1. xbxb dbdb dtdt γ nvnv θ xtxt npnp hphp ngng α H f ground plane image plane (inverse) gravity ground plane orientation ground plane height object vertical orientation real world height object depth camera center focal length object pitch and roll angles object landmarks

2. ground plane inverse gravity √ vertical surface candidate 1 vertical surface candidate 2 ground plane vertical surface candidate 1 inverse gravity vertical surface candidate 2 X

3. ground plane vertical surface candidate inverse gravity object candidate √ ground plane vertical surface candidate inverse gravity X

7. √ √ √ √ X Local 3D context Global 3D context Best hypothesis

8. (inverse) gravity ground plane orientation valid invalid (#1) invalid (#2) invalid (#1) incompatible (#3) incompatible (#4) ground plane

9. (a) (b)

11. bounding box object mask orientation landmarks object maskback-projected mask occlusion mask After object is detected:

12. closer object farther object closer object farther object occlusion mask of the farther object intersection region of the two object masks √ X

13. w l β

14. ground plane vertical surface candidate object candidate inverse gravity

15. supporting plane 1 supporting plane 2

19. 2 3 45 6 1

20. Generate object/surface candidates Propose global 3D geometry hypotheses by object/surface candidates Evaluate each hypothesis by inferring validity of object/surface candidates Select the best hypothesis and its associated validity of object/surface candidates

21. xbxb dbdb dtdt γ nvnv θ xtxt npnp hphp ngng α H f ground plane image plane (inverse) gravity ground plane orientation ground plane height object vertical orientation real world height object depth camera center focal length object pitch and roll angles object landmarks