Rigidity Preserving Image Transformations and Equivariance in Perspective

We characterize the class of image plane transformations which realize rigid camera motions and call these ‘rigidity preserving’. It turns out that only rigidity preserving are homographies corresponding to rotating camera. In particular, 2D translations pinhole images not preserving. Hence, when using CNNs for 3D inference tasks, it can be beneficial modify inductive bias from equivariance w.r.t. rotational homographies. investigate how with respect approximated in CNNs, test our ideas on 6D object pose estimation. Experimentally, we improve a competitive baseline.