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import os
import numpy as np
def iou_batch(bboxes1, bboxes2):
"""
From SORT: Computes IOU between two bboxes in the form [x1,y1,x2,y2]
"""
bboxes2 = np.expand_dims(bboxes2, 0)
bboxes1 = np.expand_dims(bboxes1, 1)
xx1 = np.maximum(bboxes1[..., 0], bboxes2[..., 0])
yy1 = np.maximum(bboxes1[..., 1], bboxes2[..., 1])
xx2 = np.minimum(bboxes1[..., 2], bboxes2[..., 2])
yy2 = np.minimum(bboxes1[..., 3], bboxes2[..., 3])
w = np.maximum(0., xx2 - xx1)
h = np.maximum(0., yy2 - yy1)
wh = w * h
o = wh / ((bboxes1[..., 2] - bboxes1[..., 0]) * (bboxes1[..., 3] - bboxes1[..., 1])
+ (bboxes2[..., 2] - bboxes2[..., 0]) * (bboxes2[..., 3] - bboxes2[..., 1]) - wh)
return(o)
def giou_batch(bboxes1, bboxes2):
"""
:param bbox_p: predict of bbox(N,4)(x1,y1,x2,y2)
:param bbox_g: groundtruth of bbox(N,4)(x1,y1,x2,y2)
:return:
"""
# for details should go to https://arxiv.org/pdf/1902.09630.pdf
# ensure predict's bbox form
bboxes2 = np.expand_dims(bboxes2, 0)
bboxes1 = np.expand_dims(bboxes1, 1)
xx1 = np.maximum(bboxes1[..., 0], bboxes2[..., 0])
yy1 = np.maximum(bboxes1[..., 1], bboxes2[..., 1])
xx2 = np.minimum(bboxes1[..., 2], bboxes2[..., 2])
yy2 = np.minimum(bboxes1[..., 3], bboxes2[..., 3])
w = np.maximum(0., xx2 - xx1)
h = np.maximum(0., yy2 - yy1)
wh = w * h
iou = wh / ((bboxes1[..., 2] - bboxes1[..., 0]) * (bboxes1[..., 3] - bboxes1[..., 1])
+ (bboxes2[..., 2] - bboxes2[..., 0]) * (bboxes2[..., 3] - bboxes2[..., 1]) - wh)
xxc1 = np.minimum(bboxes1[..., 0], bboxes2[..., 0])
yyc1 = np.minimum(bboxes1[..., 1], bboxes2[..., 1])
xxc2 = np.maximum(bboxes1[..., 2], bboxes2[..., 2])
yyc2 = np.maximum(bboxes1[..., 3], bboxes2[..., 3])
wc = xxc2 - xxc1
hc = yyc2 - yyc1
assert((wc > 0).all() and (hc > 0).all())
area_enclose = wc * hc
giou = iou - (area_enclose - wh) / area_enclose
giou = (giou + 1.)/2.0 # resize from (-1,1) to (0,1)
return giou
def diou_batch(bboxes1, bboxes2):
"""
:param bbox_p: predict of bbox(N,4)(x1,y1,x2,y2)
:param bbox_g: groundtruth of bbox(N,4)(x1,y1,x2,y2)
:return:
"""
# for details should go to https://arxiv.org/pdf/1902.09630.pdf
# ensure predict's bbox form
bboxes2 = np.expand_dims(bboxes2, 0)
bboxes1 = np.expand_dims(bboxes1, 1)
# calculate the intersection box
xx1 = np.maximum(bboxes1[..., 0], bboxes2[..., 0])
yy1 = np.maximum(bboxes1[..., 1], bboxes2[..., 1])
xx2 = np.minimum(bboxes1[..., 2], bboxes2[..., 2])
yy2 = np.minimum(bboxes1[..., 3], bboxes2[..., 3])
w = np.maximum(0., xx2 - xx1)
h = np.maximum(0., yy2 - yy1)
wh = w * h
iou = wh / ((bboxes1[..., 2] - bboxes1[..., 0]) * (bboxes1[..., 3] - bboxes1[..., 1])
+ (bboxes2[..., 2] - bboxes2[..., 0]) * (bboxes2[..., 3] - bboxes2[..., 1]) - wh)
centerx1 = (bboxes1[..., 0] + bboxes1[..., 2]) / 2.0
centery1 = (bboxes1[..., 1] + bboxes1[..., 3]) / 2.0
centerx2 = (bboxes2[..., 0] + bboxes2[..., 2]) / 2.0
centery2 = (bboxes2[..., 1] + bboxes2[..., 3]) / 2.0
inner_diag = (centerx1 - centerx2) ** 2 + (centery1 - centery2) ** 2
xxc1 = np.minimum(bboxes1[..., 0], bboxes2[..., 0])
yyc1 = np.minimum(bboxes1[..., 1], bboxes2[..., 1])
xxc2 = np.maximum(bboxes1[..., 2], bboxes2[..., 2])
yyc2 = np.maximum(bboxes1[..., 3], bboxes2[..., 3])
outer_diag = (xxc2 - xxc1) ** 2 + (yyc2 - yyc1) ** 2
diou = iou - inner_diag / outer_diag
return (diou + 1) / 2.0 # resize from (-1,1) to (0,1)
def ciou_batch(bboxes1, bboxes2):
"""
:param bbox_p: predict of bbox(N,4)(x1,y1,x2,y2)
:param bbox_g: groundtruth of bbox(N,4)(x1,y1,x2,y2)
:return:
"""
# for details should go to https://arxiv.org/pdf/1902.09630.pdf
# ensure predict's bbox form
bboxes2 = np.expand_dims(bboxes2, 0)
bboxes1 = np.expand_dims(bboxes1, 1)
# calculate the intersection box
xx1 = np.maximum(bboxes1[..., 0], bboxes2[..., 0])
yy1 = np.maximum(bboxes1[..., 1], bboxes2[..., 1])
xx2 = np.minimum(bboxes1[..., 2], bboxes2[..., 2])
yy2 = np.minimum(bboxes1[..., 3], bboxes2[..., 3])
w = np.maximum(0., xx2 - xx1)
h = np.maximum(0., yy2 - yy1)
wh = w * h
iou = wh / ((bboxes1[..., 2] - bboxes1[..., 0]) * (bboxes1[..., 3] - bboxes1[..., 1])
+ (bboxes2[..., 2] - bboxes2[..., 0]) * (bboxes2[..., 3] - bboxes2[..., 1]) - wh)
centerx1 = (bboxes1[..., 0] + bboxes1[..., 2]) / 2.0
centery1 = (bboxes1[..., 1] + bboxes1[..., 3]) / 2.0
centerx2 = (bboxes2[..., 0] + bboxes2[..., 2]) / 2.0
centery2 = (bboxes2[..., 1] + bboxes2[..., 3]) / 2.0
inner_diag = (centerx1 - centerx2) ** 2 + (centery1 - centery2) ** 2
xxc1 = np.minimum(bboxes1[..., 0], bboxes2[..., 0])
yyc1 = np.minimum(bboxes1[..., 1], bboxes2[..., 1])
xxc2 = np.maximum(bboxes1[..., 2], bboxes2[..., 2])
yyc2 = np.maximum(bboxes1[..., 3], bboxes2[..., 3])
outer_diag = (xxc2 - xxc1) ** 2 + (yyc2 - yyc1) ** 2
w1 = bboxes1[..., 2] - bboxes1[..., 0]
h1 = bboxes1[..., 3] - bboxes1[..., 1]
w2 = bboxes2[..., 2] - bboxes2[..., 0]
h2 = bboxes2[..., 3] - bboxes2[..., 1]
# prevent dividing over zero. add one pixel shift
h2 = h2 + 1.
h1 = h1 + 1.
arctan = np.arctan(w2/h2) - np.arctan(w1/h1)
v = (4 / (np.pi ** 2)) * (arctan ** 2)
S = 1 - iou
alpha = v / (S+v)
ciou = iou - inner_diag / outer_diag - alpha * v
return (ciou + 1) / 2.0 # resize from (-1,1) to (0,1)
def ct_dist(bboxes1, bboxes2):
"""
Measure the center distance between two sets of bounding boxes,
this is a coarse implementation, we don't recommend using it only
for association, which can be unstable and sensitive to frame rate
and object speed.
"""
bboxes2 = np.expand_dims(bboxes2, 0)
bboxes1 = np.expand_dims(bboxes1, 1)
centerx1 = (bboxes1[..., 0] + bboxes1[..., 2]) / 2.0
centery1 = (bboxes1[..., 1] + bboxes1[..., 3]) / 2.0
centerx2 = (bboxes2[..., 0] + bboxes2[..., 2]) / 2.0
centery2 = (bboxes2[..., 1] + bboxes2[..., 3]) / 2.0
ct_dist2 = (centerx1 - centerx2) ** 2 + (centery1 - centery2) ** 2
ct_dist = np.sqrt(ct_dist2)
# The linear rescaling is a naive version and needs more study
ct_dist = ct_dist / ct_dist.max()
return ct_dist.max() - ct_dist # resize to (0,1)
def speed_direction_batch(dets, tracks):
tracks = tracks[..., np.newaxis]
CX1, CY1 = (dets[:,0] + dets[:,2])/2.0, (dets[:,1]+dets[:,3])/2.0
CX2, CY2 = (tracks[:,0] + tracks[:,2]) /2.0, (tracks[:,1]+tracks[:,3])/2.0
dx = CX1 - CX2
dy = CY1 - CY2
norm = np.sqrt(dx**2 + dy**2) + 1e-6
dx = dx / norm
dy = dy / norm
return dy, dx # size: num_track x num_det
def linear_assignment(cost_matrix):
try:
import lap
_, x, y = lap.lapjv(cost_matrix, extend_cost=True)
return np.array([[y[i],i] for i in x if i >= 0]) #
except ImportError:
from scipy.optimize import linear_sum_assignment
x, y = linear_sum_assignment(cost_matrix)
return np.array(list(zip(x, y)))
def associate_detections_to_trackers(detections,trackers,iou_threshold = 0.3):
"""
Assigns detections to tracked object (both represented as bounding boxes)
Returns 3 lists of matches, unmatched_detections and unmatched_trackers
"""
if(len(trackers)==0):
return np.empty((0,2),dtype=int), np.arange(len(detections)), np.empty((0,5),dtype=int)
iou_matrix = iou_batch(detections, trackers)
if min(iou_matrix.shape) > 0:
a = (iou_matrix > iou_threshold).astype(np.int32)
if a.sum(1).max() == 1 and a.sum(0).max() == 1:
matched_indices = np.stack(np.where(a), axis=1)
else:
matched_indices = linear_assignment(-iou_matrix)
else:
matched_indices = np.empty(shape=(0,2))
unmatched_detections = []
for d, det in enumerate(detections):
if(d not in matched_indices[:,0]):
unmatched_detections.append(d)
unmatched_trackers = []
for t, trk in enumerate(trackers):
if(t not in matched_indices[:,1]):
unmatched_trackers.append(t)
#filter out matched with low IOU
matches = []
for m in matched_indices:
if(iou_matrix[m[0], m[1]]<iou_threshold):
unmatched_detections.append(m[0])
unmatched_trackers.append(m[1])
else:
matches.append(m.reshape(1,2))
if(len(matches)==0):
matches = np.empty((0,2),dtype=int)
else:
matches = np.concatenate(matches,axis=0)
return matches, np.array(unmatched_detections), np.array(unmatched_trackers)
def associate(detections, trackers, iou_threshold, velocities, previous_obs, vdc_weight):
if(len(trackers)==0):
return np.empty((0,2),dtype=int), np.arange(len(detections)), np.empty((0,5),dtype=int)
Y, X = speed_direction_batch(detections, previous_obs)
inertia_Y, inertia_X = velocities[:,0], velocities[:,1]
inertia_Y = np.repeat(inertia_Y[:, np.newaxis], Y.shape[1], axis=1)
inertia_X = np.repeat(inertia_X[:, np.newaxis], X.shape[1], axis=1)
diff_angle_cos = inertia_X * X + inertia_Y * Y
diff_angle_cos = np.clip(diff_angle_cos, a_min=-1, a_max=1)
diff_angle = np.arccos(diff_angle_cos)
diff_angle = (np.pi /2.0 - np.abs(diff_angle)) / np.pi
valid_mask = np.ones(previous_obs.shape[0])
valid_mask[np.where(previous_obs[:,4]<0)] = 0
iou_matrix = iou_batch(detections, trackers)
scores = np.repeat(detections[:,-1][:, np.newaxis], trackers.shape[0], axis=1)
# iou_matrix = iou_matrix * scores # a trick sometiems works, we don't encourage this
valid_mask = np.repeat(valid_mask[:, np.newaxis], X.shape[1], axis=1)
angle_diff_cost = (valid_mask * diff_angle) * vdc_weight
angle_diff_cost = angle_diff_cost.T
angle_diff_cost = angle_diff_cost * scores
if min(iou_matrix.shape) > 0:
a = (iou_matrix > iou_threshold).astype(np.int32)
if a.sum(1).max() == 1 and a.sum(0).max() == 1:
matched_indices = np.stack(np.where(a), axis=1)
else:
matched_indices = linear_assignment(-(iou_matrix+angle_diff_cost))
else:
matched_indices = np.empty(shape=(0,2))
unmatched_detections = []
for d, det in enumerate(detections):
if(d not in matched_indices[:,0]):
unmatched_detections.append(d)
unmatched_trackers = []
for t, trk in enumerate(trackers):
if(t not in matched_indices[:,1]):
unmatched_trackers.append(t)
# filter out matched with low IOU
matches = []
for m in matched_indices:
if(iou_matrix[m[0], m[1]]<iou_threshold):
unmatched_detections.append(m[0])
unmatched_trackers.append(m[1])
else:
matches.append(m.reshape(1,2))
if(len(matches)==0):
matches = np.empty((0,2),dtype=int)
else:
matches = np.concatenate(matches,axis=0)
return matches, np.array(unmatched_detections), np.array(unmatched_trackers)
def associate_kitti(detections, trackers, det_cates, iou_threshold,
velocities, previous_obs, vdc_weight):
if(len(trackers)==0):
return np.empty((0,2),dtype=int), np.arange(len(detections)), np.empty((0,5),dtype=int)
"""
Cost from the velocity direction consistency
"""
Y, X = speed_direction_batch(detections, previous_obs)
inertia_Y, inertia_X = velocities[:,0], velocities[:,1]
inertia_Y = np.repeat(inertia_Y[:, np.newaxis], Y.shape[1], axis=1)
inertia_X = np.repeat(inertia_X[:, np.newaxis], X.shape[1], axis=1)
diff_angle_cos = inertia_X * X + inertia_Y * Y
diff_angle_cos = np.clip(diff_angle_cos, a_min=-1, a_max=1)
diff_angle = np.arccos(diff_angle_cos)
diff_angle = (np.pi /2.0 - np.abs(diff_angle)) / np.pi
valid_mask = np.ones(previous_obs.shape[0])
valid_mask[np.where(previous_obs[:,4]<0)]=0
valid_mask = np.repeat(valid_mask[:, np.newaxis], X.shape[1], axis=1)
scores = np.repeat(detections[:,-1][:, np.newaxis], trackers.shape[0], axis=1)
angle_diff_cost = (valid_mask * diff_angle) * vdc_weight
angle_diff_cost = angle_diff_cost.T
angle_diff_cost = angle_diff_cost * scores
"""
Cost from IoU
"""
iou_matrix = iou_batch(detections, trackers)
"""
With multiple categories, generate the cost for catgory mismatch
"""
num_dets = detections.shape[0]
num_trk = trackers.shape[0]
cate_matrix = np.zeros((num_dets, num_trk))
for i in range(num_dets):
for j in range(num_trk):
if det_cates[i] != trackers[j, 4]:
cate_matrix[i][j] = -1e6
cost_matrix = - iou_matrix -angle_diff_cost - cate_matrix
if min(iou_matrix.shape) > 0:
a = (iou_matrix > iou_threshold).astype(np.int32)
if a.sum(1).max() == 1 and a.sum(0).max() == 1:
matched_indices = np.stack(np.where(a), axis=1)
else:
matched_indices = linear_assignment(cost_matrix)
else:
matched_indices = np.empty(shape=(0,2))
unmatched_detections = []
for d, det in enumerate(detections):
if(d not in matched_indices[:,0]):
unmatched_detections.append(d)
unmatched_trackers = []
for t, trk in enumerate(trackers):
if(t not in matched_indices[:,1]):
unmatched_trackers.append(t)
#filter out matched with low IOU
matches = []
for m in matched_indices:
if(iou_matrix[m[0], m[1]]<iou_threshold):
unmatched_detections.append(m[0])
unmatched_trackers.append(m[1])
else:
matches.append(m.reshape(1,2))
if(len(matches)==0):
matches = np.empty((0,2),dtype=int)
else:
matches = np.concatenate(matches,axis=0)
return matches, np.array(unmatched_detections), np.array(unmatched_trackers) |