Calculation/ Implementation of the real 3D Intersection over Union (IoU) of two Bounding Boxes with 9 Degrees of Freedom

Question

I have two 3D bounding boxes with 9 degrees of freedom (3 translation, 3 dimensions, 3 rotations). Now I want to calculate the Intersection over Union (IoU) also known as Jaccard Index of them:

I know this has already been implemented for the case of a single rotation (around the z-axis) using the bird's eye view, however I am looking for a solution, where the 3D bounding boxes can be rotated around all axes (x, y, z).

So far I did not find any approaches. I would probably start by calculating all intersection points and then try to calculate volumes using tetrahedrons. Any links or hints are welcome!

Answer 1

You can find an implementation for 3D-oriented bounding boxes accompanying the objectron benchmark. Their IoU metric takes two boxes as input and calculates the intersection volume based on the Sutherland-Hodgman Polygon clipping algorithm. A detailed answer is also described in the in the paper.