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# Ultralytics YOLO 🚀, GPL-3.0 license
import numpy as np
import scipy
from scipy.spatial.distance import cdist
from .kalman_filter import chi2inv95
try:
import lap # for linear_assignment
assert lap.__version__ # verify package is not directory
except (ImportError, AssertionError, AttributeError):
from ultralytics.yolo.utils.checks import check_requirements
check_requirements('lap>=0.4') # install
import lap
def merge_matches(m1, m2, shape):
O, P, Q = shape
m1 = np.asarray(m1)
m2 = np.asarray(m2)
M1 = scipy.sparse.coo_matrix((np.ones(len(m1)), (m1[:, 0], m1[:, 1])), shape=(O, P))
M2 = scipy.sparse.coo_matrix((np.ones(len(m2)), (m2[:, 0], m2[:, 1])), shape=(P, Q))
mask = M1 * M2
match = mask.nonzero()
match = list(zip(match[0], match[1]))
unmatched_O = tuple(set(range(O)) - {i for i, j in match})
unmatched_Q = tuple(set(range(Q)) - {j for i, j in match})
return match, unmatched_O, unmatched_Q
def _indices_to_matches(cost_matrix, indices, thresh):
matched_cost = cost_matrix[tuple(zip(*indices))]
matched_mask = (matched_cost <= thresh)
matches = indices[matched_mask]
unmatched_a = tuple(set(range(cost_matrix.shape[0])) - set(matches[:, 0]))
unmatched_b = tuple(set(range(cost_matrix.shape[1])) - set(matches[:, 1]))
return matches, unmatched_a, unmatched_b
def linear_assignment(cost_matrix, thresh, use_lap=True):
# Linear assignment implementations with scipy and lap.lapjv
if cost_matrix.size == 0:
return np.empty((0, 2), dtype=int), tuple(range(cost_matrix.shape[0])), tuple(range(cost_matrix.shape[1]))
if use_lap:
_, x, y = lap.lapjv(cost_matrix, extend_cost=True, cost_limit=thresh)
matches = [[ix, mx] for ix, mx in enumerate(x) if mx >= 0]
unmatched_a = np.where(x < 0)[0]
unmatched_b = np.where(y < 0)[0]
else:
# Scipy linear sum assignment is NOT working correctly, DO NOT USE
y, x = scipy.optimize.linear_sum_assignment(cost_matrix) # row y, col x
matches = np.asarray([[i, x] for i, x in enumerate(x) if cost_matrix[i, x] <= thresh])
unmatched = np.ones(cost_matrix.shape)
for i, xi in matches:
unmatched[i, xi] = 0.0
unmatched_a = np.where(unmatched.all(1))[0]
unmatched_b = np.where(unmatched.all(0))[0]
return matches, unmatched_a, unmatched_b
def ious(atlbrs, btlbrs):
"""
Compute cost based on IoU
:type atlbrs: list[tlbr] | np.ndarray
:type atlbrs: list[tlbr] | np.ndarray
:rtype ious np.ndarray
"""
ious = np.zeros((len(atlbrs), len(btlbrs)), dtype=np.float32)
if ious.size == 0:
return ious
ious = bbox_ious(np.ascontiguousarray(atlbrs, dtype=np.float32), np.ascontiguousarray(btlbrs, dtype=np.float32))
return ious
def iou_distance(atracks, btracks):
"""
Compute cost based on IoU
:type atracks: list[STrack]
:type btracks: list[STrack]
:rtype cost_matrix np.ndarray
"""
if (len(atracks) > 0 and isinstance(atracks[0], np.ndarray)) \
or (len(btracks) > 0 and isinstance(btracks[0], np.ndarray)):
atlbrs = atracks
btlbrs = btracks
else:
atlbrs = [track.tlbr for track in atracks]
btlbrs = [track.tlbr for track in btracks]
_ious = ious(atlbrs, btlbrs)
return 1 - _ious # cost matrix
def v_iou_distance(atracks, btracks):
"""
Compute cost based on IoU
:type atracks: list[STrack]
:type btracks: list[STrack]
:rtype cost_matrix np.ndarray
"""
if (len(atracks) > 0 and isinstance(atracks[0], np.ndarray)) \
or (len(btracks) > 0 and isinstance(btracks[0], np.ndarray)):
atlbrs = atracks
btlbrs = btracks
else:
atlbrs = [track.tlwh_to_tlbr(track.pred_bbox) for track in atracks]
btlbrs = [track.tlwh_to_tlbr(track.pred_bbox) for track in btracks]
_ious = ious(atlbrs, btlbrs)
return 1 - _ious # cost matrix
def embedding_distance(tracks, detections, metric='cosine'):
"""
:param tracks: list[STrack]
:param detections: list[BaseTrack]
:param metric:
:return: cost_matrix np.ndarray
"""
cost_matrix = np.zeros((len(tracks), len(detections)), dtype=np.float32)
if cost_matrix.size == 0:
return cost_matrix
det_features = np.asarray([track.curr_feat for track in detections], dtype=np.float32)
# for i, track in enumerate(tracks):
# cost_matrix[i, :] = np.maximum(0.0, cdist(track.smooth_feat.reshape(1,-1), det_features, metric))
track_features = np.asarray([track.smooth_feat for track in tracks], dtype=np.float32)
cost_matrix = np.maximum(0.0, cdist(track_features, det_features, metric)) # Normalized features
return cost_matrix
def gate_cost_matrix(kf, cost_matrix, tracks, detections, only_position=False):
if cost_matrix.size == 0:
return cost_matrix
gating_dim = 2 if only_position else 4
gating_threshold = chi2inv95[gating_dim]
measurements = np.asarray([det.to_xyah() for det in detections])
for row, track in enumerate(tracks):
gating_distance = kf.gating_distance(track.mean, track.covariance, measurements, only_position)
cost_matrix[row, gating_distance > gating_threshold] = np.inf
return cost_matrix
def fuse_motion(kf, cost_matrix, tracks, detections, only_position=False, lambda_=0.98):
if cost_matrix.size == 0:
return cost_matrix
gating_dim = 2 if only_position else 4
gating_threshold = chi2inv95[gating_dim]
measurements = np.asarray([det.to_xyah() for det in detections])
for row, track in enumerate(tracks):
gating_distance = kf.gating_distance(track.mean, track.covariance, measurements, only_position, metric='maha')
cost_matrix[row, gating_distance > gating_threshold] = np.inf
cost_matrix[row] = lambda_ * cost_matrix[row] + (1 - lambda_) * gating_distance
return cost_matrix
def fuse_iou(cost_matrix, tracks, detections):
if cost_matrix.size == 0:
return cost_matrix
reid_sim = 1 - cost_matrix
iou_dist = iou_distance(tracks, detections)
iou_sim = 1 - iou_dist
fuse_sim = reid_sim * (1 + iou_sim) / 2
# det_scores = np.array([det.score for det in detections])
# det_scores = np.expand_dims(det_scores, axis=0).repeat(cost_matrix.shape[0], axis=0)
return 1 - fuse_sim # fuse cost
def fuse_score(cost_matrix, detections):
if cost_matrix.size == 0:
return cost_matrix
iou_sim = 1 - cost_matrix
det_scores = np.array([det.score for det in detections])
det_scores = np.expand_dims(det_scores, axis=0).repeat(cost_matrix.shape[0], axis=0)
fuse_sim = iou_sim * det_scores
return 1 - fuse_sim # fuse_cost
def bbox_ious(box1, box2, eps=1e-7):
"""Boxes are x1y1x2y2
box1: np.array of shape(nx4)
box2: np.array of shape(mx4)
returns: np.array of shape(nxm)
"""
# Get the coordinates of bounding boxes
b1_x1, b1_y1, b1_x2, b1_y2 = box1.T
b2_x1, b2_y1, b2_x2, b2_y2 = box2.T
# Intersection area
inter_area = (np.minimum(b1_x2[:, None], b2_x2) - np.maximum(b1_x1[:, None], b2_x1)).clip(0) * \
(np.minimum(b1_y2[:, None], b2_y2) - np.maximum(b1_y1[:, None], b2_y1)).clip(0)
# box2 area
box1_area = (b1_x2 - b1_x1) * (b1_y2 - b1_y1)
box2_area = (b2_x2 - b2_x1) * (b2_y2 - b2_y1)
return inter_area / (box2_area + box1_area[:, None] - inter_area + eps)
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