Abstract
In this paper, we present a method for the fast and accurate computation of the local cross-correlation of 3D vectorial data. Given spherical patches of 3D vector fields, our method computes the full cross-correlation over all possible rotations and allows an accurate estimation of the rotation offset between two patches. Our approach is based on a novel harmonic representation for 3D vector fields located on spherical surfaces which allows us to apply the convolution theorem and perform a fast correlation in the frequency domain. The theoretical advances presented in this paper can be applied to various computer vision and pattern recognition problems, such as finding corresponding points on vector fields for registration problems, key point detection on vector fields or designing local vector field features.
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References
Barrera, R., Estevez, G., Giraldo, J.: Vector spherical harmonics and their application to magnetostatic. Eur. J. Phys. 6, 287–294 (1985)
Brink, D., Satchler, G.: Angular Momentum, 2nd edn. Clarendon Press, Oxford (1968)
Fehr, J., Reisert, M., Burkhardt, H.: Fast and accurate rotation estimation on the 2-sphere without correspondences. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part II. LNCS, vol. 5303, pp. 239–251. Springer, Heidelberg (2008)
Frigo, M., Johnson, S.G.: The design and implementation of FFTW3. Proceedings of the IEEE 93(2), 216–231 (2005); special issue on ”Program Generation, Optimization, and Platform Adaptation”
Groemer, H.: Geometric Applications of Fourier Series and Spherical Harmonics. Cambridge University Press, Cambridge (1996)
Hill, E.: The theory of vector spherical harmonics. Am. J. Phys. 22, 211–214 (1954)
Kovacs, J.A., Wriggers, W.: Fast rotational matching. Acta Crystallogr (58), 1282–1286 (2002)
Makadia, A., Daniilidis, K.: Rotation recovery from spherical images without correspondences. IEEE Transactions on Pattern Analysis and Machine Intelligence 28(7) (2006)
Reisert, M., Burkhardt, H.: Efficient tensor voting with 3d tensorial harmonics. In: CVPR Workshop on Tensors, 2008, Anchorage, Alaska (2008)
Stephens, M.: Vector correlation. Biometrica 66, 41–48 (1979)
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Fehr, J., Reisert, M., Burkhardt, H. (2009). Cross-Correlation and Rotation Estimation of Local 3D Vector Field Patches. In: Bebis, G., et al. Advances in Visual Computing. ISVC 2009. Lecture Notes in Computer Science, vol 5875. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10331-5_27
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DOI: https://doi.org/10.1007/978-3-642-10331-5_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-10330-8
Online ISBN: 978-3-642-10331-5
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