  The most popular evaluation metric for object detection in 2D images is
Intersection over Union (IoU). Existing implementations of the IoU metric for
3D object detection usually neglect one or more degrees of freedom. In this
paper, we first derive the analytic solution for three dimensional bounding
boxes. As a second contribution, a closed-form solution of the volume-to-volume
distance is derived. Finally, the Bounding Box Disparity is proposed as a
combined positive continuous metric. We provide open source implementations of
the three metrics as standalone python functions, as well as extensions to the
Open3D library and as ROS nodes.
