  Rotation equivariance has recently become a strongly desired property in the
3D deep learning community. Yet most existing methods focus on equivariance
regarding a global input rotation while ignoring the fact that rotation
symmetry has its own spatial support. Specifically, we consider the object
detection problem in 3D scenes, where an object bounding box should be
equivariant regarding the object pose, independent of the scene motion. This
suggests a new desired property we call object-level rotation equivariance. To
incorporate object-level rotation equivariance into 3D object detectors, we
need a mechanism to extract equivariant features with local object-level
spatial support while being able to model cross-object context information. To
this end, we propose Equivariant Object detection Network (EON) with a rotation
equivariance suspension design to achieve object-level equivariance. EON can be
applied to modern point cloud object detectors, such as VoteNet and PointRCNN,
enabling them to exploit object rotation symmetry in scene-scale inputs. Our
experiments on both indoor scene and autonomous driving datasets show that
significant improvements are obtained by plugging our EON design into existing
state-of-the-art 3D object detectors.
