This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
A 3D Shape Constraint on Video
June 2006 (vol. 28 no. 6)
pp. 1018-1023
We propose to combine the information from multiple motion fields by enforcing a constraint on the surface normals (3D shape) of the scene in view. The fact that the shape vectors in the different views are related only by rotation can be formulated as a rank = 3 constraint. This constraint is implemented in an algorithm which solves 3D motion and structure estimation as a practical constrained minimization. Experiments demonstrate its usefulness as a tool in structure from motion providing very accurate estimates of 3D motion.

[1] C. Baillard and A. Zisserman, “Automatic Reconstruction of Piecewise Planar Models from Multiple Views,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 559-565, 1999.
[2] M.J. Black, “Combining Intensity and Motion for Incremental Segmentation and Tracking over Long Image Sequences,” Proc. European Conf. Computer Vision, pp. 485-493, 1992.
[3] M.J. Black and P. Anandan, “Robust Dynamic Motion Estimation over Time,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 296-302, 1991.
[4] T. Brodsky, C. Fermüller, and Y. Aloimonos, “Structure from Motion: Beyond the Epipolar Constraint,” Int'l J. Computer Vision, vol. 37, pp. 231-258, 2000.
[5] S. Carlson and D. Weinshall, “Dual Computation of Projective Shape and Camera Positions from Multiple Images,” Int'l J. Computer Vision, vol. 27, no. 3, pp. 227-241, 1998.
[6] L. Cheong, C. Fermüller, and Y. Aloimonos, “Effects of Errors in the Viewing Geometry on Shape Estimation,” Computer Vision and Image Understanding, vol. 71, pp. 356-372, 1998.
[7] K. Daniilidis and H.-H. Nagel, “Analytical Results on Error Sensitivity of Motion Estimation from Two Views,” Image and Vision Computing, vol. 8, pp. 297-303, 1990.
[8] A. Dick, P. Torr, and R. Cipolla, “Automatic 3D Modelling of Architecture,” Proc. British Machine Vision Conf., pp. 372-381, 2000.
[9] O.D. Faugeras and T. Papadopoulo, “A Nonlinear Method for Estimating the Projective Geometry of 3 Views,” Proc. Int'l Conf. Computer Vision, pp. 477-484, 1998.
[10] C. Fermüller and Y. Aloimonos, “Observability of 3D Motion,” Int'l J. Computer Vision, vol. 37, pp. 43-63, 2000.
[11] D. Forsyth, S. Ioffe, and J. Haddon, “Bayesian Structure from Motion,” Proc. European Conf. Computer Vision, pp. 660-665, 1999.
[12] D.J. Heeger and A.D. Jepson, “Subspace Methods for Recovering Rigid Motion I: Algorithm and Implementation,” Int'l J. Computer Vision, vol. 7, pp. 95-117, 1992.
[13] S.J. Maybank, “Algorithm for Analysing Optical Flow Based on the Least-Squares Method,” Image and Vision Computing, vol. 4, pp. 38-42, 1986.
[14] J. Oliensis, “A Multi-Frame Structure-from-Motion Algorithm under Perspective Projection,” Int'l J. Computer Vision, vol. 34, no. 2, pp. 163-192, 1999.
[15] E. Polak, Optimization: Algorithm and Consistent Approximation. Springer, 1996.
[16] G. Qian and R. Chellappa, “Structure from Motion Using Sequential Monte Carlo Methods,” Int'l J. Computer Vision, vol. 59, pp. 5-31, 2004.
[17] A. Shashua and S. Avidan, “The Rank Constraint in Multiple ($>=3$ ) View Geometry,” Proc. European Conf. Computer Vision (ECCV), pp. 196-206, 1996.
[18] A. Shashua and M. Werman, “On the Trilinear Tensor of Three Perspective Views and Its Underlying Geometry,” Proc. Int'l Conf. Computer Vision, 1995.
[19] M.E. Spetsakis and J. Aloimonos, “A Unified Theory of Structure from Motion,” Proc. DARPA Image Understanding Workshop, pp. 271-283, 1990.
[20] B. Triggs, P. McLauchlan, R. Hartley, and A. Fitzgibbon, “Bundle Adjustment— A Modern Synthesis,” Vision Algorithms: Theory and Practice, B. Triggs, A. Zisserman, and R. Szeliski, eds., Springer Verlag, 2000.
[21] R. Vidal and J. Oliensis, “Structure from Planar Motions with Small Baselines,” Proc. European Conf. Computer Vision, vol. 2, pp. 383-398, 2002.
[22] L. Zelnik-Manor and M. Irani, “Multi-View Subspace Constraints on Homographies,” Proc. Int'l Conf. Computer Vision, 1999.
[23] L. Zelnik-Manor and M. Irani, “Multi-Frame Estimation of Planar Motion,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 22, no. 10, pp. 1105-1116, Oct. 2000.

Index Terms:
Three-dimensional motion estimation, integration of motion fields, decoupling translation from rotation, shape and rotation.
Citation:
Hui Ji, Cornelia Fermuller, "A 3D Shape Constraint on Video," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 28, no. 6, pp. 1018-1023, June 2006, doi:10.1109/TPAMI.2006.109
Usage of this product signifies your acceptance of the Terms of Use.