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.
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