其中I_k 代表输入数据;函数convolution代表卷积过程; P_k 代表特征图; f_{cn} 代表全连接网络; l_k 代表输出标签。它也可以被描述为: CNN(I_k) = f_{cn}(\text{convolution}(I_k)) \quad \text{(3)} \\理论上,卷积神经网络在小范围内享有旋转等变性。如(2)所示, P_k 不会因旋转而有很大变化。
We present the R otation E quivariant CO nvolutional Neural Network (RECO), a model specifically designed for pedestrian trajectory prediction using rotation equivariant convolutions. We evaluate our model on challenging real-world human trajectory forecasting datasets and show that it achieves ...
3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data We present a convolutional network that is equivariant to rigid body motions. The model uses scalar-, vector-, and tensor fields over 3D Euclidean space to represent data, and equivariant convolutions to map between suc...
Cesa, General E(2)-equivariant steerable CNNs, in: Proceedings of the Neural Information Processing Systems, 2019. Google Scholar [15] M. Finzi, S. Stanton, P. Izmailov, A.G. Wilson, Generalizing convolutional neural networks for equivariance to Lie groups on arbitrary continuous data, in: ...
CNNs on Surfaces using Rotation-Equivariant Features Update 2022If you are looking into using HSN for your own learning task, we would recommend giving DeltaConv a look. It works on point clouds as well as meshes (simply use the vertex positions) and is a lot more efficient in time and ...
Equivariant Ricci flow with surgery and applications to finite group actions on geometric 3-manifolds P, one can break up the procedure into several steps: Suppose that P decomposes as the disjoint union P = P1∪˙ P2 of G-invariant subfamilies Pi... J Dinkelbach,B Leeb - 《Geometry & ...
descriptors, we propose a position-aware convolution, which can better learn spatial information of local structures. Moreover, we also propose a feature-based hypothesis proposer. It leverages rotation-equivariant features that encode fine-grained structure orientations to generate reliable model ...
Redet: A rotation-equivariant detector for aerial object detection. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, Nashville, TN, USA, 20–25 June 2021; pp. 2786–2795. [Google Scholar] Disclaimer/Publisher’s Note: The statements, opinions and data ...
R. Berk, “A special group structure and equivariant estimation,” Ann. Math. Statist.,38, No. 5, 1436–1445 (1967). 5.R. A. Fisher, “Dispersion on a sphere,” Proc. Roy. Statist. Soc., Ser. A,217, 295–305 (1953). About this Article Title Estimation of a rotation ...
To achieve more group equivariances, rotation group equivariant convolutions(RGEC) are proposed to acquire both translation and rotation group equivariances.However, previous work paid more attention to the number of parameters and usually ignored other resource costs. In this paper, we construct our...