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# Ultralytics YOLO 🚀, AGPL-3.0 license
import numpy as np
import scipy
from scipy.spatial.distance import cdist
from ultralytics.utils.metrics import bbox_ioa
try:
import lap # for linear_assignment
assert lap.__version__ # verify package is not directory
except (ImportError, AssertionError, AttributeError):
from ultralytics.utils.checks import check_requirements
check_requirements('lapx>=0.5.2') # update to lap package from https://github.com/rathaROG/lapx
import lap
def linear_assignment(cost_matrix, thresh, use_lap=True):
"""
Perform linear assignment using scipy or lap.lapjv.
Args:
cost_matrix (np.ndarray): The matrix containing cost values for assignments.
thresh (float): Threshold for considering an assignment valid.
use_lap (bool, optional): Whether to use lap.lapjv. Defaults to True.
Returns:
(tuple): Tuple containing matched indices, unmatched indices from 'a', and unmatched indices from 'b'.
"""
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:
# https://github.com/gatagat/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:
# https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.linear_sum_assignment.html
x, y = scipy.optimize.linear_sum_assignment(cost_matrix) # row x, col y
matches = np.asarray([[x[i], y[i]] for i in range(len(x)) if cost_matrix[x[i], y[i]] <= thresh])
if len(matches) == 0:
unmatched_a = list(np.arange(cost_matrix.shape[0]))
unmatched_b = list(np.arange(cost_matrix.shape[1]))
else:
unmatched_a = list(set(np.arange(cost_matrix.shape[0])) - set(matches[:, 0]))
unmatched_b = list(set(np.arange(cost_matrix.shape[1])) - set(matches[:, 1]))
return matches, unmatched_a, unmatched_b
def iou_distance(atracks, btracks):
"""
Compute cost based on Intersection over Union (IoU) between tracks.
Args:
atracks (list[STrack] | list[np.ndarray]): List of tracks 'a' or bounding boxes.
btracks (list[STrack] | list[np.ndarray]): List of tracks 'b' or bounding boxes.
Returns:
(np.ndarray): Cost matrix computed based on IoU.
"""
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 = np.zeros((len(atlbrs), len(btlbrs)), dtype=np.float32)
if len(atlbrs) and len(btlbrs):
ious = bbox_ioa(np.ascontiguousarray(atlbrs, dtype=np.float32),
np.ascontiguousarray(btlbrs, dtype=np.float32),
iou=True)
return 1 - ious # cost matrix
def embedding_distance(tracks, detections, metric='cosine'):
"""
Compute distance between tracks and detections based on embeddings.
Args:
tracks (list[STrack]): List of tracks.
detections (list[BaseTrack]): List of detections.
metric (str, optional): Metric for distance computation. Defaults to 'cosine'.
Returns:
(np.ndarray): Cost matrix computed based on embeddings.
"""
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 fuse_score(cost_matrix, detections):
"""
Fuses cost matrix with detection scores to produce a single similarity matrix.
Args:
cost_matrix (np.ndarray): The matrix containing cost values for assignments.
detections (list[BaseTrack]): List of detections with scores.
Returns:
(np.ndarray): Fused similarity matrix.
"""
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
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