4(7):1067-1072
[7]Q. Chen and G. Medioni, A Volumetric Stereo Matching Method:Application to Image-Based Modeling. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition,1999:29-34
[8]G. G. Slabaugh, W. B. Culbetson, T. Malzbender etc, Methods for Volumetric Reconstruction of Visual Scenes. International Journal of Computer Vision, 2004,57(3):179-199
[9]K. N. Kutulakos and S.M.Seitz, A Theory of Shape by Space Carving. International Journal on Computer Vision,1999,38(3):199-218
[10]Slabaugh, T, Malzbender and W. B. Culbertson, Volumetric Warping for Voxel Coloring on an Infinite Domain.3D Structure from Multiple Images for Large Scale Environments(SMILE),2000:41-50
[11]G. G. Slabaugh, W.B,Culbertson, T. Malzbender and R. Schafer, A survey of volumetric scene reconstruction methods from photographs. International Workshop on Volume Graphics,2001:81-100
[12]G. G. Slabaugh, R.Schafer, and M. Hans, Image-based photo Hulls.1st International Symposium on 3D Processing. Visualization and Transmission, 2002:704-708
[13]G. G. Slabaugh, Novel Volumetric Scene Reconstruction Methods for New View Synthesis. Ph.D. Thesis, Georgia Institute of Technology,2002
[14]O. Faugeras, What Can be Seen in Three Dimension with an Uncalibrated Stereo Rig? Computer Vision ECCV'92,1992:563-578
[15]O. Faugeras, Stratification of three-dimensional Vision:Projective, Affine, and Metric Representations,. J. Opt. Soc. Am,1995,12(3):465-484
[16]http://www.cim.mcgill.ca/-dparks/CornerDetector/index.htm
[17]M. Pilu, Uncalibrated Stereo Correspondence by Singular Value Decomposition. Technical Report HPL-97-96,1999
[18]B. Triggs, Joint Feature Distributions for Image Corrospondence. Proceedings of International Conference on Computer Vision,2001,201-208
[19]Z. Zhang, R. Deriche, O. Faugeras and Q. T. Luong, A Robust Technique for Matching Two Uncalibrated Images Through the Recovery of the Unknown Epipolar Geometry. Artificial Intelligence Journal,1995,78:87-119
[20]A.W. Fitzgibbon, Robust Registration of 2D and 3D Point Sets. Image and Vision Computing,2003,21:1145-1153
[21]S. Arya, D. M. Mount, M. S. Netanyahu, R. Silverman and A. Y. Wu, An Optional Algorithm for Approximate nearest Neighbor Searching Fixed Dimensions. Journal of ACM,1998,45(6):891-923
[22]D. Liebowitz and A. Zisserman, Metric Rectification for Perspective Images of Planes. In Proceeding of the Conference on Computer Vision and Pattern Recognition,1998:482-488
[23]M. Polleyfeys, Self-Calibration and Metric 3D Reconstruction from Uncalibrated Image Sequences. PhD thesis,1999
[24]Y. I. Abdel-Aziz and H. M. Karara, Direct Linear Transformation from Comparator Coordinates into Object Space Coordinates. ASP Symposium on Colse-Range Photogrammetry,1971:1-18
[25]R. Tsai, R. Lenz, A Technique for Fully Automomous and Efficient 3D Robotics Hand/Eye Calibration. IEEE Trans. Robotics and Automation,1989, 5(3):345-358
[26]R. Tsai, An Efficient and Accurate Camera Calibration Technique for 3D Machine Vision. Proc. CVPR'86,1986:364-374
[27]Z.Y. Zhang, Flexible Camera Calibration by Viewing a Plane from Unknown Orientations. Proc. ICCV'99,1999:666-673
[28]X. Q. Meng and Z. Y. Hu, A New Easy Camera Calibration Technique Based on Circular Points. Pattern Recognition,2003,36(5):1155-1164
[29]Y. Wu, H. Zhu, Z. Hu, and F. Wu, Camera Calibration from the Quasi-Affine Invariance of Two Parallel Circles. The 8th European Conference on Computer Vision (ECCV),2004:190-202
[30]P. Gurdjos, P. Sturm, and Y. Wu, Euclidean Structure from N>=2 Parallel Circles:Theory and Algorithms. The 10th European Conference on Computer Vision (ECCV),2006:238-252
[31]Y. Wu, X. Li, F. Wu, and Z. Hu. Coplanar Circles, Quasi-Affine Invariance and Calibration. Image and Vision Computing,2006,24(4):319-326
[32]马颂德,张正友,计算机视觉——计算理论与算法基础,科学出版社,1998.
[33]胡占义,吴福朝,基于主动视觉摄像机标定方法.计算机学报,2002,25(11)：1149-1156
[34]吴福朝,李华,胡占义,基于主动视觉的摄像机自标定方法研究,自动化学报,2001,27(6)：752-762
[35]S. Utcke and A. Zisserman, Projective Reconstruction of Surfaces of Revolution. Pattern Recognition,25th DAGM Symposium,2003:265-272
[36]K. Y, K. Wong and P. R. S. Mendonca, Reconstruction of Surfaces of Revolution from Single Uncalibrated Views. Image and Vision Computing,2004,22(10): 829-836
[37]K.Y. K. Wong, Structure and Motion from Silhouttes. PhD thesis, University of Cambrige,2001
[38]K. Y, K. Wong, P. R. S Mendonca and R. Cipolla, Camera Calibration from symmetry, Proceedings Ninth IMA Conference,2001:217-222
[39]K. Y, K. Wong, P. R. S Mendonca and R. Cipolla, Reconstruction of Surfaces of Recvolution from Single Uncalibrated Views, Proceedings British Machine Vision Conference,2002:93-102
[40]K. Y, K. Wong, P. R. S Mendonca and R. Cipolla, Camera Calibration from Surfaces of Recvolution. IEEE Transactions Pattern Analysis and Machine Intelligence,2003,25(2):147-161
[41]C.Colombo, A. D. Bimbo and F. Pernici, Uncalibrated 3D Metric Reconstruction and Flattened Texture Acquisition from a single View of a Surface of Revolution. Proceedings 1 st International Symposium on 3D Data Processing Visualization and Transmission,2002:277-284
[42]C. Colombo, A. D. Bimbo and F. Pernici, Metric 3D Reconstruction and Texture Acquisition of a Surface of Revolution from a Single Uncalibrated View. IEEE Transactions on Pattern Analysis and Machine Intelligence,2005,27(1):99-114
[43]C. Colombo, D. Comanducci and A. D. Bimbo, Camera Calibration with Two Arbitrary Coaxial Circles. Proceedings 9th European Conference on Computer Vision,2006:265-276
[44]C. Colombo, A. D. Bimbo and F. Pernici, Image Mosaicing from Uncalibrated Views of a Surface of Revolution. Proceedings 15th British Machine Vision Conference,2004:407-416
[45]Y. H Wu, G. H. Wang and F. C. Wu, Euclidean Reconstruction of a Circular Truncated Cone only from its Uncalibrated Contours. Image and Vision Computing,2006,24(8):810-818
[46]Y. H Wu, X. J. Li, F. C. Wu and Z. Y. Hu, Coplanar Circles, Quasi-affine Invariance and Calibration, Image and Vision Computing,2006,24:319-326
[47]Y. H Wu, H. Z. Zhu, Z. Y. Hu and F. C. Wu, Camera Calibration from Quasi-affine Invariance of Two Parallel Circles, Compute Vision-ECCV 2004, 2004:190-202
[48]Baungart, Geometric Modeling for Computer Vision. California:Stanford University,1974
[49]S. Sullivan and J. Ponce, Automatic Model Construction, Pose Estimation and Object Recognition from Photographs Using Triangular Splines, IEEE Transactions Pattern Analysis and Machine Intelligence,1998,20(10): 1091-1097
[50]R. Szelisli, Shape from Rotation. Proceedings IEEE Conference Computer and Pattern Recognition,1991:625-631
[51]A. W. Fitzgibbon, G. Cross, and A. Zissman, Automatic 3D Model Construction for Turn-Table Sequences. SMILE,1998:155-170
[52]P. R.S. Mendonca, K. R. K. Wong, and R. Cippolla, Epipolar Geometry from Profiles under Circular Motion, IEEE Transansactions on Pattern Analysis and Machine Intelligence,23(6):604-616 (2001)
[53]G. Jiang, H. T. Tsui, L. Quan and S.Q.Liu, Recovering the Geometry of Single Axis Motion by Fitting Conic. Proc IEEE Conf. Computer Vision and Pattern Recognition,2001:293-298
[54]G. Jiang, H.T.Tsui, L.Quan, and A. Zisserman, Single Axis Motion Geometry by Fitting Conic. Proc European Conf. Computer Vision,2002:537-551
[55]G. Jiang, L. Quan, and H. T. Tsui, Circular Motion Geometry by Minimal 2 Points in 4 Images. Proc. Ninth Int'l Conf. Computer Vision,2003:221-227
[56]G. Jiang, L. Quan, and H.T.Tsui, Circular Motion Geometry by Minimal Data. IEEE. Trans. Pattern Analysis and Machine Intelligence,2004,26(6):721-731
[57]G. Jiang, L. Quan, and H.T.Tsui, Outer-Looking Circular Motion Analysis of Large Image Sequences. IEEE. Trans. Pattern Analysis and Machine Intelligence, 2005,27(2):271-277
[58]David Lowe. Distinctive Image Features From Scale-Invariant Keypoints. International Journal of Computer Vision.2004,60(2):91-110
[59]S. Arya, D. M. Mount, N. S. Netanyahu, R. Silverman and A. Y. Wu. An Optional Algorithm For Approximate Nearest Neighbor Searching Fixed Dimensions. Journal Of the ACM.1998,45(6):891-923