iccv iccv2013 iccv2013-280 iccv2013-280-reference knowledge-graph by maker-knowledge-mining
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Author: Jae-Hak Kim, Yuchao Dai, Hongdong Li, Xin Du, Jonghyuk Kim
Abstract: We present a new multi-view 3D Euclidean reconstruction method for arbitrary uncalibrated radially-symmetric cameras, which needs no calibration or any camera model parameters other than radial symmetry. It is built on the radial 1D camera model [25], a unified mathematical abstraction to different types of radially-symmetric cameras. We formulate the problem of multi-view reconstruction for radial 1D cameras as a matrix rank minimization problem. Efficient implementation based on alternating direction continuation is proposed to handle scalability issue for real-world applications. Our method applies to a wide range of omnidirectional cameras including both dioptric and catadioptric (central and non-central) cameras. Additionally, our method deals with complete and incomplete measurements under a unified framework elegantly. Experiments on both synthetic and real images from various types of cameras validate the superior performance of our new method, in terms of numerical accuracy and robustness.
[1] A. Agrawal, Y. Taguchi, and S. Ramalingam. Analytical forward projection for axial non-central dioptric and catadioptric cameras. In ECCV, pages 129–143. 2010.
[2] A. Agrawal, Y. Taguchi, and S. Ramalingam. Beyond Alhazen’s problem: Analytical projection model for non-central catadioptric cameras with quadric mirrors. In CVPR, pages 2993–3000, 2011.
[3] R. Angst, C. Zach, and M. Pollefeys. The generalized trace-norm and its application to structure-from-motion problems. In ICCV, pages 2502–2509, 2011.
[4] E. Cand e`s, X. Li, Y. Ma, and J. Wright. Robust principal component analysis? J. ACM, 58(3): 11:1–37, 2011.
[5] Y. Dai, H. Li, and M. He. Projective multiview structure and motion from element-wise factorization. PAMI, 35(9):2238–2251, 2013.
[6] M. Fazel, H. Hindi, and S. Boyd. A rank minimization heuristic with application to minimum order system approximation. In Proceedings of the American Control Conference, pages 4734–4739, 2001.
[7] A. Fitzgibbon. Simultaneous linear estimation of multiple view geometry and lens distortion. In CVPR, pages 125–132, 2001.
[8] C. Geyer and K. Daniilidis. Structure and motion from uncalibrated catadioptric views. In CVPR, pages 279–286, 2001 .
[9] R. Hartley and S. B. Kang. Parameter-free radial distortion correction with center of distortion estimation. PAMI, 29(8): 1309–1321, 2007.
[10] R. Hartley and A. Zisserman. Multiple View Geometry in Computer Vision. Cambridge University Press, Second edition, 2004.
[11] J.-H. Kim, H. Li, and R. Hartley. Motion estimation for nonoverlapping multicamera rigs: Linear algebraic and L-infinity geometric solutions. PAMI, 32(6): 1044–1059, 2010.
[12] M. Lhuillier. Automatic scene structure and camera motion using a catadioptric system. CVIU, 109(2): 186 203, 2008.
[13] H. Li, R. Hartley, and J.-H. Kim. A linear approach to motion estimation using generalized camera models. In CVPR, pages 1–8, 2008.
[14] Z. Lin, M. Chen, and Y. Ma. The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted Low-Rank Matrices. ArXiv e-prints, Sept. 2010.
[15] R. Liu, Z. Lin, F. De la Torre, and Z. Su. Fixed-rank representation for unsupervised visual learning. In CVPR, pages 598–605, 2012.
[16] B. Miˇ cuˇ s ı´k and T. Pajdla. Autocalibration 3d reconstruction with non-central catadioptric cameras. In CVPR, pages 58–65, 2004.
[17] B. Miˇ cuˇ s ı´k and T. Pajdla. Structure from motion with wide circular field of view cameras. PAMI, 28(7): 1135–1 149, 2006.
[18] J. Oliensis and R. Hartley. Iterative extensions of the Sturm/Triggs algorithm: Convergence and nonconvergence. PAMI, 29(12):2217– 2233, 2007.
[19] R. Pless. Using many cameras as one. In CVPR, 2003.
[20] S. Ramalingam, P. Sturm, and E. Boyer. A factorization based selfcalibration for radially symmetric cameras. In 3DPVT, pages 480– 487, 2006.
[21] S. Ramalingam, P. Sturm, and S. Lodha. Theory and calibration for –
[22]
[23]
[24]
[25]
[26]
[27] axial cameras. In ACCV, pages 704–713. 2006. P. Sturm. Multi-view geometry for general camera models. In CVPR, pages 206–212, 2005. J.-P. Tardif, P. Sturm, and S. Roy. Self-calibration of a general radially symmetric distortion model. In ECCV, pages 186–199. 2006. J.-P. Tardif, P. Sturm, and S. Roy. Plane-based self-calibration of radial distortion. In ICCV, pages 1–8, 2007. S. Thirthala and M. Pollefeys. Radial multi-focal tensors. Int J Comput Vis, 96(2): 195–21 1, 2012. K. Toh, M. Todd, and R. Tutuncu. SDPT3 a Matlab software package for semidefinite programming. Optimization Methods and Software, 11:545–581, 1999. B. Triggs. Factorization methods for projective structure and motion. In CVPR, pages 845–851, 1996. — 11990033