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Reasoning about 3D objects based on 2D images is challenging due tovariations in appearance caused by viewing the object from differentorientations. Tasks such as object classification are invariant to 3D rotationsand other such as pose estimation are equivariant. However, imposingequivariance as a model constraint is typically not possible with 2D imageinput because we do not have an a priori model of how the image changes underout-of-plane object rotations. The only $\mathrm{SO}(3)$-equivariant modelsthat currently exist require point cloud or voxel input rather than 2D images.In this paper, we propose a novel architecture based on icosahedral groupconvolutions that reasons in $\mathrm{SO(3)}$ by learning a projection of theinput image onto an icosahedron. The resulting model is approximatelyequivariant to rotation in $\mathrm{SO}(3)$. We apply this model to object poseestimation and shape classification tasks and find that it outperformsreasonable baselines. Project website:\url{https://dmklee.github.io/image2icosahedral}

Image to Icosahedral Projection for $\mathrm{SO}(3)$ Object Reasoning from Single-View Images