  Monocular 3D object detection is a challenging task because depth information
is difficult to obtain from 2D images. A subset of viewpoint-agnostic monocular
3D detection methods also do not explicitly leverage scene homography or
geometry during training, meaning that a model trained thusly can detect
objects in images from arbitrary viewpoints. Such works predict the projections
of the 3D bounding boxes on the image plane to estimate the location of the 3D
boxes, but these projections are not rectangular so the calculation of IoU
between these projected polygons is not straightforward. This work proposes an
efficient, fully differentiable algorithm for the calculation of IoU between
two convex polygons, which can be utilized to compute the IoU between two 3D
bounding box footprints viewed from an arbitrary angle. We test the performance
of the proposed polygon IoU loss (PIoU loss) on three state-of-the-art
viewpoint-agnostic 3D detection models. Experiments demonstrate that the
proposed PIoU loss converges faster than L1 loss and that in 3D detection
models, a combination of PIoU loss and L1 loss gives better results than L1
loss alone (+1.64% AP70 for MonoCon on cars, +0.18% AP70 for RTM3D on cars, and
+0.83%/+2.46% AP50/AP25 for MonoRCNN on cyclists).
