import numpy as np from scipy.optimize import linear_sum_assignment from filterpy.kalman import KalmanFilter def linear_assignment(cost_matrix): x, y = linear_sum_assignment(cost_matrix) return np.array(list(zip(x, y))) def iou_batch(bb_test, bb_gt): """ From SORT: Computes IOU between two bboxes in the form [x1,y1,x2,y2] """ bb_test = np.expand_dims(bb_test, 1) bb_gt = np.expand_dims(bb_gt, 0) xx1 = np.maximum(bb_test[..., 0], bb_gt[..., 0]) yy1 = np.maximum(bb_test[..., 1], bb_gt[..., 1]) xx2 = np.minimum(bb_test[..., 2], bb_gt[..., 2]) yy2 = np.minimum(bb_test[..., 3], bb_gt[..., 3]) w = np.maximum(0., xx2 - xx1) h = np.maximum(0., yy2 - yy1) wh = w * h o = wh / ((bb_test[..., 2] - bb_test[..., 0]) * (bb_test[..., 3] - bb_test[..., 1]) + (bb_gt[..., 2] - bb_gt[..., 0]) * (bb_gt[..., 3] - bb_gt[..., 1]) - wh) return o def convert_bbox_to_z(bbox): """ Takes a bounding box in the form [x1,y1,x2,y2] and returns z in the form [x,y,s,r] where x,y is the centre of the box and s is the scale/area and r is the aspect ratio """ w = bbox[2] - bbox[0] h = bbox[3] - bbox[1] x = bbox[0] + w / 2. y = bbox[1] + h / 2. s = w * h # scale is just area r = w / float(h) return np.array([x, y, s, r]).reshape((4, 1)) def convert_x_to_bbox(x, score=None): """ Takes a bounding box in the centre form [x,y,s,r] and returns it in the form [x1,y1,x2,y2] where x1,y1 is the top left and x2,y2 is the bottom right """ w = np.sqrt(x[2] * x[3]) h = x[2] / w if score is None: return np.array([x[0] - w / 2., x[1] - h / 2., x[0] + w / 2., x[1] + h / 2.]).reshape((1, 4)) else: return np.array([x[0] - w / 2., x[1] - h / 2., x[0] + w / 2., x[1] + h / 2., score]).reshape((1, 5)) class KalmanBoxTracker(object): """ This class represents the internal state of individual tracked objects observed as bbox. """ count = 0 def __init__(self, bbox): """ Initialises a tracker using initial bounding box. """ self.kf = KalmanFilter(dim_x=7, dim_z=4) self.kf.F = np.array([[1, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1]]) self.kf.H = np.array([[1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0]]) self.kf.R[2:, 2:] *= 10. self.kf.P[4:, 4:] *= 1000. # give high uncertainty to the unobservable initial velocities self.kf.P *= 10. self.kf.Q[-1, -1] *= 0.01 self.kf.Q[4:, 4:] *= 0.01 self.kf.x[:4] = convert_bbox_to_z(bbox) self.time_since_update = 0 self.id = KalmanBoxTracker.count KalmanBoxTracker.count += 1 self.history = [] self.hits = 0 self.hit_streak = 0 self.age = 0 def update(self, bbox): """ Updates the state vector with observed bbox. """ self.time_since_update = 0 self.history = [] self.hits += 1 self.hit_streak += 1 self.kf.update(convert_bbox_to_z(bbox)) def predict(self): """ Advances the state vector and returns the predicted bounding box estimate. """ if (self.kf.x[6] + self.kf.x[2]) <= 0: self.kf.x[6] *= 0.0 self.kf.predict() self.age += 1 if self.time_since_update > 0: self.hit_streak = 0 self.time_since_update += 1 self.history.append(convert_x_to_bbox(self.kf.x)) return self.history[-1] def get_state(self): """ Returns the current bounding box estimate. """ return convert_x_to_bbox(self.kf.x) class Sort(object): def __init__(self, max_age=5, min_hits=2, iou_threshold=0.3): """ Sets key parameters for SORT """ self.max_age = max_age self.min_hits = min_hits self.iou_threshold = iou_threshold self.trackers = [] self.frame_count = 0 def update(self, dets=np.empty((0, 5))): """ Params: dets - a numpy array of detections in the format [[x1,y1,x2,y2,score],...] Requires: this method must be called once for each frame even with empty detections. Returns the a similar array, where the last column is the object ID. NOTE: The number of objects returned may differ from the number of detections provided. """ self.frame_count += 1 trks = np.zeros((len(self.trackers), 5)) to_del = [] ret = [] for t, trk in enumerate(trks): pos = self.trackers[t].predict()[0] trk[:] = [pos[0], pos[1], pos[2], pos[3], 0] if np.any(np.isnan(pos)): to_del.append(t) trks = np.ma.compress_rows(np.ma.masked_invalid(trks)) for t in reversed(to_del): self.trackers.pop(t) matched, unmatched_dets, unmatched_trks = associate_detections_to_trackers(dets, trks, self.iou_threshold) # update matched trackers with assigned detections for m in matched: self.trackers[m[1]].update(dets[m[0], :]) # create and initialise new trackers for unmatched detections for i in unmatched_dets: trk = KalmanBoxTracker(dets[i, :]) self.trackers.append(trk) i = len(self.trackers) for trk in reversed(self.trackers): d = trk.get_state()[0] if (trk.time_since_update < 1) and (trk.hit_streak >= self.min_hits or self.frame_count <= self.min_hits): ret.append(np.concatenate((d, [trk.id + 1])).reshape(1, -1)) # +1 as MOT benchmark requires positive i -= 1 # remove dead tracklet if trk.time_since_update > self.max_age: self.trackers.pop(i) if len(ret) > 0: return np.concatenate(ret) return np.empty((0, 5)) 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, unmatched_trackers """ if len(trackers) == 0: return np.empty((0, 2), dtype=int), np.arange(len(detections)), np.empty((0, 1), 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) 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)