├── __init__.py ├── README.md ├── __pycache__ ├── track.cpython-35.pyc ├── track.cpython-37.pyc ├── __init__.cpython-35.pyc ├── __init__.cpython-37.pyc ├── tracker.cpython-35.pyc ├── tracker.cpython-37.pyc ├── detection.cpython-35.pyc ├── detection.cpython-37.pyc ├── iou_matching.cpython-35.pyc ├── iou_matching.cpython-37.pyc ├── kalman_filter.cpython-35.pyc ├── kalman_filter.cpython-37.pyc ├── nn_matching.cpython-35.pyc ├── nn_matching.cpython-37.pyc ├── linear_assignment.cpython-35.pyc └── linear_assignment.cpython-37.pyc ├── detection.py ├── iou_matching.py ├── track.py ├── tracker.py ├── nn_matching.py ├── linear_assignment.py ├── kalman_filter.py └── LICENSE /__init__.py: -------------------------------------------------------------------------------- 1 | # vim: expandtab:ts=4:sw=4 2 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # deepsort-IMM 2 | Improve the Kalman-Filter in deepsort with IMM 3 | -------------------------------------------------------------------------------- /__pycache__/track.cpython-35.pyc: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/EricBooob/deepsort-IMM/HEAD/__pycache__/track.cpython-35.pyc -------------------------------------------------------------------------------- /__pycache__/track.cpython-37.pyc: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/EricBooob/deepsort-IMM/HEAD/__pycache__/track.cpython-37.pyc -------------------------------------------------------------------------------- /__pycache__/__init__.cpython-35.pyc: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/EricBooob/deepsort-IMM/HEAD/__pycache__/__init__.cpython-35.pyc 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-------------------------------------------------------------------------------- https://raw.githubusercontent.com/EricBooob/deepsort-IMM/HEAD/__pycache__/linear_assignment.cpython-37.pyc -------------------------------------------------------------------------------- /detection.py: -------------------------------------------------------------------------------- 1 | # vim: expandtab:ts=4:sw=4 2 | import numpy as np 3 | 4 | 5 | class Detection(object): 6 | """ 7 | This class represents a bounding box detection in a single image. 8 | 9 | Parameters 10 | ---------- 11 | tlwh : array_like 12 | Bounding box in format `(x, y, w, h)`. 13 | confidence : float 14 | Detector confidence score. 15 | feature : array_like 16 | A feature vector that describes the object contained in this image. 17 | 18 | Attributes 19 | ---------- 20 | tlwh : ndarray 21 | Bounding box in format `(top left x, top left y, width, height)`. 22 | confidence : ndarray 23 | Detector confidence score. 24 | feature : ndarray | NoneType 25 | A feature vector that describes the object contained in this image. 26 | 27 | """ 28 | 29 | def __init__(self, tlwh, confidence, feature): 30 | self.tlwh = np.asarray(tlwh, dtype=np.float) 31 | self.confidence = float(confidence) 32 | self.feature = np.asarray(feature, dtype=np.float32) 33 | 34 | def to_tlbr(self): 35 | """Convert bounding box to format `(min x, min y, max x, max y)`, i.e., 36 | `(top left, bottom right)`. 37 | """ 38 | ret = self.tlwh.copy() 39 | ret[2:] += ret[:2] 40 | return ret 41 | 42 | def to_xyah(self): 43 | """Convert bounding box to format `(center x, center y, aspect ratio, 44 | height)`, where the aspect ratio is `width / height`. 45 | """ 46 | ret = self.tlwh.copy() 47 | ret[:2] += ret[2:] / 2 48 | ret[2] /= ret[3] 49 | return ret 50 | -------------------------------------------------------------------------------- /iou_matching.py: -------------------------------------------------------------------------------- 1 | # vim: expandtab:ts=4:sw=4 2 | from __future__ import absolute_import 3 | import numpy as np 4 | from . import linear_assignment 5 | 6 | 7 | def iou(bbox, candidates): 8 | """Computer intersection over union. 9 | 10 | Parameters 11 | ---------- 12 | bbox : ndarray 13 | A bounding box in format `(top left x, top left y, width, height)`. 14 | candidates : ndarray 15 | A matrix of candidate bounding boxes (one per row) in the same format 16 | as `bbox`. 17 | 18 | Returns 19 | ------- 20 | ndarray 21 | The intersection over union in [0, 1] between the `bbox` and each 22 | candidate. A higher score means a larger fraction of the `bbox` is 23 | occluded by the candidate. 24 | 25 | """ 26 | bbox_tl, bbox_br = bbox[:2], bbox[:2] + bbox[2:] 27 | candidates_tl = candidates[:, :2] 28 | candidates_br = candidates[:, :2] + candidates[:, 2:] 29 | 30 | tl = np.c_[np.maximum(bbox_tl[0], candidates_tl[:, 0])[:, np.newaxis], 31 | np.maximum(bbox_tl[1], candidates_tl[:, 1])[:, np.newaxis]] 32 | br = np.c_[np.minimum(bbox_br[0], candidates_br[:, 0])[:, np.newaxis], 33 | np.minimum(bbox_br[1], candidates_br[:, 1])[:, np.newaxis]] 34 | wh = np.maximum(0., br - tl) 35 | 36 | area_intersection = wh.prod(axis=1) 37 | area_bbox = bbox[2:].prod() 38 | area_candidates = candidates[:, 2:].prod(axis=1) 39 | return area_intersection / (area_bbox + area_candidates - area_intersection) 40 | 41 | 42 | def iou_cost(tracks, detections, track_indices=None, 43 | detection_indices=None): 44 | """An intersection over union distance metric. 45 | 46 | Parameters 47 | ---------- 48 | tracks : List[deep_sort.track.Track] 49 | A list of tracks. 50 | detections : List[deep_sort.detection.Detection] 51 | A list of detections. 52 | track_indices : Optional[List[int]] 53 | A list of indices to tracks that should be matched. Defaults to 54 | all `tracks`. 55 | detection_indices : Optional[List[int]] 56 | A list of indices to detections that should be matched. Defaults 57 | to all `detections`. 58 | 59 | Returns 60 | ------- 61 | ndarray 62 | Returns a cost matrix of shape 63 | len(track_indices), len(detection_indices) where entry (i, j) is 64 | `1 - iou(tracks[track_indices[i]], detections[detection_indices[j]])`. 65 | 66 | """ 67 | if track_indices is None: 68 | track_indices = np.arange(len(tracks)) 69 | if detection_indices is None: 70 | detection_indices = np.arange(len(detections)) 71 | 72 | cost_matrix = np.zeros((len(track_indices), len(detection_indices))) 73 | for row, track_idx in enumerate(track_indices): 74 | if tracks[track_idx].time_since_update > 1: 75 | cost_matrix[row, :] = linear_assignment.INFTY_COST 76 | continue 77 | 78 | bbox = tracks[track_idx].to_tlwh() 79 | candidates = np.asarray([detections[i].tlwh for i in detection_indices]) 80 | cost_matrix[row, :] = 1. - iou(bbox, candidates) 81 | return cost_matrix 82 | -------------------------------------------------------------------------------- /track.py: -------------------------------------------------------------------------------- 1 | # vim: expandtab:ts=4:sw=4 2 | 3 | 4 | class TrackState: 5 | """ 6 | Enumeration type for the single target track state. Newly created tracks are 7 | classified as `tentative` until enough evidence has been collected. Then, 8 | the track state is changed to `confirmed`. Tracks that are no longer alive 9 | are classified as `deleted` to mark them for removal from the set of active 10 | tracks. 11 | 12 | """ 13 | 14 | Tentative = 1 15 | Confirmed = 2 16 | Deleted = 3 17 | 18 | 19 | class Track: 20 | """ 21 | A single target track with state space `(x, y, a, h)` and associated 22 | velocities, where `(x, y)` is the center of the bounding box, `a` is the 23 | aspect ratio and `h` is the height. 24 | 25 | Parameters 26 | ---------- 27 | mean : ndarray 28 | Mean vector of the initial state distribution. 29 | covariance : ndarray 30 | Covariance matrix of the initial state distribution. 31 | track_id : int 32 | A unique track identifier. 33 | n_init : int 34 | Number of consecutive detections before the track is confirmed. The 35 | track state is set to `Deleted` if a miss occurs within the first 36 | `n_init` frames. 37 | max_age : int 38 | The maximum number of consecutive misses before the track state is 39 | set to `Deleted`. 40 | feature : Optional[ndarray] 41 | Feature vector of the detection this track originates from. If not None, 42 | this feature is added to the `features` cache. 43 | 44 | Attributes 45 | ---------- 46 | mean : ndarray 47 | Mean vector of the initial state distribution. 48 | covariance : ndarray 49 | Covariance matrix of the initial state distribution. 50 | track_id : int 51 | A unique track identifier. 52 | hits : int 53 | Total number of measurement updates. 54 | age : int 55 | Total number of frames since first occurance. 56 | time_since_update : int 57 | Total number of frames since last measurement update. 58 | state : TrackState 59 | The current track state. 60 | features : List[ndarray] 61 | A cache of features. On each measurement update, the associated feature 62 | vector is added to this list. 63 | 64 | """ 65 | 66 | def __init__(self, mean, covariance, track_id, n_init, max_age, feature=None): 67 | self.mean = mean 68 | self.covariance = covariance 69 | # self.mean1 = mean1 70 | # self.covariance1 = covariance1 71 | # self.mean2 = mean2 72 | # self.covariance2 = covariance2 73 | self.track_id = track_id 74 | self.hits = 1 75 | self.age = 1 76 | self.time_since_update = 0 77 | 78 | self.state = TrackState.Tentative 79 | self.features = [] 80 | if feature is not None: 81 | self.features.append(feature) 82 | 83 | self._n_init = n_init 84 | self._max_age = max_age 85 | 86 | def to_tlwh(self): 87 | """Get current position in bounding box format `(top left x, top left y, 88 | width, height)`. 89 | 90 | Returns 91 | ------- 92 | ndarray 93 | The bounding box. 94 | 95 | """ 96 | ret = self.mean[:4].copy() 97 | ret[2] *= ret[3] 98 | ret[:2] -= ret[2:] / 2 99 | return ret 100 | 101 | def to_tlbr(self): 102 | """Get current position in bounding box format `(min x, miny, max x, 103 | max y)`. 104 | 105 | Returns 106 | ------- 107 | ndarray 108 | The bounding box. 109 | 110 | """ 111 | ret = self.to_tlwh() 112 | ret[2:] = ret[:2] + ret[2:] 113 | return ret 114 | 115 | def predict(self, kf): 116 | """Propagate the state distribution to the current time step using a 117 | Kalman filter prediction step. 118 | 119 | Parameters 120 | ---------- 121 | kf : kalman_filter.KalmanFilter 122 | The Kalman filter. 123 | 124 | """ 125 | self.mean, self.covariance = kf.predict(self.mean, self.covariance) 126 | 127 | self.age += 1 128 | self.time_since_update += 1 129 | 130 | def update(self, kf, detection): 131 | """Perform Kalman filter measurement update step and update the feature 132 | cache. 133 | 134 | Parameters 135 | ---------- 136 | kf : kalman_filter.KalmanFilter 137 | The Kalman filter. 138 | detection : Detection 139 | The associated detection. 140 | 141 | """ 142 | self.mean, self.covariance = kf.update(self.mean, self.covariance, detection.to_xyah()) 143 | self.features.append(detection.feature) 144 | 145 | self.hits += 1 146 | self.time_since_update = 0 147 | if self.state == TrackState.Tentative and self.hits >= self._n_init: 148 | self.state = TrackState.Confirmed 149 | 150 | def mark_missed(self): 151 | """Mark this track as missed (no association at the current time step). 152 | """ 153 | if self.state == TrackState.Tentative: 154 | self.state = TrackState.Deleted 155 | elif self.time_since_update > self._max_age: 156 | self.state = TrackState.Deleted 157 | 158 | def is_tentative(self): 159 | """Returns True if this track is tentative (unconfirmed). 160 | """ 161 | return self.state == TrackState.Tentative 162 | 163 | def is_confirmed(self): 164 | """Returns True if this track is confirmed.""" 165 | return self.state == TrackState.Confirmed 166 | 167 | def is_deleted(self): 168 | """Returns True if this track is dead and should be deleted.""" 169 | return self.state == TrackState.Deleted 170 | -------------------------------------------------------------------------------- /tracker.py: -------------------------------------------------------------------------------- 1 | # vim: expandtab:ts=4:sw=4 2 | from __future__ import absolute_import 3 | import numpy as np 4 | from . import kalman_filter 5 | from . import linear_assignment 6 | from . import iou_matching 7 | from .track import Track 8 | 9 | 10 | class Tracker: 11 | """ 12 | This is the multi-target tracker. 13 | 14 | Parameters 15 | ---------- 16 | metric : nn_matching.NearestNeighborDistanceMetric 17 | A distance metric for measurement-to-track association. 18 | max_age : int 19 | Maximum number of missed misses before a track is deleted. 20 | n_init : int 21 | Number of consecutive detections before the track is confirmed. The 22 | track state is set to `Deleted` if a miss occurs within the first 23 | `n_init` frames. 24 | 25 | Attributes 26 | ---------- 27 | metric : nn_matching.NearestNeighborDistanceMetric 28 | The distance metric used for measurement to track association. 29 | max_age : int 30 | Maximum number of missed misses before a track is deleted. 31 | n_init : int 32 | Number of frames that a track remains in initialization phase. 33 | kf : kalman_filter.KalmanFilter 34 | A Kalman filter to filter target trajectories in image space. 35 | tracks : List[Track] 36 | The list of active tracks at the current time step. 37 | 38 | """ 39 | 40 | def __init__(self, metric, max_iou_distance=0.7, max_age=30, n_init=3): 41 | self.metric = metric 42 | self.max_iou_distance = max_iou_distance 43 | self.max_age = max_age 44 | self.n_init = n_init 45 | 46 | self.kf = kalman_filter.KalmanFilter() 47 | self.tracks = [] 48 | self._next_id = 1 49 | 50 | def predict(self): 51 | """Propagate track state distributions one time step forward. 52 | 53 | This function should be called once every time step, before `update`. 54 | """ 55 | for track in self.tracks: 56 | track.predict(self.kf) 57 | 58 | def update(self, detections): 59 | """Perform measurement update and track management. 60 | 61 | Parameters 62 | ---------- 63 | detections : List[deep_sort.detection.Detection] 64 | A list of detections at the current time step. 65 | 66 | """ 67 | # Run matching cascade. 68 | matches, unmatched_tracks, unmatched_detections = \ 69 | self._match(detections) 70 | 71 | # Update track set. 72 | for track_idx, detection_idx in matches: 73 | self.tracks[track_idx].update( 74 | self.kf, detections[detection_idx]) 75 | for track_idx in unmatched_tracks: 76 | self.tracks[track_idx].mark_missed() 77 | for detection_idx in unmatched_detections: 78 | self._initiate_track(detections[detection_idx]) 79 | self.tracks = [t for t in self.tracks if not t.is_deleted()] 80 | 81 | # Update distance metric. 82 | active_targets = [t.track_id for t in self.tracks if t.is_confirmed()] 83 | features, targets = [], [] 84 | for track in self.tracks: 85 | if not track.is_confirmed(): 86 | continue 87 | features += track.features 88 | targets += [track.track_id for _ in track.features] 89 | track.features = [] 90 | self.metric.partial_fit( 91 | np.asarray(features), np.asarray(targets), active_targets) 92 | 93 | def _match(self, detections): 94 | 95 | def gated_metric(tracks, dets, track_indices, detection_indices): 96 | features = np.array([dets[i].feature for i in detection_indices]) 97 | targets = np.array([tracks[i].track_id for i in track_indices]) 98 | cost_matrix = self.metric.distance(features, targets) 99 | cost_matrix = linear_assignment.gate_cost_matrix( 100 | self.kf, cost_matrix, tracks, dets, track_indices, 101 | detection_indices) 102 | 103 | return cost_matrix 104 | 105 | # Split track set into confirmed and unconfirmed tracks. 106 | confirmed_tracks = [ 107 | i for i, t in enumerate(self.tracks) if t.is_confirmed()] 108 | unconfirmed_tracks = [ 109 | i for i, t in enumerate(self.tracks) if not t.is_confirmed()] 110 | 111 | # Associate confirmed tracks using appearance features. 112 | matches_a, unmatched_tracks_a, unmatched_detections = \ 113 | linear_assignment.matching_cascade( 114 | gated_metric, self.metric.matching_threshold, self.max_age, 115 | self.tracks, detections, confirmed_tracks) 116 | 117 | # Associate remaining tracks together with unconfirmed tracks using IOU. 118 | iou_track_candidates = unconfirmed_tracks + [ 119 | k for k in unmatched_tracks_a if 120 | self.tracks[k].time_since_update == 1] 121 | unmatched_tracks_a = [ 122 | k for k in unmatched_tracks_a if 123 | self.tracks[k].time_since_update != 1] 124 | matches_b, unmatched_tracks_b, unmatched_detections = \ 125 | linear_assignment.min_cost_matching( 126 | iou_matching.iou_cost, self.max_iou_distance, self.tracks, 127 | detections, iou_track_candidates, unmatched_detections) 128 | 129 | matches = matches_a + matches_b 130 | unmatched_tracks = list(set(unmatched_tracks_a + unmatched_tracks_b)) 131 | return matches, unmatched_tracks, unmatched_detections 132 | 133 | def _initiate_track(self, detection): 134 | mean, covariance = self.kf.initiate(detection.to_xyah()) 135 | #, mean1, covariance1, mean2, covariance2 136 | self.tracks.append(Track( 137 | mean, covariance, self._next_id, self.n_init, self.max_age, detection.feature)) 138 | self._next_id += 1 139 | -------------------------------------------------------------------------------- /nn_matching.py: -------------------------------------------------------------------------------- 1 | # vim: expandtab:ts=4:sw=4 2 | import numpy as np 3 | 4 | 5 | def _pdist(a, b): 6 | """Compute pair-wise squared distance between points in `a` and `b`. 7 | 8 | Parameters 9 | ---------- 10 | a : array_like 11 | An NxM matrix of N samples of dimensionality M. 12 | b : array_like 13 | An LxM matrix of L samples of dimensionality M. 14 | 15 | Returns 16 | ------- 17 | ndarray 18 | Returns a matrix of size len(a), len(b) such that eleement (i, j) 19 | contains the squared distance between `a[i]` and `b[j]`. 20 | 21 | """ 22 | a, b = np.asarray(a), np.asarray(b) 23 | if len(a) == 0 or len(b) == 0: 24 | return np.zeros((len(a), len(b))) 25 | a2, b2 = np.square(a).sum(axis=1), np.square(b).sum(axis=1) 26 | r2 = -2. * np.dot(a, b.T) + a2[:, None] + b2[None, :] 27 | r2 = np.clip(r2, 0., float(np.inf)) 28 | return r2 29 | 30 | 31 | def _cosine_distance(a, b, data_is_normalized=False): 32 | """Compute pair-wise cosine distance between points in `a` and `b`. 33 | 34 | Parameters 35 | ---------- 36 | a : array_like 37 | An NxM matrix of N samples of dimensionality M. 38 | b : array_like 39 | An LxM matrix of L samples of dimensionality M. 40 | data_is_normalized : Optional[bool] 41 | If True, assumes rows in a and b are unit length vectors. 42 | Otherwise, a and b are explicitly normalized to lenght 1. 43 | 44 | Returns 45 | ------- 46 | ndarray 47 | Returns a matrix of size len(a), len(b) such that eleement (i, j) 48 | contains the squared distance between `a[i]` and `b[j]`. 49 | 50 | """ 51 | if not data_is_normalized: 52 | a = np.asarray(a) / np.linalg.norm(a, axis=1, keepdims=True) 53 | b = np.asarray(b) / np.linalg.norm(b, axis=1, keepdims=True) 54 | return 1. - np.dot(a, b.T) 55 | 56 | 57 | def _nn_euclidean_distance(x, y): 58 | """ Helper function for nearest neighbor distance metric (Euclidean). 59 | 60 | Parameters 61 | ---------- 62 | x : ndarray 63 | A matrix of N row-vectors (sample points). 64 | y : ndarray 65 | A matrix of M row-vectors (query points). 66 | 67 | Returns 68 | ------- 69 | ndarray 70 | A vector of length M that contains for each entry in `y` the 71 | smallest Euclidean distance to a sample in `x`. 72 | 73 | """ 74 | distances = _pdist(x, y) 75 | return np.maximum(0.0, distances.min(axis=0)) 76 | 77 | 78 | def _nn_cosine_distance(x, y): 79 | """ Helper function for nearest neighbor distance metric (cosine). 80 | 81 | Parameters 82 | ---------- 83 | x : ndarray 84 | A matrix of N row-vectors (sample points). 85 | y : ndarray 86 | A matrix of M row-vectors (query points). 87 | 88 | Returns 89 | ------- 90 | ndarray 91 | A vector of length M that contains for each entry in `y` the 92 | smallest cosine distance to a sample in `x`. 93 | 94 | """ 95 | distances = _cosine_distance(x, y) 96 | return distances.min(axis=0) 97 | 98 | 99 | class NearestNeighborDistanceMetric(object): 100 | """ 101 | A nearest neighbor distance metric that, for each target, returns 102 | the closest distance to any sample that has been observed so far. 103 | 104 | Parameters 105 | ---------- 106 | metric : str 107 | Either "euclidean" or "cosine". 108 | matching_threshold: float 109 | The matching threshold. Samples with larger distance are considered an 110 | invalid match. 111 | budget : Optional[int] 112 | If not None, fix samples per class to at most this number. Removes 113 | the oldest samples when the budget is reached. 114 | 115 | Attributes 116 | ---------- 117 | samples : Dict[int -> List[ndarray]] 118 | A dictionary that maps from target identities to the list of samples 119 | that have been observed so far. 120 | 121 | """ 122 | 123 | def __init__(self, metric, matching_threshold, budget=None): 124 | 125 | 126 | if metric == "euclidean": 127 | self._metric = _nn_euclidean_distance 128 | elif metric == "cosine": 129 | self._metric = _nn_cosine_distance 130 | else: 131 | raise ValueError( 132 | "Invalid metric; must be either 'euclidean' or 'cosine'") 133 | self.matching_threshold = matching_threshold 134 | self.budget = budget 135 | self.samples = {} 136 | 137 | def partial_fit(self, features, targets, active_targets): 138 | """Update the distance metric with new data. 139 | 140 | Parameters 141 | ---------- 142 | features : ndarray 143 | An NxM matrix of N features of dimensionality M. 144 | targets : ndarray 145 | An integer array of associated target identities. 146 | active_targets : List[int] 147 | A list of targets that are currently present in the scene. 148 | 149 | """ 150 | for feature, target in zip(features, targets): 151 | self.samples.setdefault(target, []).append(feature) 152 | if self.budget is not None: 153 | self.samples[target] = self.samples[target][-self.budget:] 154 | self.samples = {k: self.samples[k] for k in active_targets} 155 | 156 | def distance(self, features, targets): 157 | """Compute distance between features and targets. 158 | 159 | Parameters 160 | ---------- 161 | features : ndarray 162 | An NxM matrix of N features of dimensionality M. 163 | targets : List[int] 164 | A list of targets to match the given `features` against. 165 | 166 | Returns 167 | ------- 168 | ndarray 169 | Returns a cost matrix of shape len(targets), len(features), where 170 | element (i, j) contains the closest squared distance between 171 | `targets[i]` and `features[j]`. 172 | 173 | """ 174 | cost_matrix = np.zeros((len(targets), len(features))) 175 | for i, target in enumerate(targets): 176 | cost_matrix[i, :] = self._metric(self.samples[target], features) 177 | return cost_matrix 178 | -------------------------------------------------------------------------------- /linear_assignment.py: -------------------------------------------------------------------------------- 1 | # vim: expandtab:ts=4:sw=4 2 | from __future__ import absolute_import 3 | import numpy as np 4 | from sklearn.utils.linear_assignment_ import linear_assignment 5 | from . import kalman_filter 6 | 7 | 8 | INFTY_COST = 1e+5 9 | 10 | 11 | def min_cost_matching( 12 | distance_metric, max_distance, tracks, detections, track_indices=None, 13 | detection_indices=None): 14 | """Solve linear assignment problem. 15 | 16 | Parameters 17 | ---------- 18 | distance_metric : Callable[List[Track], List[Detection], List[int], List[int]) -> ndarray 19 | The distance metric is given a list of tracks and detections as well as 20 | a list of N track indices and M detection indices. The metric should 21 | return the NxM dimensional cost matrix, where element (i, j) is the 22 | association cost between the i-th track in the given track indices and 23 | the j-th detection in the given detection_indices. 24 | max_distance : float 25 | Gating threshold. Associations with cost larger than this value are 26 | disregarded. 27 | tracks : List[track.Track] 28 | A list of predicted tracks at the current time step. 29 | detections : List[detection.Detection] 30 | A list of detections at the current time step. 31 | track_indices : List[int] 32 | List of track indices that maps rows in `cost_matrix` to tracks in 33 | `tracks` (see description above). 34 | detection_indices : List[int] 35 | List of detection indices that maps columns in `cost_matrix` to 36 | detections in `detections` (see description above). 37 | 38 | Returns 39 | ------- 40 | (List[(int, int)], List[int], List[int]) 41 | Returns a tuple with the following three entries: 42 | * A list of matched track and detection indices. 43 | * A list of unmatched track indices. 44 | * A list of unmatched detection indices. 45 | 46 | """ 47 | if track_indices is None: 48 | track_indices = np.arange(len(tracks)) 49 | if detection_indices is None: 50 | detection_indices = np.arange(len(detections)) 51 | 52 | if len(detection_indices) == 0 or len(track_indices) == 0: 53 | return [], track_indices, detection_indices # Nothing to match. 54 | 55 | cost_matrix = distance_metric( 56 | tracks, detections, track_indices, detection_indices) 57 | cost_matrix[cost_matrix > max_distance] = max_distance + 1e-5 58 | indices = linear_assignment(cost_matrix) 59 | 60 | matches, unmatched_tracks, unmatched_detections = [], [], [] 61 | for col, detection_idx in enumerate(detection_indices): 62 | if col not in indices[:, 1]: 63 | unmatched_detections.append(detection_idx) 64 | for row, track_idx in enumerate(track_indices): 65 | if row not in indices[:, 0]: 66 | unmatched_tracks.append(track_idx) 67 | for row, col in indices: 68 | track_idx = track_indices[row] 69 | detection_idx = detection_indices[col] 70 | if cost_matrix[row, col] > max_distance: 71 | unmatched_tracks.append(track_idx) 72 | unmatched_detections.append(detection_idx) 73 | else: 74 | matches.append((track_idx, detection_idx)) 75 | return matches, unmatched_tracks, unmatched_detections 76 | 77 | 78 | def matching_cascade( 79 | distance_metric, max_distance, cascade_depth, tracks, detections, 80 | track_indices=None, detection_indices=None): 81 | """Run matching cascade. 82 | 83 | Parameters 84 | ---------- 85 | distance_metric : Callable[List[Track], List[Detection], List[int], List[int]) -> ndarray 86 | The distance metric is given a list of tracks and detections as well as 87 | a list of N track indices and M detection indices. The metric should 88 | return the NxM dimensional cost matrix, where element (i, j) is the 89 | association cost between the i-th track in the given track indices and 90 | the j-th detection in the given detection indices. 91 | max_distance : float 92 | Gating threshold. Associations with cost larger than this value are 93 | disregarded. 94 | cascade_depth: int 95 | The cascade depth, should be se to the maximum track age. 96 | tracks : List[track.Track] 97 | A list of predicted tracks at the current time step. 98 | detections : List[detection.Detection] 99 | A list of detections at the current time step. 100 | track_indices : Optional[List[int]] 101 | List of track indices that maps rows in `cost_matrix` to tracks in 102 | `tracks` (see description above). Defaults to all tracks. 103 | detection_indices : Optional[List[int]] 104 | List of detection indices that maps columns in `cost_matrix` to 105 | detections in `detections` (see description above). Defaults to all 106 | detections. 107 | 108 | Returns 109 | ------- 110 | (List[(int, int)], List[int], List[int]) 111 | Returns a tuple with the following three entries: 112 | * A list of matched track and detection indices. 113 | * A list of unmatched track indices. 114 | * A list of unmatched detection indices. 115 | 116 | """ 117 | if track_indices is None: 118 | track_indices = list(range(len(tracks))) 119 | if detection_indices is None: 120 | detection_indices = list(range(len(detections))) 121 | 122 | unmatched_detections = detection_indices 123 | matches = [] 124 | for level in range(cascade_depth): 125 | if len(unmatched_detections) == 0: # No detections left 126 | break 127 | 128 | track_indices_l = [ 129 | k for k in track_indices 130 | if tracks[k].time_since_update == 1 + level 131 | ] 132 | if len(track_indices_l) == 0: # Nothing to match at this level 133 | continue 134 | 135 | matches_l, _, unmatched_detections = \ 136 | min_cost_matching( 137 | distance_metric, max_distance, tracks, detections, 138 | track_indices_l, unmatched_detections) 139 | matches += matches_l 140 | unmatched_tracks = list(set(track_indices) - set(k for k, _ in matches)) 141 | return matches, unmatched_tracks, unmatched_detections 142 | 143 | 144 | def gate_cost_matrix( 145 | kf, cost_matrix, tracks, detections, track_indices, detection_indices, 146 | gated_cost=INFTY_COST, only_position=False): 147 | """Invalidate infeasible entries in cost matrix based on the state 148 | distributions obtained by Kalman filtering. 149 | 150 | Parameters 151 | ---------- 152 | kf : The Kalman filter. 153 | cost_matrix : ndarray 154 | The NxM dimensional cost matrix, where N is the number of track indices 155 | and M is the number of detection indices, such that entry (i, j) is the 156 | association cost between `tracks[track_indices[i]]` and 157 | `detections[detection_indices[j]]`. 158 | tracks : List[track.Track] 159 | A list of predicted tracks at the current time step. 160 | detections : List[detection.Detection] 161 | A list of detections at the current time step. 162 | track_indices : List[int] 163 | List of track indices that maps rows in `cost_matrix` to tracks in 164 | `tracks` (see description above). 165 | detection_indices : List[int] 166 | List of detection indices that maps columns in `cost_matrix` to 167 | detections in `detections` (see description above). 168 | gated_cost : Optional[float] 169 | Entries in the cost matrix corresponding to infeasible associations are 170 | set this value. Defaults to a very large value. 171 | only_position : Optional[bool] 172 | If True, only the x, y position of the state distribution is considered 173 | during gating. Defaults to False. 174 | 175 | Returns 176 | ------- 177 | ndarray 178 | Returns the modified cost matrix. 179 | 180 | """ 181 | gating_dim = 2 if only_position else 4 182 | gating_threshold = kalman_filter.chi2inv95[gating_dim] 183 | measurements = np.asarray( 184 | [detections[i].to_xyah() for i in detection_indices]) 185 | for row, track_idx in enumerate(track_indices): 186 | track = tracks[track_idx] 187 | gating_distance = kf.gating_distance( 188 | track.mean, track.covariance, measurements, only_position) 189 | cost_matrix[row, gating_distance > gating_threshold] = gated_cost 190 | return cost_matrix 191 | -------------------------------------------------------------------------------- /kalman_filter.py: -------------------------------------------------------------------------------- 1 | # vim: expandtab:ts=4:sw=4 2 | import numpy as np 3 | import scipy.linalg 4 | 5 | 6 | """ 7 | Table for the 0.95 quantile of the chi-square distribution with N degrees of 8 | freedom (contains values for N=1, ..., 9). Taken from MATLAB/Octave's chi2inv 9 | function and used as Mahalanobis gating threshold. 10 | """ 11 | chi2inv95 = { 12 | 1: 3.8415, 13 | 2: 5.9915, 14 | 3: 7.8147, 15 | 4: 9.4877, 16 | 5: 11.070, 17 | 6: 12.592, 18 | 7: 14.067, 19 | 8: 15.507, 20 | 9: 16.919} 21 | 22 | 23 | class KalmanFilter(object): 24 | """ 25 | A simple Kalman filter for tracking bounding boxes in image space. 26 | 27 | The 8-dimensional state space 28 | 29 | x, y, a, h, vx, vy, va, vh 30 | 31 | contains the bounding box center position (x, y), aspect ratio a, height h, 32 | and their respective velocities. 33 | 34 | Object motion follows a constant velocity model. The bounding box location 35 | (x, y, a, h) is taken as direct observation of the state space (linear 36 | observation model). 37 | 38 | """ 39 | 40 | def __init__(self): 41 | ndim, dt, alpha, zero = 4, 1., 0.5, 0 42 | # Create Kalman filter model matrices 1 constant velocity model. 43 | self._motion_mat1 = np.eye(3 * ndim, 3 * ndim) 44 | for i in range(ndim): 45 | self._motion_mat1[i, ndim + i] = dt 46 | for i in range(ndim): 47 | self._motion_mat1[2 * ndim + i, 2 * ndim + i] = zero 48 | self._update_mat1 = np.eye(2 * ndim, 3 * ndim) 49 | a = self._motion_mat1 50 | b = self._update_mat1 51 | # Create Kalman filter model matrices 2 constant acceleration model. 52 | self._motion_mat2 = np.eye(3 * ndim, 3 * ndim) 53 | c = self._motion_mat2 54 | for i in range(2 * ndim): 55 | self._motion_mat2[i, ndim + i] = dt 56 | for i in range(ndim): 57 | self._motion_mat2[i, 2 * ndim + i] = alpha 58 | self._update_mat2 = np.eye(2*ndim, 3 * ndim) 59 | d = self._update_mat2 60 | # Motion and observation uncertainty are chosen relative to the current 61 | # state estimate. These weights control the amount of uncertainty in 62 | # the model. This is a bit hacky. 63 | self._std_weight_position = 1. / 20 64 | self._std_weight_velocity1 = 1. / 160 65 | self._std_weight_velocity2 = 1. / 20 66 | self._std_weight_acceleration = 1. / 160 67 | # self.imm_weightCV = 0.5 68 | # self.imm_weightCA = 0.5 69 | # self.imm_paraCT = CT model weight 70 | self.imm_weight = np.array([0.1, 0.9]) 71 | 72 | def initiate(self, measurement): 73 | """Create track from unassociated measurement. 74 | 75 | Parameters 76 | ---------- 77 | measurement : ndarray 78 | Bounding box coordinates (x, y, a, h) with center position (x, y), 79 | aspect ratio a, and height h. 80 | 81 | Returns 82 | ------- 83 | (ndarray, ndarray) 84 | Returns the mean vector (8 dimensional) and covariance matrix (8x8 85 | dimensional) of the new track. Unobserved velocities are initialized 86 | to 0 mean. 87 | 88 | """ 89 | mean_pos = measurement 90 | mean_vel = np.zeros_like(mean_pos) 91 | mean_acc = np.zeros_like(mean_vel) 92 | mean_zero = np.zeros_like(mean_acc) 93 | mean1 = np.r_[mean_pos, mean_vel, mean_zero] 94 | mean2 = np.r_[mean_pos, mean_vel, mean_acc] 95 | 96 | std1 = [ 97 | 2 * self._std_weight_position * measurement[3], 98 | 2 * self._std_weight_position * measurement[3], 99 | 1e-2, 100 | 2 * self._std_weight_position * measurement[3], 101 | 10 * self._std_weight_velocity1 * measurement[3], 102 | 10 * self._std_weight_velocity1 * measurement[3], 103 | 1e-5, 104 | 10 * self._std_weight_velocity1 * measurement[3], 0, 0, 0, 0] 105 | 106 | std2 = [ 107 | 2 * self._std_weight_position * measurement[3], 108 | 2 * self._std_weight_position * measurement[3], 109 | 1e-2, 110 | 2 * self._std_weight_position * measurement[3], 111 | 2 * self._std_weight_velocity2 * measurement[3], 112 | 2 * self._std_weight_velocity2 * measurement[3], 113 | 1e-2, 114 | 2 * self._std_weight_velocity2 * measurement[3], 115 | 10 * self._std_weight_acceleration * measurement[3], 116 | 10 * self._std_weight_acceleration * measurement[3], 117 | 1e-5, 118 | 10 * self._std_weight_acceleration * measurement[3]] 119 | covariance1 = np.diag(np.square(std1)) 120 | covariance2 = np.diag(np.square(std2)) 121 | mean = mean2 122 | # mean = self.imm_weight[0] * mean1 + self.imm_weight[1] * mean2 123 | # covariance = self.imm_weight[0] * covariance1 + self.imm_weight[1] * covariance2 124 | covariance = covariance2 125 | 126 | # covariance = self.imm_weight[0] * (covariance1 + (mean1 - mean) * (mean1 - mean).T) +\ 127 | # self.imm_weight[1] * (covariance2 + (mean2 - mean) * (mean2 - mean).T) 128 | return mean, covariance 129 | 130 | def predict(self, mean, covariance): 131 | 132 | """Run Kalman filter prediction step. 133 | 134 | Parameters 135 | ---------- 136 | mean : ndarray 137 | The 12 dimensional mean vector of the object state at the previous 138 | time step. 139 | covariance : ndarray 140 | The 8x8 dimensional covariance matrix of the object state at the 141 | previous time step. 142 | 143 | Returns 144 | ------- 145 | (ndarray, ndarray) 146 | Returns the mean vector and covariance matrix of the predicted 147 | state. Unobserved velocities are initialized to 0 mean. 148 | 149 | """ 150 | std_pos = [ 151 | self._std_weight_position * mean[3], 152 | self._std_weight_position * mean[3], 153 | 1e-2, 154 | self._std_weight_position * mean[3]] 155 | std_vel1 = [ 156 | self._std_weight_velocity1 * mean[3], 157 | self._std_weight_velocity1 * mean[3], 158 | 1e-2, 159 | self._std_weight_velocity1 * mean[3]] 160 | std_vel2 = [ 161 | self._std_weight_velocity2 * mean[3], 162 | self._std_weight_velocity2 * mean[3], 163 | 1e-5, 164 | self._std_weight_velocity2 * mean[3]] 165 | std_acc = [ 166 | self._std_weight_acceleration * mean[3], 167 | self._std_weight_acceleration * mean[3], 168 | 1e-5, 169 | self._std_weight_acceleration * mean[3]] 170 | std_zero = [0, 0, 0, 0] 171 | motion_cov1 = np.diag(np.square(np.r_[std_pos, std_vel1, std_zero])) 172 | motion_cov2 = np.diag(np.square(np.r_[std_pos, std_vel2, std_acc])) 173 | 174 | # a = mean 175 | 176 | mean1 = np.dot(self._motion_mat1, mean) 177 | mean2 = np.dot(self._motion_mat2, mean) 178 | covariance1 = np.linalg.multi_dot(( 179 | self._motion_mat1, covariance, self._motion_mat1.T)) + motion_cov1 180 | covariance2 = np.linalg.multi_dot(( 181 | self._motion_mat2, covariance, self._motion_mat2.T)) + motion_cov2 182 | 183 | mean = self.imm_weight[0] * mean1 + self.imm_weight[1] * mean2 184 | covariance = self.imm_weight[0] * covariance1 + self.imm_weight[1] * covariance2 185 | # covariance = self.imm_weight[0] * (covariance1 + (mean1 - mean) * (mean1 - mean).T) + \ 186 | # self.imm_weight[1] * (covariance2 + (mean2 - mean) * (mean2 - mean).T) 187 | 188 | return mean, covariance 189 | 190 | def project(self, mean, covariance): 191 | """Project state distribution to measurement space. 192 | 193 | Parameters 194 | ---------- 195 | mean : ndarray 196 | The state's mean vector (12 dimensional array). 197 | covariance : ndarray 198 | The state's covariance matrix (12x12 dimensional). 199 | 200 | Returns 201 | ------- 202 | (ndarray, ndarray) 203 | Returns the projected mean and covariance matrix of the given state 204 | estimate. 205 | 206 | """ 207 | std1 = [ 208 | self._std_weight_position * mean[3], 209 | self._std_weight_position * mean[3], 210 | 1e-1, 211 | self._std_weight_position * mean[3], 0, 0, 0, 0] 212 | 213 | std2 = [ 214 | self._std_weight_position * mean[3], 215 | self._std_weight_position * mean[3], 216 | 1e-1, 217 | self._std_weight_position * mean[3], 218 | self._std_weight_velocity2 * mean[3], 219 | self._std_weight_velocity2 * mean[3], 220 | 1e-1, 221 | self._std_weight_velocity2 * mean[3]] 222 | 223 | innovation_cov1 = np.diag(np.square(std1)) 224 | innovation_cov2 = np.diag(np.square(std2)) 225 | 226 | mean1 = np.dot(self._update_mat1, mean) 227 | mean2 = np.dot(self._update_mat2, mean) 228 | 229 | covariance1 = np.linalg.multi_dot(( 230 | self._update_mat1, covariance, self._update_mat1.T)) 231 | 232 | covariance2 = np.linalg.multi_dot(( 233 | self._update_mat2, covariance, self._update_mat2.T)) 234 | 235 | return mean1, covariance1 + innovation_cov1, mean2, covariance2 + innovation_cov2 236 | 237 | def update(self, mean, covariance, measurement): 238 | """Run Kalman filter correction step. 239 | 240 | Parameters 241 | ---------- 242 | mean : ndarray 243 | The predicted state's mean vector (8 dimensional). 244 | covariance : ndarray 245 | The state's covariance matrix (8x8 dimensional). 246 | measurement : ndarray 247 | The 8 dimensional measurement vector (x, y, a, h), where (x, y) 248 | is the center position, a the aspect ratio, and h the height of the 249 | bounding box. 250 | 251 | Returns 252 | ------- 253 | (ndarray, ndarray) 254 | Returns the measurement-corrected state distribution. 255 | 256 | """ 257 | projected_mean1, projected_cov1, projected_mean2, projected_cov2 = self.project( 258 | mean, covariance) 259 | 260 | chol_factor1, lower = scipy.linalg.cho_factor( 261 | projected_cov1, lower=True, check_finite=False) 262 | chol_factor2, lower = scipy.linalg.cho_factor( 263 | projected_cov2, lower=True, check_finite=False) 264 | 265 | kalman_gain1 = scipy.linalg.cho_solve( 266 | (chol_factor1, lower), np.dot(covariance, self._update_mat2.T).T, 267 | check_finite=False).T 268 | kalman_gain2 = scipy.linalg.cho_solve( 269 | (chol_factor2, lower), np.dot(covariance, self._update_mat2.T).T, 270 | check_finite=False).T 271 | 272 | innovation1 = np.r_[measurement, np.zeros(4)] - projected_mean1 273 | innovation2 = np.r_[measurement, np.zeros(4)] - projected_mean2 274 | 275 | new_mean1 = mean + np.dot(innovation1, kalman_gain1.T) 276 | new_mean2 = mean + np.dot(innovation2, kalman_gain2.T) 277 | 278 | new_covariance1 = covariance - np.linalg.multi_dot(( 279 | kalman_gain1, projected_cov1, kalman_gain1.T)) 280 | new_covariance2 = covariance - np.linalg.multi_dot(( 281 | kalman_gain2, projected_cov2, kalman_gain2.T)) 282 | 283 | new_mean = self.imm_weight[0] * new_mean1 + self.imm_weight[1] * new_mean2 284 | new_covariance = self.imm_weight[0] * new_covariance1 + self.imm_weight[1] * new_covariance2 285 | # new_covariance = self.imm_weight[0] * (new_covariance1 + (new_mean1 - new_mean) * (new_mean1 - new_mean).T) + \ 286 | # self.imm_weight[1] * (new_covariance2 + (new_mean2 - new_mean) * (new_mean2 - new_mean).T) 287 | 288 | return new_mean, new_covariance 289 | 290 | def gating_distance(self, mean, covariance, measurements, 291 | only_position=False): 292 | """Compute gating distance between state distribution and measurements. 293 | 294 | A suitable distance threshold can be obtained from `chi2inv95`. If 295 | `only_position` is False, the chi-square distribution has 4 degrees of 296 | freedom, otherwise 2. 297 | 298 | Parameters 299 | ---------- 300 | mean : ndarray 301 | Mean vector over the state distribution (12 dimensional). 302 | covariance : ndarray 303 | Covariance of the state distribution (12x12 dimensional). 304 | measurements : ndarray 305 | An Nx4 dimensional matrix of N measurements, each in 306 | format (x, y, a, h) where (x, y) is the bounding box center 307 | position, a the aspect ratio, and h the height. 308 | only_position : Optional[bool] 309 | If True, distance computation is done with respect to the bounding 310 | box center position only. 311 | 312 | Returns 313 | ------- 314 | ndarray 315 | Returns an array of length N, where the i-th element contains the 316 | squared Mahalanobis distance between (mean, covariance) and 317 | `measurements[i]`. 318 | 319 | """ 320 | mean1, covariance1, mean2, covariance2 = self.project(mean, covariance) 321 | 322 | if only_position: 323 | mean1, covariance1 = mean1[:2], covariance1[:2, :2] 324 | measurements = measurements[:, :2] 325 | if only_position: 326 | mean2, covariance2 = mean2[:2], covariance2[:2, :2] 327 | measurements = measurements[:, :2] 328 | 329 | cholesky_factor1 = np.linalg.cholesky(covariance2) 330 | cholesky_factor2 = np.linalg.cholesky(covariance2) 331 | 332 | row = int( measurements.size / 4 ) 333 | measurements = np.c_[measurements, np.zeros((row, 4))] 334 | d1 = measurements - mean1 335 | d2 = measurements - mean2 336 | 337 | z1 = scipy.linalg.solve_triangular( 338 | cholesky_factor1, d1.T, lower=True, check_finite=False, 339 | overwrite_b=True) 340 | z2 = scipy.linalg.solve_triangular( 341 | cholesky_factor2, d2.T, lower=True, check_finite=False, 342 | overwrite_b=True) 343 | 344 | squared_maha1 = np.sum(z1 * z1, axis=0) 345 | squared_maha2 = np.sum(z2 * z2, axis=0) 346 | squared_maha = self.imm_weight[0] * squared_maha1 + self.imm_weight[1] * squared_maha2 347 | 348 | return squared_maha 349 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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Such new versions will 567 | be similar in spirit to the present version, but may differ in detail to 568 | address new problems or concerns. 569 | 570 | Each version is given a distinguishing version number. If the 571 | Program specifies that a certain numbered version of the GNU General 572 | Public License "or any later version" applies to it, you have the 573 | option of following the terms and conditions either of that numbered 574 | version or of any later version published by the Free Software 575 | Foundation. If the Program does not specify a version number of the 576 | GNU General Public License, you may choose any version ever published 577 | by the Free Software Foundation. 578 | 579 | If the Program specifies that a proxy can decide which future 580 | versions of the GNU General Public License can be used, that proxy's 581 | public statement of acceptance of a version permanently authorizes you 582 | to choose that version for the Program. 583 | 584 | Later license versions may give you additional or different 585 | permissions. However, no additional obligations are imposed on any 586 | author or copyright holder as a result of your choosing to follow a 587 | later version. 588 | 589 | 15. Disclaimer of Warranty. 590 | 591 | THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY 592 | APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT 593 | HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY 594 | OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, 595 | THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 596 | PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM 597 | IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF 598 | ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 599 | 600 | 16. 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Interpretation of Sections 15 and 16. 613 | 614 | If the disclaimer of warranty and limitation of liability provided 615 | above cannot be given local legal effect according to their terms, 616 | reviewing courts shall apply local law that most closely approximates 617 | an absolute waiver of all civil liability in connection with the 618 | Program, unless a warranty or assumption of liability accompanies a 619 | copy of the Program in return for a fee. 620 | 621 | END OF TERMS AND CONDITIONS 622 | 623 | How to Apply These Terms to Your New Programs 624 | 625 | If you develop a new program, and you want it to be of the greatest 626 | possible use to the public, the best way to achieve this is to make it 627 | free software which everyone can redistribute and change under these terms. 628 | 629 | To do so, attach the following notices to the program. It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | 635 | Copyright (C) 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | Copyright (C) 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | --------------------------------------------------------------------------------