Engineering Applications of Noncommutative Harmonic Analysis: With Emphasis on Rotation and Motion Groups

By Gregory S. Chirikjian, A. Kyatkin, Ac Buckingham. 2000

335 citations recorded by the source corpus.

Subfields: Astronomy and Astrophysics, Computational Mechanics

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Citations in the corpus

SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks (2020, neutral): “where Q is an orthogonal, N×N , change-of-basis matrix [4]; each D` for ` = 0, 1, 2, .”
CubeNet: Equivariance to 3D Rotation and Translation (2018, background): “These definitions are not our contribution and can be found in textbooks such as [7], but we have tried to standardize them and simplify notation.”
Two-Dimensional Fourier Transforms in Polar Coordinates (2011, background): “(Chirikjian and Kyatkin, 2001) instead of the usual Cartesian coordinates, which is most useful when the function being transformed is naturally describable in polar coordinates.”
Pointwise Rotation-Invariant Network with Adaptive Sampling and 3D Spherical Voxel Convolution (2018, background): “; ) = Z()Y()Z( ) (13) where 2[0;2ˇ];2[0;ˇ];and 2[0;2ˇ], and Z/Y are rotations around Z/Y axes. Haar Measure of SO(3) The normalized Haar measure is dR= d 2ˇ dsin( ) 2 d 2ˇ : (14) The Haar measure [11,18] is invariant because it has the property that Z SO(3) f(R0R)dR= Z SO(3) f(R)dR; (15) for any R02”
FFTs on the Rotation Group (2008, background): “Beyond theoretical interest, the existence and implementation of an FFT for SO(3) has many potential applications [ 2 ].”
Correspondence-free Structure from Motion (2007, methodology): “Using a similar approach as seen above, we can develop a Fourier transform on the rotation group SO(3) (Chirikjian and Kyatkin, 2000).”
Explorations in Homeomorphic Variational Auto-Encoding (2018, background): “The problem of defining distributions on homogeneous spaces, including Lie groups, was investigated in (Chirikjian & Kyatkin, 2000; Chirikjian, 2010; Chirikjian & Kyatkin, 2016; Chirikjian, 2012).”
B-Spline CNNs on Lie Groups (2019, methodology): “These are specialized G-CNNs in which the kernels are expanded in circlar/spherical harmonics and computations take place using the basis coefficients only (Chirikjian & Kyatkin, 2000; Franken, 2008; Almsick, 2007; Skibbe & Reisert, 2017).”