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sort.py
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214
sort.py
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import numpy as np
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from scipy.optimize import linear_sum_assignment
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from filterpy.kalman import KalmanFilter
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def linear_assignment(cost_matrix):
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x, y = linear_sum_assignment(cost_matrix)
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return np.array(list(zip(x, y)))
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def iou_batch(bb_test, bb_gt):
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"""
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From SORT: Computes IOU between two bboxes in the form [x1,y1,x2,y2]
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"""
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bb_test = np.expand_dims(bb_test, 1)
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bb_gt = np.expand_dims(bb_gt, 0)
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xx1 = np.maximum(bb_test[..., 0], bb_gt[..., 0])
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yy1 = np.maximum(bb_test[..., 1], bb_gt[..., 1])
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xx2 = np.minimum(bb_test[..., 2], bb_gt[..., 2])
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yy2 = np.minimum(bb_test[..., 3], bb_gt[..., 3])
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w = np.maximum(0., xx2 - xx1)
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h = np.maximum(0., yy2 - yy1)
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wh = w * h
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o = wh / ((bb_test[..., 2] - bb_test[..., 0]) * (bb_test[..., 3] - bb_test[..., 1])
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+ (bb_gt[..., 2] - bb_gt[..., 0]) * (bb_gt[..., 3] - bb_gt[..., 1]) - wh)
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return o
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def convert_bbox_to_z(bbox):
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"""
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Takes a bounding box in the form [x1,y1,x2,y2] and returns z in the form
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[x,y,s,r] where x,y is the centre of the box and s is the scale/area and r is
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the aspect ratio
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"""
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w = bbox[2] - bbox[0]
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h = bbox[3] - bbox[1]
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x = bbox[0] + w / 2.
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y = bbox[1] + h / 2.
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s = w * h # scale is just area
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r = w / float(h)
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return np.array([x, y, s, r]).reshape((4, 1))
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def convert_x_to_bbox(x, score=None):
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"""
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Takes a bounding box in the centre form [x,y,s,r] and returns it in the form
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[x1,y1,x2,y2] where x1,y1 is the top left and x2,y2 is the bottom right
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"""
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w = np.sqrt(x[2] * x[3])
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h = x[2] / w
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if score is None:
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return np.array([x[0] - w / 2., x[1] - h / 2., x[0] + w / 2., x[1] + h / 2.]).reshape((1, 4))
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else:
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return np.array([x[0] - w / 2., x[1] - h / 2., x[0] + w / 2., x[1] + h / 2., score]).reshape((1, 5))
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class KalmanBoxTracker(object):
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"""
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This class represents the internal state of individual tracked objects observed as bbox.
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"""
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count = 0
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def __init__(self, bbox):
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"""
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Initialises a tracker using initial bounding box.
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"""
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self.kf = KalmanFilter(dim_x=7, dim_z=4)
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self.kf.F = np.array([[1, 0, 0, 0, 1, 0, 0],
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[0, 1, 0, 0, 0, 1, 0],
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[0, 0, 1, 0, 0, 0, 1],
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[0, 0, 0, 1, 0, 0, 0],
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[0, 0, 0, 0, 1, 0, 0],
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[0, 0, 0, 0, 0, 1, 0],
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[0, 0, 0, 0, 0, 0, 1]])
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self.kf.H = np.array([[1, 0, 0, 0, 0, 0, 0],
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[0, 1, 0, 0, 0, 0, 0],
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[0, 0, 1, 0, 0, 0, 0],
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[0, 0, 0, 1, 0, 0, 0]])
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self.kf.R[2:, 2:] *= 10.
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self.kf.P[4:, 4:] *= 1000. # give high uncertainty to the unobservable initial velocities
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self.kf.P *= 10.
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self.kf.Q[-1, -1] *= 0.01
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self.kf.Q[4:, 4:] *= 0.01
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self.kf.x[:4] = convert_bbox_to_z(bbox)
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self.time_since_update = 0
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self.id = KalmanBoxTracker.count
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KalmanBoxTracker.count += 1
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self.history = []
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self.hits = 0
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self.hit_streak = 0
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self.age = 0
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def update(self, bbox):
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"""
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Updates the state vector with observed bbox.
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"""
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self.time_since_update = 0
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self.history = []
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self.hits += 1
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self.hit_streak += 1
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self.kf.update(convert_bbox_to_z(bbox))
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def predict(self):
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"""
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Advances the state vector and returns the predicted bounding box estimate.
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"""
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if (self.kf.x[6] + self.kf.x[2]) <= 0:
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self.kf.x[6] *= 0.0
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self.kf.predict()
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self.age += 1
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if self.time_since_update > 0:
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self.hit_streak = 0
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self.time_since_update += 1
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self.history.append(convert_x_to_bbox(self.kf.x))
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return self.history[-1]
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def get_state(self):
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"""
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Returns the current bounding box estimate.
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"""
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return convert_x_to_bbox(self.kf.x)
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class Sort(object):
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def __init__(self, max_age=5, min_hits=2, iou_threshold=0.3):
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"""
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Sets key parameters for SORT
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"""
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self.max_age = max_age
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self.min_hits = min_hits
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self.iou_threshold = iou_threshold
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self.trackers = []
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self.frame_count = 0
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def update(self, dets=np.empty((0, 5))):
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"""
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Params:
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dets - a numpy array of detections in the format [[x1,y1,x2,y2,score],...]
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Requires: this method must be called once for each frame even with empty detections.
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Returns the a similar array, where the last column is the object ID.
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NOTE: The number of objects returned may differ from the number of detections provided.
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"""
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self.frame_count += 1
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trks = np.zeros((len(self.trackers), 5))
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to_del = []
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ret = []
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for t, trk in enumerate(trks):
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pos = self.trackers[t].predict()[0]
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trk[:] = [pos[0], pos[1], pos[2], pos[3], 0]
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if np.any(np.isnan(pos)):
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to_del.append(t)
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trks = np.ma.compress_rows(np.ma.masked_invalid(trks))
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for t in reversed(to_del):
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self.trackers.pop(t)
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matched, unmatched_dets, unmatched_trks = associate_detections_to_trackers(dets, trks, self.iou_threshold)
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# update matched trackers with assigned detections
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for m in matched:
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self.trackers[m[1]].update(dets[m[0], :])
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# create and initialise new trackers for unmatched detections
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for i in unmatched_dets:
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trk = KalmanBoxTracker(dets[i, :])
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self.trackers.append(trk)
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i = len(self.trackers)
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for trk in reversed(self.trackers):
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d = trk.get_state()[0]
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if (trk.time_since_update < 1) and (trk.hit_streak >= self.min_hits or self.frame_count <= self.min_hits):
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ret.append(np.concatenate((d, [trk.id + 1])).reshape(1, -1)) # +1 as MOT benchmark requires positive
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i -= 1
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# remove dead tracklet
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if trk.time_since_update > self.max_age:
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self.trackers.pop(i)
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if len(ret) > 0:
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return np.concatenate(ret)
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return np.empty((0, 5))
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def associate_detections_to_trackers(detections, trackers, iou_threshold=0.3):
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"""
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Assigns detections to tracked object (both represented as bounding boxes)
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Returns 3 lists of matches, unmatched_detections, unmatched_trackers
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"""
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if len(trackers) == 0:
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return np.empty((0, 2), dtype=int), np.arange(len(detections)), np.empty((0, 1), dtype=int)
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iou_matrix = iou_batch(detections, trackers)
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if min(iou_matrix.shape) > 0:
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a = (iou_matrix > iou_threshold).astype(np.int32)
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if a.sum(1).max() == 1 and a.sum(0).max() == 1:
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matched_indices = np.stack(np.where(a), axis=1)
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else:
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matched_indices = linear_assignment(-iou_matrix)
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else:
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matched_indices = np.empty(shape=(0, 2))
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unmatched_detections = []
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for d, det in enumerate(detections):
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if d not in matched_indices[:, 0]:
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unmatched_detections.append(d)
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unmatched_trackers = []
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for t, trk in enumerate(trackers):
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if t not in matched_indices[:, 1]:
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unmatched_trackers.append(t)
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matches = []
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for m in matched_indices:
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if iou_matrix[m[0], m[1]] < iou_threshold:
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unmatched_detections.append(m[0])
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unmatched_trackers.append(m[1])
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else:
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matches.append(m.reshape(1, 2))
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if len(matches) == 0:
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matches = np.empty((0, 2), dtype=int)
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else:
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matches = np.concatenate(matches, axis=0)
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return matches, np.array(unmatched_detections), np.array(unmatched_trackers)
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