[2006.14616] An Analysis of SVD for Deep Rotation Estimationopen searchopen navigation menucontact arXivarXiv Twitter

Symmetric orthogonalization via SVD, and closely related procedures, are well-known techniques for projecting matrices onto $O(n)$ or $SO(n)$. These tools have long been used for applications in computer vision, for example optimal 3D alignment problems solved by orthogonal Procrustes, rotation averaging, or Essential matrix decomposition. Despite its utility in different settings, SVD orthogonalization as a procedure for producing rotation matrices is typically overlooked in deep learning models, where the preferences tend toward classic representations like unit quaternions, Euler angles, and axis-angle, or more recently-introduced methods. Despite the importance of 3D rotations in computer vision and robotics, a single universally effective representation is still missing. Here, we explore the viability of SVD orthogonalization for 3D rotations in neural networks. We present a theoretical analysis that shows SVD is the natural choice for projecting onto the rotation group. Our exten

7 mentions: @hillbig@slam_hub@hillbig@kiamada@_machc
Keywords: svd
Date: 2020/06/26 12:52

Referring Tweets

@hillbig NNで特殊直交群SO(n)で表される回転を推定する場合、クオータニオンやオイラー角で表現し、それを推定することが多いが、3x3の行列を出力した後SVDを経てSO(n)を推定する表現方法の方が理論的にも実用的にも精度が高い。t.co/9auIIADSeK
@slam_hub 深層学習における性質の良い回転表現を提案. 回転行列を一度9パラメータで表現し,SVDによる特殊直交化によりSO(3)空間へマップする. 深層学習タスクにおいてクォータニオンやangle-axisベクトルなどの他の回転表現より高精度に姿勢を求めることが可能. t.co/eXV1lEhjwb t.co/WVhQcNGBad
@hillbig When NNs estimate 3D rotation matrix SO(3), they often use Euler angles or quaternion representation. Actually, SVD orthogonalization (output 3x3 matrix followed by SVD and special orthogonalization) achieves better accuracy theoretically and practically. t.co/9auIIADSeK
@_machc In this new paper, we provide theoretical and empirical arguments about the best way to do deep pose regression: t.co/Bs4HgJHRqV With @kiamada, @jakelevMtl, @KefanChen7, @Jimantha, @akanazawa, and @rostamiz. t.co/hElHMGIdoX

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