publication . Preprint . 2018

Spherical CNNs

Cohen, Taco S.; Geiger, Mario; Koehler, Jonas; Welling, Max;
Open Access English
  • Published: 30 Jan 2018
Abstract
Convolutional Neural Networks (CNNs) have become the method of choice for learning problems involving 2D planar images. However, a number of problems of recent interest have created a demand for models that can analyze spherical images. Examples include omnidirectional vision for drones, robots, and autonomous cars, molecular regression problems, and global weather and climate modelling. A naive application of convolutional networks to a planar projection of the spherical signal is destined to fail, because the space-varying distortions introduced by such a projection will make translational weight sharing ineffective. In this paper we introduce the building blo...
Subjects
ACM Computing Classification System: ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION
free text keywords: Computer Science - Machine Learning, Statistics - Machine Learning
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38 references, page 1 of 3

L. C. Blum and J.-L. Reymond. 970 million druglike small molecules for virtual screening in the chemical universe database GDB-13. J. Am. Chem. Soc., 131:8732, 2009.

W. Boomsma and J. Frellsen. Spherical convolutions and their application in molecular modelling. In I Guyon, U V Luxburg, S Bengio, H Wallach, R Fergus, S Vishwanathan, and R Garnett, editors, Advances in Neural Information Processing Systems 30, pages 3436-3446. Curran Associates, Inc., 2017. [OpenAIRE]

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G.S. Chirikjian and A.B. Kyatkin. Engineering Applications of Noncommutative Harmonic Analysis. CRC Press, 1 edition, may 2001. ISBN 9781420041767. [OpenAIRE]

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T.S. Cohen and M. Welling. Steerable CNNs. In ICLR, 2017.

T.S. Cohen, M. Geiger, J. Koehler, and M. Welling. Convolutional networks for spherical signals. In ICML Workshop on Principled Approaches to Deep Learning, 2017.

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J.B. Drake, P.H. Worley, and E.F. D'Azevedo. Algorithm 888: Spherical harmonic transform algorithms. ACM Trans. Math. Softw., 35(3):23:1-23:23, 2008. doi: 10.1145/1391989.1404581.

J.R. Driscoll and D.M. Healy. Computing Fourier transforms and convolutions on the 2-sphere. Advances in applied mathematics, 1994.

G.B. Folland. A Course in Abstract Harmonic Analysis. CRC Press, 1995.

R. Gens and P. Domingos. Deep Symmetry Networks. In Advances in Neural Information Processing Systems (NIPS), 2014.

B. Gutman, Y. Wang, T. Chan, P.M. Thompson, and others. Shape registration with spherical cross correlation. 2nd MICCAI workshop, 2008.

N. Guttenberg, N. Virgo, O. Witkowski, H. Aoki, and R. Kanai. Permutation-equivariant neural networks applied to dynamics prediction. 2016. [OpenAIRE]

38 references, page 1 of 3
Related research
Abstract
Convolutional Neural Networks (CNNs) have become the method of choice for learning problems involving 2D planar images. However, a number of problems of recent interest have created a demand for models that can analyze spherical images. Examples include omnidirectional vision for drones, robots, and autonomous cars, molecular regression problems, and global weather and climate modelling. A naive application of convolutional networks to a planar projection of the spherical signal is destined to fail, because the space-varying distortions introduced by such a projection will make translational weight sharing ineffective. In this paper we introduce the building blo...
Subjects
ACM Computing Classification System: ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION
free text keywords: Computer Science - Machine Learning, Statistics - Machine Learning
Download from
38 references, page 1 of 3

L. C. Blum and J.-L. Reymond. 970 million druglike small molecules for virtual screening in the chemical universe database GDB-13. J. Am. Chem. Soc., 131:8732, 2009.

W. Boomsma and J. Frellsen. Spherical convolutions and their application in molecular modelling. In I Guyon, U V Luxburg, S Bengio, H Wallach, R Fergus, S Vishwanathan, and R Garnett, editors, Advances in Neural Information Processing Systems 30, pages 3436-3446. Curran Associates, Inc., 2017. [OpenAIRE]

A.X. Chang, T. Funkhouser, L. Guibas, P. Hanrahan, Q. Huang, Z. Li, S. Savarese, M. Savva, S. Song, H. Su, et al. Shapenet: An information-rich 3d model repository. arXiv preprint arXiv:1512.03012, 2015. [OpenAIRE]

G.S. Chirikjian and A.B. Kyatkin. Engineering Applications of Noncommutative Harmonic Analysis. CRC Press, 1 edition, may 2001. ISBN 9781420041767. [OpenAIRE]

T.S. Cohen and M. Welling. Group equivariant convolutional networks. In Proceedings of The 33rd International Conference on Machine Learning (ICML), volume 48, pages 2990-2999, 2016.

T.S. Cohen and M. Welling. Steerable CNNs. In ICLR, 2017.

T.S. Cohen, M. Geiger, J. Koehler, and M. Welling. Convolutional networks for spherical signals. In ICML Workshop on Principled Approaches to Deep Learning, 2017.

S. Dieleman, K. W. Willett, and J. Dambre. Rotation-invariant convolutional neural networks for galaxy morphology prediction. Monthly Notices of the Royal Astronomical Society, 450(2), 2015.

S. Dieleman, J. De Fauw, and K. Kavukcuoglu. Exploiting Cyclic Symmetry in Convolutional Neural Networks. In International Conference on Machine Learning (ICML), 2016. [OpenAIRE]

J.B. Drake, P.H. Worley, and E.F. D'Azevedo. Algorithm 888: Spherical harmonic transform algorithms. ACM Trans. Math. Softw., 35(3):23:1-23:23, 2008. doi: 10.1145/1391989.1404581.

J.R. Driscoll and D.M. Healy. Computing Fourier transforms and convolutions on the 2-sphere. Advances in applied mathematics, 1994.

G.B. Folland. A Course in Abstract Harmonic Analysis. CRC Press, 1995.

R. Gens and P. Domingos. Deep Symmetry Networks. In Advances in Neural Information Processing Systems (NIPS), 2014.

B. Gutman, Y. Wang, T. Chan, P.M. Thompson, and others. Shape registration with spherical cross correlation. 2nd MICCAI workshop, 2008.

N. Guttenberg, N. Virgo, O. Witkowski, H. Aoki, and R. Kanai. Permutation-equivariant neural networks applied to dynamics prediction. 2016. [OpenAIRE]

38 references, page 1 of 3
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