Abstract
Estimating planar projective transform (homography) from a pair of images is a classical problem in computer vision. In this paper, we propose a novel algorithm for direct registering two point sets in \(\mathbb R^2\) using projective transform without using intensity values. In this very general context, there is no easily established correspondences that can be used to estimate the projective transform, and most of the existing techniques become either inadequate or inappropriate. While the planar projective transforms form an eight-dimensional Lie group, we show that for registering 2D point sets, the search space for the homographies can be effectively reduced to a three-dimensional space. To further improve on the running time without significantly reducing the accuracy of the registration, we propose a matching cost function constructed using local polynomial moments of the point sets and a coarse to fine approach. The resulting registration algorithm has linear time complexity with respect to the number of input points. We have validated the algorithm using points sets collected from real images. Preliminary experimental results are encouraging and they show that the proposed method is both efficient and accurate.
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References
Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision, 2nd edn. Cambridge University Press, Cambridge (2003)
Lowe, D.: Distinctive image features from scale-invariant keypoints. Int. J. Computer Vision 60, 91–110 (2004)
Nemeth, J., Domokos, C., Kato, Z.: Recovering planar homographies between 2d shapes. In: Proc. Int. Conf. on Computer Vision, pp. 889–892 (2009)
Fischler, M., Bolles, R.: Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography. Communications of the ACM 24, 381–395 (1981)
van Gool, L., Moons, T., Pauwels, E., Oosterlinck, A.: Vision and Lies approach to invariance. Image and Vision Computing 13, 259–277 (1995)
Flusser, J., Suk, T.: Projective moment invariants. IEEE Transactions on Pattern Analysis and Machine Intelligence 26, 1364–1367 (2004)
Domokos, C., Kato, Z., Francos, J.M.: Parametric estimation of affine deformations of binary images. In: Proc. of Int. Conf. on Acoustics, Speech, and Signal Processing, pp. 889–892 (2008)
Baird, H.: Model-based image matching using location. MIT Press, Cambridge (1984)
Besl, P., Jain, R.: Three dimensional object recognition. ACM Computing Surveys 17, 75–145 (1985)
Grimson, E.: Object recognition by computer: The role of geometric constraints. MIT Press, Cambridge (1990)
Hinton, G., Williams, C., Revow, M.: Adaptive elastic models for hand-printed character recognition. In: Advances in Neural Information Systems, pp. 512–519 (1992)
Huttenlocher, D., Klanderman, G., Rucklidge, W.: Comparing images using the Hausdorff distance. IEEE Transactions on Pattern Analysis and Machine Intelligence 15, 850–863 (1993)
Feldmar, J., Ayache, N.: Rigid, affine and locally affine registration of free-form surfaces. Int. J. Computer Vision 18, 99–119 (1996)
Metaxas, D., Koh, E., Badler, N.: Multi-level shape representation using global deformation and locally adaptive finite elements. Int. J. Computer Vision 25, 49–61 (1997)
Hofmann, T., Buhmann, J.: Pairwise data clustering by deterministic annealing. IEEE Transactions on Pattern Analysis and Machine Intelligence 19, 1–14 (1997)
Cross, A., Hancock, E.: Graph matching with a dual-step EM algorithm. IEEE Transactions on Pattern Analysis and Machine Intelligence 20, 1236–1253 (1998)
Gold, S., Rangarajan, A., Liu, C., Pappu, S., Mjolsness, E.: New algorithms for 2d and 3d point matching: pose estimation and correspondence. Pattern Recognition 31, 1019–1031 (1998)
Chui, H., Rangarajan, A.: A new point matching algorithm for non-rigid registration. Computer Vision and Image Understanding 89, 114–141 (2003)
Cao, Y., Miller, M., Winlow, R., Younes, L.: Large deformation diffeomorphic metric mapping of vector fields. IEEE Trans. on Med. Img. 24, 1216–1230 (2005)
Ho, J., Peter, A., Rangarajan, A., Yang, M.H.: An algebraic approach to affine registration of point sets. In: Proc. Int. Conf. on Computer Vision, pp. 1335–1340 (2009)
Huttenlocher, D., Klanderman, G., Rucklidge, W.: Comparing images using the Hausdorff distance. IEEE Transactions on Pattern Analysis and Machine Intelligence, 850–863 (1993)
Ridler, T., Calvard, S.: Picture thresholding using an iterative selection method. SMC 8, 629–632 (1978)
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© 2011 Springer-Verlag Berlin Heidelberg
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Chi, YT., Ho, J., Yang, MH. (2011). A Direct Method for Estimating Planar Projective Transform. In: Kimmel, R., Klette, R., Sugimoto, A. (eds) Computer Vision – ACCV 2010. ACCV 2010. Lecture Notes in Computer Science, vol 6493. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19309-5_21
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DOI: https://doi.org/10.1007/978-3-642-19309-5_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-19308-8
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