# Copyright (c) Facebook, Inc. and its affiliates.
#
# This source code is licensed under the MIT license found in the
# LICENSE file in the root directory of this source tree.
""" Helper functions for calculating 2D and 3D bounding box IoU.
Collected and written by Charles R. Qi
Last modified: Jul 2019
"""
from __future__ import print_function
import torch
import numpy as np
from scipy.spatial import ConvexHull
def polygon_clip(subjectPolygon, clipPolygon):
""" Clip a polygon with another polygon.
Ref: https://rosettacode.org/wiki/Sutherland-Hodgman_polygon_clipping#Python
Args:
subjectPolygon: a list of (x,y) 2d points, any polygon.
clipPolygon: a list of (x,y) 2d points, has to be *convex*
Note:
**points have to be counter-clockwise ordered**
Return:
a list of (x,y) vertex point for the intersection polygon.
"""
def inside(p):
return(cp2[0]-cp1[0])*(p[1]-cp1[1]) > (cp2[1]-cp1[1])*(p[0]-cp1[0])
def computeIntersection():
dc = [ cp1[0] - cp2[0], cp1[1] - cp2[1] ]
dp = [ s[0] - e[0], s[1] - e[1] ]
n1 = cp1[0] * cp2[1] - cp1[1] * cp2[0]
n2 = s[0] * e[1] - s[1] * e[0]
n3 = 1.0 / (dc[0] * dp[1] - dc[1] * dp[0])
return [(n1*dp[0] - n2*dc[0]) * n3, (n1*dp[1] - n2*dc[1]) * n3]
outputList = subjectPolygon
cp1 = clipPolygon[-1]
for clipVertex in clipPolygon:
cp2 = clipVertex
inputList = outputList
outputList = []
s = inputList[-1]
for subjectVertex in inputList:
e = subjectVertex
if inside(e):
if not inside(s):
outputList.append(computeIntersection())
outputList.append(e)
elif inside(s):
outputList.append(computeIntersection())
s = e
cp1 = cp2
if len(outputList) == 0:
return None
return(outputList)
def poly_area(x,y):
""" Ref: http://stackoverflow.com/questions/24467972/calculate-area-of-polygon-given-x-y-coordinates """
return 0.5*np.abs(np.dot(x,np.roll(y,1))-np.dot(y,np.roll(x,1)))
def convex_hull_intersection(p1, p2):
""" Compute area of two convex hull's intersection area.
p1,p2 are a list of (x,y) tuples of hull vertices.
return a list of (x,y) for the intersection and its volume
"""
inter_p = polygon_clip(p1,p2)
if inter_p is not None:
hull_inter = ConvexHull(inter_p)
return inter_p, hull_inter.volume
else:
return None, 0.0
def box3d_vol(corners):
''' corners: (8,3) no assumption on axis direction '''
a = np.sqrt(np.sum((corners[0,:] - corners[1,:])**2))
b = np.sqrt(np.sum((corners[1,:] - corners[2,:])**2))
c = np.sqrt(np.sum((corners[0,:] - corners[4,:])**2))
return a*b*c
def is_clockwise(p):
x = p[:,0]
y = p[:,1]
return np.dot(x,np.roll(y,1))-np.dot(y,np.roll(x,1)) > 0
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.
'''
# 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)]
area1 = poly_area(np.array(rect1)[:,0], np.array(rect1)[:,1])
area2 = poly_area(np.array(rect2)[:,0], np.array(rect2)[:,1])
inter, inter_area = convex_hull_intersection(rect1, rect2)
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
def get_iou(bb1, bb2):
"""
Calculate the Intersection over Union (IoU) of two 2D bounding boxes.
Parameters
----------
bb1 : dict
Keys: {'x1', 'x2', 'y1', 'y2'}
The (x1, y1) position is at the top left corner,
the (x2, y2) position is at the bottom right corner
bb2 : dict
Keys: {'x1', 'x2', 'y1', 'y2'}
The (x, y) position is at the top left corner,
the (x2, y2) position is at the bottom right corner
Returns
-------
float
in [0, 1]
"""
assert bb1['x1'] < bb1['x2']
assert bb1['y1'] < bb1['y2']
assert bb2['x1'] < bb2['x2']
assert bb2['y1'] < bb2['y2']
# determine the coordinates of the intersection rectangle
x_left = max(bb1['x1'], bb2['x1'])
y_top = max(bb1['y1'], bb2['y1'])
x_right = min(bb1['x2'], bb2['x2'])
y_bottom = min(bb1['y2'], bb2['y2'])
if x_right < x_left or y_bottom < y_top:
return 0.0
# The intersection of two axis-aligned bounding boxes is always an
# axis-aligned bounding box
intersection_area = (x_right - x_left) * (y_bottom - y_top)
# compute the area of both AABBs
bb1_area = (bb1['x2'] - bb1['x1']) * (bb1['y2'] - bb1['y1'])
bb2_area = (bb2['x2'] - bb2['x1']) * (bb2['y2'] - bb2['y1'])
# compute the intersection over union by taking the intersection
# area and dividing it by the sum of prediction + ground-truth
# areas - the interesection area
iou = intersection_area / float(bb1_area + bb2_area - intersection_area)
assert iou >= 0.0
assert iou <= 1.0
return iou
def box2d_iou(box1, box2):
''' Compute 2D bounding box IoU.
Input:
box1: tuple of (xmin,ymin,xmax,ymax)
box2: tuple of (xmin,ymin,xmax,ymax)
Output:
iou: 2D IoU scalar
'''
return get_iou({'x1':box1[0], 'y1':box1[1], 'x2':box1[2], 'y2':box1[3]}, \
{'x1':box2[0], 'y1':box2[1], 'x2':box2[2], 'y2':box2[3]})
# -----------------------------------------------------------
# Convert from box parameters to
# -----------------------------------------------------------
def roty(t):
"""Rotation about the y-axis."""
c = np.cos(t)
s = np.sin(t)
return np.array([[c, 0, s],
[0, 1, 0],
[-s, 0, c]])
def roty_batch(t):
"""Rotation about the y-axis.
t: (x1,x2,...xn)
return: (x1,x2,...,xn,3,3)
"""
input_shape = t.shape
output = np.zeros(tuple(list(input_shape)+[3,3]))
c = np.cos(t)
s = np.sin(t)
output[...,0,0] = c
output[...,0,2] = s
output[...,1,1] = 1
output[...,2,0] = -s
output[...,2,2] = c
return output
def roty_batch_pytorch(t):
"""Rotation about the y-axis.
t: (x1,x2,...xn)
return: (x1,x2,...,xn,3,3)
"""
input_shape = t.shape
output = torch.zeros(tuple(list(input_shape)+[3,3])).cuda()
c = torch.cos(t)
s = torch.sin(t)
output[...,0,0] = c
output[...,0,2] = s
output[...,1,1] = 1
output[...,2,0] = -s
output[...,2,2] = c
return output
def rotz_batch_pytorch(t):
"""Rotation about the y-axis.
t: (x1,x2,...xn)
return: (x1,x2,...,xn,3,3)
"""
input_shape = t.shape
output = torch.zeros(tuple(list(input_shape)+[3,3])).cuda()
c = torch.cos(t)
s = torch.sin(t)
output[...,0,0] = c
output[...,0,1] = -s
output[...,1,0] = s
output[...,1,1] = c
output[...,2,2] = 1
return output
def get_3d_box(box_size, heading_angle, center):
''' box_size is array(l,w,h), heading_angle is radius clockwise from pos x axis, center is xyz of box center
output (8,3) array for 3D box cornders
Similar to utils/compute_orientation_3d
'''
R = roty(heading_angle)
l,w,h = box_size
x_corners = [l/2,l/2,-l/2,-l/2,l/2,l/2,-l/2,-l/2];
y_corners = [h/2,h/2,h/2,h/2,-h/2,-h/2,-h/2,-h/2];
z_corners = [w/2,-w/2,-w/2,w/2,w/2,-w/2,-w/2,w/2];
corners_3d = np.dot(R, np.vstack([x_corners,y_corners,z_corners]))
corners_3d[0,:] = corners_3d[0,:] + center[0];
corners_3d[1,:] = corners_3d[1,:] + center[1];
corners_3d[2,:] = corners_3d[2,:] + center[2];
corners_3d = np.transpose(corners_3d)
return corners_3d
def get_3d_box_batch(box_size, heading_angle, center):
''' box_size: [x1,x2,...,xn,3]
heading_angle: [x1,x2,...,xn]
center: [x1,x2,...,xn,3]
Return:
[x1,x3,...,xn,8,3]
'''
input_shape = heading_angle.shape
R = roty_batch(heading_angle)
l = np.expand_dims(box_size[...,0], -1) # [x1,...,xn,1]
w = np.expand_dims(box_size[...,1], -1)
h = np.expand_dims(box_size[...,2], -1)
corners_3d = np.zeros(tuple(list(input_shape)+[8,3]))
corners_3d[...,:,0] = np.concatenate((l/2,l/2,-l/2,-l/2,l/2,l/2,-l/2,-l/2), -1)
corners_3d[...,:,1] = np.concatenate((h/2,h/2,h/2,h/2,-h/2,-h/2,-h/2,-h/2), -1)
corners_3d[...,:,2] = np.concatenate((w/2,-w/2,-w/2,w/2,w/2,-w/2,-w/2,w/2), -1)
tlist = [i for i in range(len(input_shape))]
tlist += [len(input_shape)+1, len(input_shape)]
corners_3d = np.matmul(corners_3d, np.transpose(R, tuple(tlist)))
corners_3d += np.expand_dims(center, -2)
return corners_3d
'''
def get_surface_line_points_batch_pytorch(box_size, heading_angle, center):
input_shape = heading_angle.shape
R = roty_batch_pytorch(heading_angle.float())
l = box_size[...,0].unsqueeze(-1) # [x1,...,xn,1]
w = box_size[...,1].unsqueeze(-1)
h = box_size[...,2].unsqueeze(-1)
surface_3d = torch.zeros(tuple(list(input_shape)+[6,3])).cuda()
surface_3d[...,0] = torch.cat((torch.zeros_like(l),torch.zeros_like(l),l/2,-l/2,torch.zeros_like(l),torch.zeros_like(l)), -1)
surface_3d[...,1] = torch.cat((torch.zeros_like(l),torch.zeros_like(l),torch.zeros_like(l),torch.zeros_like(l),w/2,-w/2), -1)
surface_3d[...,2] = torch.cat((h/2,-h/2,torch.zeros_like(l),torch.zeros_like(l),torch.zeros_like(l),torch.zeros_like(l)), -1)
surface_3d = torch.matmul(surface_3d, R.transpose(3,2))
surface_3d += center.unsqueeze(-2)
line_3d = torch.zeros(tuple(list(input_shape)+[12,3])).cuda()
line_3d[...,0] = torch.cat((torch.zeros_like(l),torch.zeros_like(l),l/2,-l/2,torch.zeros_like(l),torch.zeros_like(l),l/2,-l/2,l/2,-l/2,l/2,-l/2), -1)
line_3d[...,1] = torch.cat((w/2,-w/2,torch.zeros_like(l),torch.zeros_like(l),w/2,-w/2,torch.zeros_like(l),torch.zeros_like(l),w/2,-w/2,-w/2,w/2), -1)
line_3d[...,2] = torch.cat((h/2,h/2,h/2,h/2,-h/2,-h/2,-h/2,-h/2,torch.zeros_like(l),torch.zeros_like(l),torch.zeros_like(l),torch.zeros_like(l)), -1)
line_3d = torch.matmul(line_3d, R.transpose(3,2))
line_3d += center.unsqueeze(-2)
return surface_3d.view(input_shape[0], input_shape[1]*6, 3).contiguous(), line_3d.view(input_shape[0], input_shape[1]*12, 3).contiguous()
'''
def get_surface_line_points_batch_pytorch(obj_size, heading_angle, center):
''' box_size: [x1,x2,...,xn,3]
heading_angle: [x1,x2,...,xn], clockwise, sunrgbd's angle is clockwise
center: [x1,x2,...,xn,3]
Return:
[x1,x3,...,xn,8,3]
'''
input_shape = heading_angle.shape
R = rotz_batch_pytorch(-heading_angle.float()) #### Add the rotz here, clockwise to counter-clockwise
offset_x = torch.zeros_like(obj_size)
offset_y = torch.zeros_like(obj_size)
offset_z = torch.zeros_like(obj_size)
offset_x[:,:,0] = 0.5#obj_size[:,:,0] / 2.0
offset_y[:,:,1] = 0.5#obj_size[:,:,1] / 2.0
offset_z[:,:,2] = 0.5#obj_size[:,:,2] / 2.0
obj_upper_surface_center = offset_z * obj_size
obj_lower_surface_center = -offset_z * obj_size
obj_front_surface_center = offset_y * obj_size
obj_back_surface_center = -offset_y * obj_size
obj_left_surface_center = offset_x * obj_size
obj_right_surface_center = -offset_x * obj_size
surface_3d = torch.cat((obj_upper_surface_center, obj_lower_surface_center, obj_front_surface_center, obj_back_surface_center, obj_left_surface_center, obj_right_surface_center), dim=1)
## Get the object line center here
obj_line_center_0 = offset_z * obj_size + offset_x * obj_size
obj_line_center_1 = offset_z * obj_size - offset_x * obj_size
obj_line_center_2 = offset_z * obj_size + offset_y * obj_size
obj_line_center_3 = offset_z * obj_size - offset_y * obj_size
obj_line_center_4 = - offset_z * obj_size + offset_x * obj_size
obj_line_center_5 = - offset_z * obj_size - offset_x * obj_size
obj_line_center_6 = - offset_z * obj_size + offset_y * obj_size
obj_line_center_7 = - offset_z * obj_size - offset_y * obj_size
obj_line_center_8 = offset_x * obj_size + offset_y * obj_size
obj_line_center_9 = offset_x * obj_size - offset_y * obj_size
obj_line_center_10 = - offset_x * obj_size + offset_y * obj_size
obj_line_center_11 = - offset_x * obj_size - offset_y * obj_size
line_3d = torch.cat((obj_line_center_0, obj_line_center_1, obj_line_center_2, obj_line_center_3, obj_line_center_4, obj_line_center_5, obj_line_center_6, obj_line_center_7, obj_line_center_8, obj_line_center_9, obj_line_center_10, obj_line_center_11), dim=1)
surface_rot = R.repeat(1,6,1,1)
surface_3d = torch.matmul(surface_3d.unsqueeze(-2), surface_rot.transpose(3,2)).squeeze(-2)
surface_center = center.repeat(1,6,1) + surface_3d#.transpose(2,1).contiguous().view(input_shape[0],6*input_shape[1],3)
line_rot = R.repeat(1,12,1,1)
line_3d = torch.matmul(line_3d.unsqueeze(-2), line_rot.transpose(3,2)).squeeze(-2)
line_center = center.repeat(1,12,1) + line_3d#.transpose(2,1).contiguous().view(input_shape[0],12*input_shape[1],3)
return surface_center, line_center
if __name__=='__main__':
# Function for polygon ploting
import matplotlib
from matplotlib.patches import Polygon
from matplotlib.collections import PatchCollection
import matplotlib.pyplot as plt
def plot_polys(plist,scale=500.0):
fig, ax = plt.subplots()
patches = []
for p in plist:
poly = Polygon(np.array(p)/scale, True)
patches.append(poly)
pc = PatchCollection(patches, cmap=matplotlib.cm.jet, alpha=0.5)
colors = 100*np.random.rand(len(patches))
pc.set_array(np.array(colors))
ax.add_collection(pc)
plt.show()
# Demo on ConvexHull
points = np.random.rand(30, 2) # 30 random points in 2-D
hull = ConvexHull(points)
# **In 2D "volume" is is area, "area" is perimeter
print(('Hull area: ', hull.volume))
for simplex in hull.simplices:
print(simplex)
# Demo on convex hull overlaps
sub_poly = [(0,0),(300,0),(300,300),(0,300)]
clip_poly = [(150,150),(300,300),(150,450),(0,300)]
inter_poly = polygon_clip(sub_poly, clip_poly)
print(poly_area(np.array(inter_poly)[:,0], np.array(inter_poly)[:,1]))
# Test convex hull interaction function
rect1 = [(50,0),(50,300),(300,300),(300,0)]
rect2 = [(150,150),(300,300),(150,450),(0,300)]
plot_polys([rect1, rect2])
inter, area = convex_hull_intersection(rect1, rect2)
print((inter, area))
if inter is not None:
print(poly_area(np.array(inter)[:,0], np.array(inter)[:,1]))
print('------------------')
rect1 = [(0.30026005199835404, 8.9408694211408424), \
(-1.1571105364358421, 9.4686676477075533), \
(0.1777082043006144, 13.154404877812102), \
(1.6350787927348105, 12.626606651245391)]
rect1 = [rect1[0], rect1[3], rect1[2], rect1[1]]
rect2 = [(0.23908745901608636, 8.8551095691132886), \
(-1.2771419487733995, 9.4269062966181956), \
(0.13138836963152717, 13.161896351296868), \
(1.647617777421013, 12.590099623791961)]
rect2 = [rect2[0], rect2[3], rect2[2], rect2[1]]
plot_polys([rect1, rect2])
inter, area = convex_hull_intersection(rect1, rect2)
print((inter, area))
