Abstract
Robot self-localization using a hemispherical camera system can be done without correspondences. We present a view-based approach using view descriptors, which enables us to efficiently compare the image signal taken at different locations. A compact representation of the image signal can be computed using Spherical Harmonics as orthonormal basis functions defined on the sphere. This is particularly useful because rotations between two representations can be found easily. Compact view descriptors stored in a database enable us to compute a likelihood for the current view corresponding to a particular position and orientation in the map.
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References
Blaer, P., Allen, P.: Topological mobile robot localization using fast vision techniques. In: International Conference on Robotics and Automation, vol. 1, May 2002, pp. 1031–1036 (2002)
Burel, G., Henoco, H.: Determination of the orientation of 3D objects using Spherical Harmonics. Graph. Models Image Process 57(5), 400–408 (1995)
Driscoll, J.R., Healy Jr., D.M.: Computing Fourier transforms and convolutions on the 2-sphere. Adv. Appl. Math. 15(2), 202–250 (1994)
The Blender Foundation. Blender (2007), http://www.blender.org
Gonzalez-Barbosa, J.-J., Lacroix, S.: Rover localization in natural environments by indexing panoramic images. In: Proceedings of the ICRA 2002 IEEE International Conference on Robotics and Automation, pp. 1365–1370. IEEE, Los Alamitos (2002)
Groemer, H.: Geometric Applications of Fourier Series and Spherical Harmonics. In: Encyclopedia of Mathematics and Its Applications, Cambridge Univ. Press (1996)
Healy Jr., D.M., Rockmore, D.N., Kostelec, P.J., Moore, S.: FFTs for the 2-sphere – improvements and variations. Journal of Fourier Analysis and Applications 9(4), 341–385 (2003)
Jogan, M., Leonardis, A.: Robust localization using an omnidirectional appearance-based subspace model of environment. Robotics and Autonomous Systems 45, 57–72 (2003)
Kazhdan, M., Funkhouser, T., Rusinkiewicz, S.: Rotation invariant Spherical Harmonic representation of 3D shape descriptors. In: Kobbelt, L., Schröder, P., Hoppe, H. (eds.) Eurographics Symposium on Geometry Processing (June 2003)
Kovacs, J.A., Wriggers, W.: Fast rotational matching. Acta Crystallographica Section D 58(8), 1282–1286 (2002)
Kröse, B., Vlassis, N., Bunschoten, R., Motomura, Y.: A probabilistic model for appearance-based robot localization. Image and Vision Computing 19(6), 381–391 (2001)
Kudlicki, A., Rowicka, M., Gilski, M., Otwinowski, Z.: An efficient routine for computing symmetric real Spherical Harmonics for high orders of expansion. Journal of Applied Crystallography 39, 501–504 (2005)
Labbani-Igbida, O., Charron, C., Mouaddib, E.M.: Extraction of Haar integral features on omnidirectional images: Application to local and global localization. In: DAGM-Symposium, pp. 334–343 (2006)
Levin, A., Szeliski, R.: Visual odometry and map correlation. In: IEEE Conf. on Comp. Vision and Pattern Recognition, June 2004, vol. I, pp. 611–618. IEEE Computer Society Press, Los Alamitos (2004)
Makadia, A., Daniilidis, K.: Direct 3D-rotation estimation from spherical images via a generalized shift theorem. In: IEEE Comp. Society Conference on Computer Vision and Pattern Recognition (CVPR 2003), vol. 2, pp. 217–224 (2003)
Makadia, A., Daniilidis, K.: Rotation recovery from spherical images without correspondences. IEEE Transactions on Pattern Analysis and Machine Intelligence 28(7), 1170–1175 (2006)
Makadia, A., Sorgi, L., Daniilidis, K.: Rotation estimation from spherical images. In: Proceedings ICPR 2004, vol. 3 (2004)
Menegatti, E., Maeda, T., Ishiguro, H.: Image-based memory for robot navigation using properties of the omnidirectional images (2004)
Menegatti, E., Zoccarato, M., Pagello, E., Ishiguro, H.: Hierarchical image-based localisation for mobile robots with monte-carlo localisation. In: Proceedings ECMR 2003, Warsaw, Poland, September 2003, pp. 13–20 (2003)
Oliver, N., Rosario, B., Pentland, A.: A bayesian computer vision system for modeling human interaction. In: Proceedings ICVS 1999, pp. 255–272 (1999)
Pajdla, T., Hlavac, V.: Zero phase representation of panoramic images for image based localization. In: Comp. Analysis of Images and Patterns, pp. 550–557 (1999)
Thrun, S., Burgard, W., Fox, D.: Probabilistic Robotics. The MIT Press, Cambridge (2005)
Weisstein, E.W.: Legendre Polynomial. A Wolfram Web Resource (2007), http://mathworld.wolfram.com/LegendrePolynomial.html
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Friedrich, H., Dederscheck, D., Krajsek, K., Mester, R. (2007). View-Based Robot Localization Using Spherical Harmonics: Concept and First Experimental Results. In: Hamprecht, F.A., Schnörr, C., Jähne, B. (eds) Pattern Recognition. DAGM 2007. Lecture Notes in Computer Science, vol 4713. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74936-3_3
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DOI: https://doi.org/10.1007/978-3-540-74936-3_3
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