Abstract
This paper presents a class of minimal solutions for the 3D-to-3D registration problem in which the sensor data are 3D points and the corresponding object data are 3D planes. In order to compute the 6 degrees-of-freedom transformation between the sensor and the object, we need at least six points on three or more planes. We systematically investigate and develop pose estimation algorithms for several configurations, including all minimal configurations, that arise from the distribution of points on planes. The degenerate configurations are also identified. We point out that many existing and unsolved 2D-to-3D and 3D-to-3D pose estimation algorithms involving points, lines, and planes can be transformed into the problem of registering points to planes. In addition to simulations, we also demonstrate the algorithm’s effectiveness in two real-world applications: registration of a robotic arm with an object using a contact sensor, and registration of 3D point clouds that were obtained using multi-view reconstruction of planar city models.
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Olsson, C., Kahl, F., Oskarsson, M.: The registration problem revisited: Optimal solutions from points, lines and planes. In: CVPR, vol. 1, pp. 1206–1213 (2006)
Besl, P., McKay, N.: A method for registration of 3D shapes. PAMI (1992)
Fitzgibbon, A.: Robust registration of 2d and 3d point sets. In: Image and Vision Computing (2003)
Chen, H.: Pose determination from line-to-plane correspondences: Existence condition and closed-form solutions. PAMI 13, 530–541 (1991)
Grimson, W., Lozano-Prez, T.: Model-based recognition and localization from sparse range or tactile data. MIT AI Lab, A.I. Memo 738 (1983)
Horn, B.: Closed-form solution of absolute orientation using unit quaternions. Journal of the Optical Society A 4, 629–642 (1987)
Li, H., Hartley, R.: The 3D-3D registration problem revisited. In: ICCV, pp. 1–8 (2007)
Enqvist, O., Josephson, K., Kahl, F.: Optimal correspondences from pairwise constraints. In: ICCV (2009)
Tu, P., Saxena, T., Hartley, R.: Recognizing objects using color-annotated adjacency graphs. In: Forsyth, D., Mundy, J.L., Di Gesú, V., Cipolla, R. (eds.) Shape, Contour, and Grouping 1999. LNCS, vol. 1681, p. 246. Springer, Heidelberg (1999)
Chen, Y., Medioni, G.: Object modeling by registration of multiple range images. In: ICRA, vol. 3, pp. 2724–2729 (1991)
Kukelova, Z., Pajdla, T.: A minimal solution to the autocalibration of radial distortion. In: CVPR (2007)
Gao, X., Hou, X., Tang, J., Cheng, H.: Complete solution classification for the perspective-three-point problem. PAMI 25, 930–943 (2003)
Stewenius, H., Nister, D., Kahl, F., Schaffalitzky, F.: A minimal solution for relative pose with unknown focal length. In: CVPR (2005)
Stewenius, H., Nister, D., Oskarsson, M., Astrom, K.: Solutions to minimal generalized relative pose problems. In: OMNIVIS (2005)
Geyer, C., Stewenius, H.: A nine-point algorithm for estimating para-catadioptric fundamental matrices. In: CVPR (2007)
Li, H., Hartley, R.: A non-iterative method for correcting lens distortion from nine-point correspondenses. In: OMNIVIS (2005)
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)
Dhome, M., Richetin, M., Lapresté, J.T., Rives, G.: Determination of the attitude of 3-D objects from a single perspective view. PAMI 11, 1265–1278 (1989)
Kukelova, Z., Bujnak, M., Pajdla, T.: Automatic generator of minimal problem solvers. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part III. LNCS, vol. 5304, pp. 302–315. Springer, Heidelberg (2008)
Nistér, D.: A minimal solution to the generalized 3-point pose problem. In: CVPR (2004)
Haralick, R., Lee, C., Ottenberg, K., Nolle, M.: Review and analysis of solutions of the three point perspective pose estimation problem. IJCV (1994)
Furukawa, Y., Ponce, J.: Accurate, dense, and robust multi-view stereopsis. PAMI (2009)
Furukawa, Y., Ponce, J.: Patch-based multi-view stereo software (2000), http://grail.cs.washington.edu/software/pmvs
Ramalingam, S., Lodha, S.: Adaptive enhancement of 3d scenes using hierarchical registration of texture-mapped 3d models. In: 3DIM (2003)
Rusinkiewicz, S., Levoy, M.: Efficient variants of the icp algorithm. In: 3DIM (2001)
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Ramalingam, S., Taguchi, Y., Marks, T.K., Tuzel, O. (2010). P2Π: A Minimal Solution for Registration of 3D Points to 3D Planes. In: Daniilidis, K., Maragos, P., Paragios, N. (eds) Computer Vision – ECCV 2010. ECCV 2010. Lecture Notes in Computer Science, vol 6315. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15555-0_32
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DOI: https://doi.org/10.1007/978-3-642-15555-0_32
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