FFTs on the Rotation Group

By Peter J. Kostelec, D. Rockmore. 2008

247 citations recorded by the source corpus.

Subfields: Aerospace Engineering, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

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Citations in the corpus

Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Network (2018, methodology): “The key idea in Spherical CNNs is to generalize convolutions using the machinery of noncommutative harmonic analysis: employing a type of generalized SO(3) Fourier transform [16, 17], Spherical CNNs transform the image to a sequence of matrices, and compute the spherical analog of convolution in Fou”
Spherical CNNs (2018, background): “…property of the Wigner D-functions, one can see that the Fourier coefﬁcients can be retrieved by computing the inner product with the Wigner D-functions: Fourier convolution theorems for SO(3) and § 2 can be found in Kostelec and Rockmore (2008); Makadia et al. (2007); Gutman et al. (2008).”
Correspondence-free Structure from Motion (2007, methodology): “As the parabolic mirror images only a little more than half the sphere, you can see the lower portion of the spherical image contains no information. Top Right: the spherical image as it would appear on the surface of the sphere. (2003) and Kostelec and Rockmore (2003), the angles α, γ , and φ will ”
Protein–protein docking by fast generalized Fourier transforms on 5D rotational manifolds (2016, unknown): “This is important, because the algorithm by Kostelec and Rockmore [15] can be easily extended to the SO (3) × ( SO (3) \ S 1 ) manifold.”
A fast algorithm for nonequispaced Fourier transforms on the rotation group (2009, methodology): “In contrast the authors of [16] use a slightly different rule as the authors consider βb = (2b+1))π 4B for b = 0, .”
Pointwise Rotation-Invariant Network with Adaptive Sampling and 3D Spherical Voxel Convolution (2018, methodology): “In practice, with analogy to SO (3) convolution, Spherical Voxel Convolution (SVC) can be efﬁciently computed by Fast Fourier Transform (FFT) (Kostelec and Rockmore 2008).”
Fully Automatic Registration of 3D Point Clouds (2006, methodology): “We are now armed with the necessary tools to write the correlation function (1) in terms of the Fourier transforms of the individual orientation histograms (readers are referred to the work in [18] for details of a complete derivation).”
GemNet: Universal Directional Graph Neural Networks for Molecules (2021, methodology): “We then deﬁne the set F TFNpool as all rotationally equivariant linear functions on the SO(3) group, i.e. all SO(3) convolutions [38].”