  Geometry plays a significant role in monocular 3D object detection. It can be
used to estimate object depth by using the perspective projection between
object's physical size and 2D projection in the image plane, which can
introduce mathematical priors into deep models. However, this projection
process also introduces error amplification, where the error of the estimated
height is amplified and reflected into the projected depth. It leads to
unreliable depth inferences and also impairs training stability. To tackle this
problem, we propose a novel Geometry Uncertainty Propagation Network (GUPNet++)
by modeling geometry projection in a probabilistic manner. This ensures depth
predictions are well-bounded and associated with a reasonable uncertainty. The
significance of introducing such geometric uncertainty is two-fold: (1). It
models the uncertainty propagation relationship of the geometry projection
during training, improving the stability and efficiency of the end-to-end model
learning. (2). It can be derived to a highly reliable confidence to indicate
the quality of the 3D detection result, enabling more reliable detection
inference. Experiments show that the proposed approach not only obtains
(state-of-the-art) SOTA performance in image-based monocular 3D detection but
also demonstrates superiority in efficacy with a simplified framework.
