  Due to the inherent ill-posed nature of 2D-3D projection, monocular 3D object
detection lacks accurate depth recovery ability. Although the deep neural
network (DNN) enables monocular depth-sensing from high-level learned features,
the pixel-level cues are usually omitted due to the deep convolution mechanism.
To benefit from both the powerful feature representation in DNN and pixel-level
geometric constraints, we reformulate the monocular object depth estimation as
a progressive refinement problem and propose a joint semantic and geometric
cost volume to model the depth error. Specifically, we first leverage neural
networks to learn the object position, dimension, and dense normalized 3D
object coordinates. Based on the object depth, the dense coordinates patch
together with the corresponding object features is reprojected to the image
space to build a cost volume in a joint semantic and geometric error manner.
The final depth is obtained by feeding the cost volume to a refinement network,
where the distribution of semantic and geometric error is regularized by direct
depth supervision. Through effectively mitigating depth error by the refinement
framework, we achieve state-of-the-art results on both the KITTI and Waymo
datasets.
