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Orientation estimation is the core to a variety of vision and robotics taskssuch as camera and object pose estimation. Deep learning has offered a way todevelop image-based orientation estimators; however, such estimators oftenrequire training on a large labeled dataset, which can be time-intensive tocollect. In this work, we explore whether self-supervised learning fromunlabeled data can be used to alleviate this issue. Specifically, we assumeaccess to estimates of the relative orientation between neighboring poses, suchthat can be obtained via a local alignment method. While self-supervisedlearning has been used successfully for translational object keypoints, in thiswork, we show that naively applying relative supervision to the rotationalgroup $SO(3)$ will often fail to converge due to the non-convexity of therotational space. To tackle this challenge, we propose a new algorithm forself-supervised orientation estimation which utilizes Modified RodriguesParameters to stereographically project the closed manifold of $SO(3)$ to theopen manifold of $\mathbb{R}^{3}$, allowing the optimization to be done in anopen Euclidean space. We empirically validate the benefits of the proposedalgorithm for rotational averaging problem in two settings: (1) directoptimization on rotation parameters, and (2) optimization of parameters of aconvolutional neural network that predicts object orientations from images. Inboth settings, we demonstrate that our proposed algorithm is able to convergeto a consistent relative orientation frame much faster than algorithms thatpurely operate in the $SO(3)$ space. Additional information can be found athttps://sites.google.com/view/deep-projective-rotation/home .

Deep Projective Rotation Estimation through Relative Supervision