3D bounding box IoU error - buggy Convex Hull Intersection

[vincentcartillier]

I am running into a potential bug in the box3d_iou computation.

Steps to reproduce

import sys
import numpy as np

sys.path.append('./utils/')
from box_util import box3d_iou

box = [[12.05 ,  3.358, -1.927],
       [12.05 ,  3.358, -2.309],
       [11.744,  3.358, -2.309],
       [11.744,  3.358, -1.927],
       [12.05 ,  3.168, -1.927],
       [12.05 ,  3.168, -2.309],
       [11.744,  3.168, -2.309],
       [11.744,  3.168, -1.927],]

box = np.array(box)
iou, iou_2d = box3d_iou(box,box)
print(iou, iou_2d)

>> 1.4911757425289889 1.4911757425290015

Expected behavior

The 3D IoU of a box with itself should be 1.0

Additional info

The issue is coming from the convex_hull_intersection() function.

For the two rectangles defined here, that function returns an area greater than the area of each rectangle.

Fix

Switching to shapely fixed the issue.

box_utils.py - L92

def box3d_iou(corners1, corners2):
    ''' Compute 3D bounding box IoU.
    Input:
        corners1: numpy array (8,3), assume up direction is negative Y
        corners2: numpy array (8,3), assume up direction is negative Y
    Output:
        iou: 3D bounding box IoU
        iou_2d: bird's eye view 2D bounding box IoU

    todo (rqi): add more description on corner points' orders.
    '''
    from shapely.geometry import Polygon

    # corner points are in counter clockwise order
    rect1 = [[corners1[i,0], corners1[i,2]] for i in range(3,-1,-1)]
    rect2 = [[corners2[i,0], corners2[i,2]] for i in range(3,-1,-1)] 

    poly1 = Polygon(rect1)
    poly2 = Polygon(rect2)

    area1 = poly1.area
    area2 = poly2.area

    inter_area = poly1.intersection(poly2).area
    
    iou_2d = inter_area/(area1+area2-inter_area)
    ymax = min(corners1[0,1], corners2[0,1])
    ymin = max(corners1[4,1], corners2[4,1])
    inter_vol = inter_area * max(0.0, ymax-ymin)
    vol1 = box3d_vol(corners1)
    vol2 = box3d_vol(corners2)
    iou = inter_vol / (vol1 + vol2 - inter_vol)
    return iou, iou_2d