  Modern neural networks use building blocks such as convolutions that are
equivariant to arbitrary 2D translations. However, these vanilla blocks are not
equivariant to arbitrary 3D translations in the projective manifold. Even then,
all monocular 3D detectors use vanilla blocks to obtain the 3D coordinates, a
task for which the vanilla blocks are not designed for. This paper takes the
first step towards convolutions equivariant to arbitrary 3D translations in the
projective manifold. Since the depth is the hardest to estimate for monocular
detection, this paper proposes Depth EquiVarIAnt NeTwork (DEVIANT) built with
existing scale equivariant steerable blocks. As a result, DEVIANT is
equivariant to the depth translations in the projective manifold whereas
vanilla networks are not. The additional depth equivariance forces the DEVIANT
to learn consistent depth estimates, and therefore, DEVIANT achieves
state-of-the-art monocular 3D detection results on KITTI and Waymo datasets in
the image-only category and performs competitively to methods using extra
information. Moreover, DEVIANT works better than vanilla networks in
cross-dataset evaluation. Code and models at
https://github.com/abhi1kumar/DEVIANT

Computer Vision and Pattern Recognition;Machine Learning