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Many settings in machine learning require the selection of a rotation representation.
On the parametrization of the three-dimensional rotation group
Stuelpnagel, J · 1964
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Practical parameterization of rotations using the exponential map
Grassia, F. S · 1998
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The essential order of approximation for neural networks
Xu, Z. and Cao, F · 2004
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Simultaneous lp-approximation order for neural networks
Xu, Z.-B. and Cao, F.-L · 2005
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Constructive approximation of discontinuous functions by neural networks
Llanas, B., Lantarón, S., and Sáinz, F. J · 2008
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Rotation manifold so(3) and its tangential vectors
Mäkinen, J · 2008
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Metrics for 3d rotations: Comparison and analysis
Huynh, D. Q · 2009
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Learning 3d object orientation from images
Saxena, A., Driemeyer, J., and Ng, A. Y · 2009
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Linear and geometric algebra
Macdonald, A · 2010
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Mujoco: A physics engine for model-based control
Todorov, E., Erez, T., and Tassa, Y · 2012
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Rotation averaging
Hartley, R., Trumpf, J., Dai, Y., and Li, H · 2013
Cited alongside, same era.
Sharp minima can generalize for deep nets
Dinh, L., Pascanu, R., Bengio, S., and Bengio, Y · 2017
Cited alongside, same era.
Modified rodrigues parameters: an efficient representation of orientation in 3d vision and graphics
Terzakis, G., Lourakis, M., and Ait-Boudaoud, D · 2018
Cited alongside, same era.
PoseCNN: A convolutional neural network for 6D object pose estimation in cluttered scenes
Xiang, Y., Schmidt, T., Narayanan, V., and Fox, D · 2018
Cited alongside, same era.
Densefusion: 6d object pose estimation by iterative dense fusion
Wang, C., Xu, D., Zhu, Y., Martín-Martín, R., Lu, C., Fei-Fei, L., and Savarese, S · 2019
Cited alongside, same era.
On the continuity of rotation representations in neural networks
Deep regression on manifolds: a 3d rotation case study
Brégier, R · 2021
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Modern koopman theory for dynamical systems
Brunton, S. L., Budišić, M., Kaiser, E., and Kutz, J. N · 2022
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Projective manifold gradient layer for deep rotation regression
Chen, J., Yin, Y., Birdal, T., Chen, B., Guibas, L. J., and Wang, H · 2022
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Position information in transformers: an overview
Dufter, P., Schmitt, M., and Schütze, H · 2022
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A loss curvature perspective on training instabilities of deep learning models
Gilmer, J., Ghorbani, B., Garg, A., Kudugunta, S., Neyshabur, B., Cardoze, D., Dahl, G. E., Nado, Z., and Firat, O · 2022
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Learning rotations
Pepe, A., Lasenby, J., and Chacón, P · 2022
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Zhou, Y., Barnes, C., Lu, J., Yang, J., and Li, H · 2019
Cited alongside, same era.
An analysis of svd for deep rotation estimation
Levinson, J., Esteves, C., Chen, K., Snavely, N., Kanazawa, A., Rostamizadeh, A., and Makadia, A · 2020
Cited alongside, same era.
A smooth representation of SO(3) for deep rotation learning with uncertainty
Peretroukhin, V., Giamou, M., Rosen, D. M., Greene, W. N., Roy, N., and Kelly, J · 2020
Cited alongside, same era.
SciPy 1.0: Fundamental algorithms for scientific computing in Python
Virtanen, P., Gommers, R., Oliphant, T. E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S. J., Brett, M., Wilson, J., Millman, K. J., Mayorov, N., Nelson, A. R. J., Jones, E., Kern, R., Larson, E., Carey, C. J., Polat, İ., Feng, Y., Moore, E. W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E. A., Harris, C. R., Archibald, A. M., Ribeiro, A. H., Pedregosa, F., van Mulbregt, P., and SciPy 1.0 Contributors · 2020
Cited alongside, same era.
Approximation capabilities of neural odes and invertible residual networks
Zhang, H., Gao, X., Unterman, J., and Arodz, T · 2020
Cited alongside, same era.
URL https://marctenbosch.com/quaternions/code.htm
Bosch, M. T., 2020a
Cited in the paper.
Let’s remove quaternions from every 3d engine, 2020b
Bosch, M. T
Cited in the paper.
Loss it right: Euclidean and riemannian metrics in learning-based visual odometry
Alvarez-Tunon, O., Brodskiy, Y., and Kayacan, E · 2023
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Understanding plasticity in neural networks
Lyle, C., Zheng, Z., Nikishin, E., Pires, B. A., Pascanu, R., and Dabney, W · 2023
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Cmu graphics lab motion capture database, 2024
LLC., M · 2024
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