Abstract
In this paper we consider the problem of recovering 3D Euclidean structure from multi-frame point correspondence data in image sequences under perspective projection. Existing approaches rely either only on geometrical constraints reflecting the rigid nature of the object, or exploit temporal information by recasting the problem into a nonlinear filtering form. In contrast, here we introduce a new constraint that implicitly exploits the temporal ordering of the frames, leading to a provably correct algorithm to find Euclidean structure (up to a single scaling factor) without the need to alternate between projective depth and motion estimation, estimate the Fundamental matrices or assume a camera motion model. Finally, the proposed approach does not require an accurate calibration of the camera. The accuracy of the algorithm is illustrated using several examples involving both synthetic and real data.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision. Cambridge Univeristy Press, Cambridge (2003)
Faugeras, O.D., Luong, Q.T., Papadopoulo, T.: The Geometry of Multiple Images. MIT Press, Cambridge (2001)
Tomasi, C., Kanade, T.: Shape and motion from image streams under orthography: a factorization method. International Journal of Computer Vision 9, 137–154 (1992)
Morita, T., Kanade, T.: A paraperspective factorization method for recovering shape and motion from image sequences. IEEE Trans. on PAMI 19, 858–867 (1997)
Poelman, C.J., Kanade, T.: A paraperspective factorization method for shape and motion recovery. IEEE Transactions on PAMI 19, 206–218 (1997)
Sturm, P., Triggs, B.: A factorization based algorithm for multi-image projective structure and motion. In: Buxton, B.F., Cipolla, R. (eds.) ECCV 1996. LNCS, vol. 1065, pp. 709–720. Springer, Heidelberg (1996)
Triggs, B.: Factorization methods for projective structure and motion. In: IEEE CVPR (1996)
Sparr, G.: Simultaneous reconstruction of scene structure and camera locations from uncalibrated image sequences. In: Int. Conf. on Pattern Recognition (1996)
Chen, G., Medioni, G.: Efficient iterative solutions to m-view projective reconstruction problem. In: IEEE CVPR, vol. 2, pp. 55–61 (1999)
Mahamud, S., Hebert, M.: Iterative projective reconstruction from multiple views. In: IEEE CVPR, vol. 2, pp. 430–437 (2000)
Hung, Y., Tang, W.: Projective reconstruction from multiple views with minimization of 2d reprojection error. International Journal of Computer Vision 66, 305–317 (2006)
Mohr, R., Veillon, F., Quan, L.: Relative 3d reconstruction using multiple uncalibrated images. In: IEEE CVPR, pp. 543–548 (1993)
Hartley, R.: Euclidean reconstruction from uncalibrated views. In: Mundy, J.L., Zisserman, A., Forsyth, D. (eds.) AICV 1993. LNCS, vol. 825, pp. 237–256. Springer, Heidelberg (1994)
Morris, D., Kanatani, K., Kanade, T.: Euclidean reconstruction from uncalibrated views. In: Triggs, B., Zisserman, A., Szeliski, R. (eds.) ICCV-WS 1999. LNCS, vol. 1883, pp. 298–375. Springer, Heidelberg (2000)
Shum, H.Y., Ke, Q., Zhang, Z.: Efficient bundle adjustment with virtual key frames: A hierarchical approach to multi-frame structure from motion. In: IEEE CVPR (1999)
Triggs, B., McLauchlan, P., Hartley, R., Fitzgibbon, A.: Bundle adjustment-a modern synthesis. In: Triggs, B., Zisserman, A., Szeliski, R. (eds.) ICCV-WS 1999. LNCS, vol. 1883, pp. 298–375. Springer, Heidelberg (2000)
Bartoli, A., Sturm, P.: Three new algorithms for projective bundle adjustment with minimum parameters. Technical Report 4236, INRIA (2001)
Oliensis, J.: Fast and accurate self-calibration. In: ICCV, pp. 745–752 (1996)
Mahamud, S., Hebert, M., Omori, Y., Ponce, J.: Provably convergent iterative methods for projective structure frommotion. In: IEEE CVPR, pp. 1018–1025 (2001)
Oliensis, J., Hartley, R.: Iterative extensions of the strum/triggs algorithm: convergence and nonconvergence. IEEE Trans. on PAMI 29, 2217–2233 (2007)
Davison, A.J., Reid, I.D., Molton, N.D., Stasse, O.: Monoslam: Real time single camera slam. IEEE Trans. on PAMI 29, 1052–1067 (2007)
Klein, G., Murray, D.: Parallel tracking and mapping for small AR workspaces. In: Proc. ISMAR 2007, Nara, Japan (November 2007)
Orsi, R.: LMIRank: software for rank constrained lmi problems (web page and software) (2005), http://rsise.anu.edu.au/robert/lmirank/
Fischler, M.A., Bolles, R.C.: Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. ACM Comm. 24, 381–395 (1981)
Kailath, T.: Linear Systems. Prentice-Hall, Englewood Cliffs (1980)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
1 Electronic Supplementary Material
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ayazoglu, M., Sznaier, M., Camps, O. (2010). Euclidean Structure Recovery from Motion in Perspective Image Sequences via Hankel Rank Minimization. In: Daniilidis, K., Maragos, P., Paragios, N. (eds) Computer Vision – ECCV 2010. ECCV 2010. Lecture Notes in Computer Science, vol 6312. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15552-9_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-15552-9_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15551-2
Online ISBN: 978-3-642-15552-9
eBook Packages: Computer ScienceComputer Science (R0)