%0 Journal Article %1 cohen2018spherical %A Cohen, Taco S. %A Geiger, Mario %A Koehler, Jonas %A Welling, Max %D 2018 %K equivariance fouriertransform rotationinvariant shrec17 so3 sphericalcnns %T Spherical CNNs %U http://arxiv.org/abs/1801.10130 %X 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 blocks for constructing spherical CNNs. We propose a definition for the spherical cross-correlation that is both expressive and rotation-equivariant. The spherical correlation satisfies a generalized Fourier theorem, which allows us to compute it efficiently using a generalized (non-commutative) Fast Fourier Transform (FFT) algorithm. We demonstrate the computational efficiency, numerical accuracy, and effectiveness of spherical CNNs applied to 3D model recognition and atomization energy regression.

@article{cohen2018spherical, 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 blocks for constructing spherical CNNs. We propose a definition for the spherical cross-correlation that is both expressive and rotation-equivariant. The spherical correlation satisfies a generalized Fourier theorem, which allows us to compute it efficiently using a generalized (non-commutative) Fast Fourier Transform (FFT) algorithm. We demonstrate the computational efficiency, numerical accuracy, and effectiveness of spherical CNNs applied to 3D model recognition and atomization energy regression.}, added-at = {2018-12-18T10:03:12.000+0100}, author = {Cohen, Taco S. and Geiger, Mario and Koehler, Jonas and Welling, Max}, biburl = {https://www.bibsonomy.org/bibtex/23b313f82ab3767b2bb588c24b0fd8385/rspezialetti}, description = {1801.10130.pdf}, interhash = {860a122cff5cbe74be7a13c94ac4563d}, intrahash = {3b313f82ab3767b2bb588c24b0fd8385}, keywords = {equivariance fouriertransform rotationinvariant shrec17 so3 sphericalcnns}, note = {cite arxiv:1801.10130Comment: Proceedings of the 6th International Conference on Learning Representations (ICLR), 2018}, timestamp = {2018-12-18T10:03:12.000+0100}, title = {Spherical CNNs}, url = {http://arxiv.org/abs/1801.10130}, year = 2018 }