Abstract
Establishing correspondence between features of a set of images has been a long-standing issue amongst the computer vision community. We propose a method that solves the multi-frame correspondence problem by imposing a rank constraint on the observed scene, i.e. rigidity is assumed. Since our algorithm is based solely on a geometrical (global) criterion, it does not suffer from issues usually associated to local methods, such as the aperture problem.
We model feature matching by introducing the assignment tensor, which allows simultaneous feature alignment for all images, thus providing a coherent solution to the calibrated multi-frame correspondence problem in a single step of linear complexity. Also, an iterative method is presented that is able to cope with the non-calibrated case. Moreover, our method is able to seamlessly reject a large number of outliers in every image, thus also handling occlusion in an integrated manner.
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 University Press, Cambridge (2000)
Nemhauser, G., Wolsey, L.: Integer and Cobinatorial Optimization. John Wiley & Sons, Chichester (1999)
Dellaert, F., et al.: Structure From Motion Without Correspondence. In: Proc. CVPR, South Carolina, USA (June 2000)
Fazel, M., Hindi, H., Boyd, S.: A Rank Minimization Heuristic with Application to Minimum Order System Approximation. In: Proc. ACC (June 2001)
Ferrari, V., Tuytelaars, T., van Gool, L.: Wide-Baseline Multiple-View Correspondences. In: Proc. ICCV (October 2003)
Heyden, A., Berthilsson, R., Sparr, G.: An iterative factorization method for projective structure and motion from image sequences. Image and Vision Computing(17) 13(1), 981–991 (1999)
Irani, M., Anandan, P.: Factorization with Uncertaint. In: Vernon, D. (ed.) ECCV 2000. LNCS, vol. 1842, pp. 539–553. Springer, Heidelberg (2000)
Kolmogorov, V., Zabih, R.: Multi-camera Scene Reconstruction via Graph Cuts. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2352, pp. 82–96. Springer, Heidelberg (2002)
Maciel, J., Costeira, J.: A Global Solution to Sparse Correspondence Problems. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(2) (February 2003)
Martinec, D., Pajdla, T.: 3D Reconstruction by Fitting Low-Rank Matrices with Data. In: Proc. CVPR (June 2005)
Oliveira, R., Costeira, J., Xavier, J.: Optimal Point Correspondence through the Use of Rank Constraints. In: Proc. CVPR, San Diego, USA (June 2005)
Roy, S., Cox, I.: A Maximum-Flow Formulation of the N-Camera Stereo Correspondence Problem. In: Proc. ICCV (January 1998)
Shafique, K., Shah, M.: A Non-Iterative Greedy Algorithm for Multi-frame Point Correspondence. In: Proc. ICCV (October 2003)
Sturm, P., Triggs, B.: A factorization based algorithm for multi-image projective structure and motion. In: Proc. ECCV, April 1996, pp. 709–720 (1996)
Tomasi, C., Kanade, T.: Shape from motion from image sreams under orthography: a factorization method. IJCV 9(2), 137–154 (1992)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Oliveira, R., Ferreira, R., Costeira, J.P. (2006). Optimal Multi-frame Correspondence with Assignment Tensors. In: Leonardis, A., Bischof, H., Pinz, A. (eds) Computer Vision – ECCV 2006. ECCV 2006. Lecture Notes in Computer Science, vol 3953. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11744078_38
Download citation
DOI: https://doi.org/10.1007/11744078_38
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-33836-9
Online ISBN: 978-3-540-33837-6
eBook Packages: Computer ScienceComputer Science (R0)