Source code for stonesoup.metricgenerator.tracktotruthmetrics

# -*- coding: utf-8 -*-
from operator import attrgetter

from .base import MetricGenerator
from ..base import Property
from ..measures import Measure
from ..types.metric import SingleTimeMetric, TimeRangeMetric
from ..types.time import TimeRange
from ..types.track import Track


[docs]class SIAPMetrics(MetricGenerator): r"""SIAP Metrics Computes the Single Integrated Air Picture (SIAP) metrics as defined by the Systems Engineering Task Force. The implementation provided here is derived from [1] and focuses on providing the SIAP attribute measures. The SIAP metrics provided require provision of ground truth information. In the original paper the calculations are dependent upon :math:`m` which corresponds to the identifying number of the sense capability which is being assessed. This is not used in this implementation, with the assumption being that the fused sensor set is being assessed. Metrics: * Continuity (C): Fraction of true objects being tracked. The output is in the range :math:`0:1`, with a target score of 1. * Ambiguity (A): Number of tracks assigned to a true object. The output is unbounded with a range of :math:`0:\infty`. The target score is 1. * Spuriousness (S): Fraction of tracks that are unassigned to a true object. The output is in the range :math:`0:1`, with a target score of 0. * Positional Accuracy (PA): Positional error of associated tracks to their respective truths. The output is a distance measure, range :math:`0:\infty`, with a target score of 0. * Velocity Accuracy (VA): Velocity error of associated tracks to their respective truths. The output is a distance measure, range :math:`0:\infty`, with a target score of 0. * Rate of track number changes (R): SIAP continuity measure. Rate of number of track changes per truth. The output is in the range :math:`0:\infty`, with a target score of 0. * Longest track Segment (LS): SIAP continuity measure. Duration of longest associated track segment per truth. The output is a float (seconds), with a target score equal to the sum of all true object lifetimes. Reference [1] Single Integrated Air Picture (SIAP) Metrics Implementation, Votruba et al, 29-10-2001 """ position_measure: Measure = Property( doc="Distance measure used in calculating position accuracy scores.") velocity_measure: Measure = Property( doc="Distance measure used in calculating velocity accuracy scores.")
[docs] def compute_metric(self, manager, **kwargs): r"""Compute metrics: .. math:: \begin{alignat*}{3} \textrm{Name} &\quad \textrm{At Time} &&\quad \textrm{TimeRange}\\ C &\quad \frac{JT({t})}{J({t})} &&\quad \frac{\sum_{t_{start}}^{t_{end}}JT({t})} {\sum_{t_{start}}^{t_{end}}J({t})}\\ A &\quad \frac{N{A}({t})}{JT({t})} &&\quad \frac{\sum_{t_{start}}^{t_{end}} N{A}({t})}{\sum_{t_{start}}^{t_{end}}JT({t})}\\ S &\quad \frac{N({t}) - N{A}({t})}{N({t})} &&\quad \frac{\sum_{t_{start}}^{t_{end}} [N({t}) - N{A}({t})]}{\sum_{t_{start}}^{t_{end}}N({t})}\\ PA &\quad \frac{{\sum_{n\in tracks}PA_{n}(t)}}{NA(t)} &&\quad \frac{\sum_{t_{start}}^{t_{end}}{\sum_{n\in tracks}PA_{n}(t)}} {\sum_{t_{start}}^{t_{end}}{NA(t)}}\\ VA &\quad \frac{{\sum_{n\in tracks}VA_{n}(t)}}{NA(t)} &&\quad \frac{\sum_{t_{start}}^{t_{end}}{\sum_{n\in tracks}VA_{n}(t)}} {\sum_{t_{start}}^{t_{end}}{NA(t)}}\\ R &\quad -- &&\quad \frac{\sum_{j\in truths}NU_j-1}{\sum_{j\in truths}TT_j}\\ LS &\quad -- &&\quad \frac{\sum_{j\in truths}T{L}_{j}}{\sum_{j\in truths}T_{j}} \end{alignat*} Parameters ---------- manager : MetricManager containing the data to be used to create the metric(s) Returns ------- : list of :class:`~.Metric` objects Generated metrics """ timestamps = manager.list_timestamps() completeness_at_times = list() ambiguity_at_times = list() spuriousness_at_times = list() position_accuracy_at_times = list() velocity_accuracy_at_times = list() J_sum = JT_sum = NA_sum = N_sum = PA_sum = VA_sum = 0 for timestamp in timestamps: Jt = self.num_truths_at_time(manager, timestamp) J_sum += Jt JTt = self.num_associated_truths_at_time(manager, timestamp) JT_sum += JTt NAt = self.num_associated_tracks_at_time(manager, timestamp) NA_sum += NAt Nt = self.num_tracks_at_time(manager, timestamp) N_sum += Nt PAt = self.accuracy_at_time(manager, timestamp, self.position_measure) PA_sum += PAt VAt = self.accuracy_at_time(manager, timestamp, self.velocity_measure) VA_sum += VAt completeness_at_times.append( SingleTimeMetric(title="SIAP Completeness at timestamp", value=JTt / Jt if Jt != 0 else 0, timestamp=timestamp, generator=self) ) ambiguity_at_times.append( SingleTimeMetric(title="SIAP Ambiguity at timestamp", value=NAt / JTt if JTt != 0 else 1, timestamp=timestamp, generator=self) ) spuriousness_at_times.append( SingleTimeMetric(title="SIAP Spuriousness at timestamp", value=(Nt - NAt) / Nt if Nt != 0 else 0, timestamp=timestamp, generator=self) ) position_accuracy_at_times.append( SingleTimeMetric(title="SIAP Position Accuracy at timestamp", value=PAt / NAt if NAt != 0 else 0, timestamp=timestamp, generator=self) ) velocity_accuracy_at_times.append( SingleTimeMetric(title="SIAP Velocity Accuracy at timestamp", value=VAt / NAt if NAt != 0 else 0, timestamp=timestamp, generator=self) ) time_range = TimeRange(min(timestamps), max(timestamps)) completeness = TimeRangeMetric(title="SIAP Completeness", value=JT_sum / J_sum if J_sum != 0 else 0, time_range=time_range, generator=self) ambiguity = TimeRangeMetric(title="SIAP Ambiguity", value=NA_sum / JT_sum if JT_sum != 0 else 1, time_range=time_range, generator=self) spuriousness = TimeRangeMetric(title="SIAP Spuriousness", value=(N_sum - NA_sum) / N_sum if N_sum != 0 else 0, time_range=time_range, generator=self) position_accuracy = TimeRangeMetric(title="SIAP Position Accuracy", value=PA_sum / NA_sum if NA_sum != 0 else 0, time_range=time_range, generator=self) velocity_accuracy = TimeRangeMetric(title="SIAP Velocity Accuracy", value=VA_sum / NA_sum if NA_sum != 0 else 0, time_range=time_range, generator=self) R = self.rate_of_track_number_changes(manager) rate_track_num = TimeRangeMetric(title="SIAP Rate of Track Number Change", value=R, time_range=time_range, generator=self) TL_sum = sum(self.longest_track_time_on_truth(manager, truth) for truth in manager.groundtruth_paths) T_sum = sum(self.truth_lifetime(truth) for truth in manager.groundtruth_paths) longest_track_seg = TimeRangeMetric(title="SIAP Longest Track Segment", value=TL_sum / T_sum if T_sum != 0 else 0, time_range=time_range, generator=self) completeness_at_times = TimeRangeMetric(title="SIAP Completeness at times", value=completeness_at_times, time_range=time_range, generator=self) ambiguity_at_times = TimeRangeMetric(title="SIAP Ambiguity at times", value=ambiguity_at_times, time_range=time_range, generator=self) spuriousness_at_times = TimeRangeMetric(title="SIAP Spuriousness at times", value=spuriousness_at_times, time_range=time_range, generator=self) position_accuracy_at_times = TimeRangeMetric(title="SIAP Position Accuracy at times", value=position_accuracy_at_times, time_range=time_range, generator=self) velocity_accuracy_at_times = TimeRangeMetric(title="SIAP Velocity Accuracy at times", value=velocity_accuracy_at_times, time_range=time_range, generator=self) return [completeness, ambiguity, spuriousness, position_accuracy, velocity_accuracy, rate_track_num, longest_track_seg, completeness_at_times, ambiguity_at_times, spuriousness_at_times, position_accuracy_at_times, velocity_accuracy_at_times]
[docs] @staticmethod def num_truths_at_time(manager, timestamp): """:math:`J(t)`. Calculate the number of true objects held by `manager` at `timestamp`. Parameters ---------- manager: MetricManager Containing the data to be used timestamp: datetime.datetime Timestamp at which to compute the value Returns ------- float Number of true objects held by `manager` at `timestamp` """ return sum( 1 for path in manager.groundtruth_paths if timestamp in (state.timestamp for state in path))
[docs] @staticmethod def num_associated_truths_at_time(manager, timestamp): """:math:`JT(t)`. Calculate the number of associated true objects held by `manager` at `timestamp`. Parameters ---------- manager: MetricManager Containing the data to be used timestamp: datetime.datetime Timestamp at which to compute the value Returns ------- float Number of associated true objects held by `manager` at `timestamp` """ associations = manager.association_set.associations_at_timestamp(timestamp) association_objects = {thing for assoc in associations for thing in assoc.objects} return sum(1 for truth in manager.groundtruth_paths if truth in association_objects)
[docs] @staticmethod def num_tracks_at_time(manager, timestamp): """:math:`N(t)`. Calculate the number of tracks held by `manager` at `timestamp`. Parameters ---------- manager: MetricManager Containing the data to be used timestamp: datetime.datetime Timestamp at which to compute the value Returns ------- float Number of tracks held by `manager` at `timestamp` """ return sum( 1 for track in manager.tracks if timestamp in (state.timestamp for state in track.states))
[docs] @staticmethod def num_associated_tracks_at_time(manager, timestamp): """:math:`NA(t)`. Calculate the number of associated tracks held by `manager` at `timestamp`. Parameters ---------- manager: MetricManager Containing the data to be used timestamp: datetime.datetime Timestamp at which to compute the value Returns ------- float Number of associated tracks held by `manager` at `timestamp`. """ associations = manager.association_set.associations_at_timestamp(timestamp) association_objects = {thing for assoc in associations for thing in assoc.objects} return sum(1 for track in manager.tracks if track in association_objects)
[docs] def accuracy_at_time(self, manager, timestamp, measure): """:math:`PA(t)` or :math:`VA(t)` (dependent on `measure`). Calculate the kinematic accuracy of track-truth associations held by `manager` at `timestamp`. Parameters ---------- manager: MetricManager Containing the data to be used timestamp: datetime.datetime Timestamp at which to compute the value measure: Measure Measure used to calculate 'distance' between truths and tracks Returns ------- float Kinematic accuracy of track-truth associations held by `manager` at `timestamp`. Note ---- This method adds the 'distance' errors for each and every association. An alternative would be to consider each true object and track at most once. """ associations = manager.association_set.associations_at_timestamp(timestamp) error_sum = 0 for association in associations: truth, track = self.truth_track_from_association(association) error_sum += measure(track[timestamp], truth[timestamp]) return error_sum
[docs] @staticmethod def truth_track_from_association(association): """Find truth and track from an association. Parameters ---------- association: Association Association that contains truth and track as its objects Returns ------- GroundTruthPath, Track True object and track that are the objects of the `association` """ truth, track = association.objects # Sets aren't ordered, so need to ensure correct path is truth/track if isinstance(truth, Track): truth, track = track, truth return truth, track
[docs] @staticmethod def total_time_tracked(manager, truth): """:math:`TT`. Calculate the total time a `truth` is tracked for by tracks contained by `manager`. Parameters ---------- manager: MetricManager Containing the data to be used truth: GroundTruthPath True object Returns ------- float Number of seconds that `truth` is tracked for """ assocs = manager.association_set.associations_including_objects([truth]) if len(assocs) == 0: return 0 truth_timestamps = sorted(state.timestamp for state in truth.states) total_time = 0 for current_time, next_time in zip(truth_timestamps[:-1], truth_timestamps[1:]): for assoc in assocs: # If both timestamps are in one association then add the difference to the total # difference and stop looking if current_time in assoc.time_range and next_time in assoc.time_range: total_time += (next_time - current_time).total_seconds() break return total_time
[docs] @staticmethod def min_num_tracks_needed_to_track(manager, truth): """:math:`NU_j`. Calculate the minimum number of tracks needed to track `truth` using tracks held by `manager`. Parameters ---------- manager: MetricManager Containing the data to be used truth: GroundTruthPath True object Returns ------- int Minimum number of tracks needed to track `truth` """ assocs = sorted(manager.association_set.associations_including_objects([truth]), key=attrgetter('time_range.end_timestamp'), reverse=True) if len(assocs) == 0: return 0 truth_timestamps = sorted(state.timestamp for state in truth.states) num_tracks_needed = 0 timestamp_index = 0 while timestamp_index < len(truth_timestamps): current_time = truth_timestamps[timestamp_index] assoc_at_time = next((assoc for assoc in assocs if current_time in assoc.time_range), None) if not assoc_at_time: timestamp_index += 1 else: end_time = assoc_at_time.time_range.end_timestamp num_tracks_needed += 1 # If not yet at the end of the truth timestamps indices, move on to the next try: # Move to next timestamp index after current association's end timestamp timestamp_index = truth_timestamps.index(end_time, timestamp_index + 1) + 1 except ValueError: break return num_tracks_needed
[docs] def rate_of_track_number_changes(self, manager): """:math:`R`. Calculate the average rate of track number changes for true objects held by `manager`. Parameters ---------- manager: MetricManager Containing the data to be used Returns ------- float Average rate of track number changes """ numerator = sum(self.min_num_tracks_needed_to_track(manager, truth) - 1 for truth in manager.groundtruth_paths) denominator = sum(self.total_time_tracked(manager, truth) for truth in manager.groundtruth_paths) return numerator / denominator if denominator != 0 else 0
[docs] @staticmethod def truth_lifetime(truth): """:math:`T`. Calculate how long `truth` exists for. Parameters ---------- truth: GroundTruthPath True object Returns ------- float Number of seconds that `truth` exists for """ timestamps = [state.timestamp for state in truth.states] return (max(timestamps) - min(timestamps)).total_seconds()
[docs] @staticmethod def longest_track_time_on_truth(manager, truth): """:math:`TL_j`. Calculate the longest time that a single track is associated to `truth` using associations held by `manager`. Parameters ---------- manager: MetricManager Containing the data to be used truth: GroundTruthPath True object Returns ------- float Number of seconds of longest association to `truth` """ assocs = manager.association_set.associations_including_objects({truth}) return max(assoc.time_range.duration.total_seconds() for assoc in assocs) if assocs else 0
[docs]class IDSIAPMetrics(SIAPMetrics): r"""ID-based SIAP Metrics SIAP metric generator that additionally computes ID-based SIAP metrics. ID-based Metrics: * ID Completeness (CID): ID-based SIAP. Fraction of true objects with an assigned ID. The output is in the range :math:`0:1`, with a target score of 1. * ID Correctness (IDC): ID-based SIAP. Fraction of true objects with correct ID assignment. The output is in the range :math:`0:1`, with a target score of 1. * ID Ambiguity (IDA): ID-based SIAP. Fraction of true objects with ambiguous ID assignment. The output is in the range :math:`0:1`, with a target score of 0. Notes ----- * This implementation assumes that track and ground truth path IDs are implemented via metadata, whereby the strings :attr:`track_id` and :attr:`truth_id` are keys to track and truth metadata entries with ID data respectively. * :class:`~.Track` types store metadata outside of their `states` attribute. Therefore the ID SIAPs make metadata comparisons via the tracks' last ID metadata values (as calling `track.metadata` will return a track's metadata at the end of its life). To provide a better implementation, one might modify :class:`~.Track` types to contain a list of `state` types that hold their own metadata. Reference [1] Single Integrated Air Picture (SIAP) Metrics Implementation, Votruba et al, 29-10-2001 """ truth_id: str = Property(doc="Metadata key for ID of each ground truth path in data-set") track_id: str = Property(doc="Metadata key for ID of each track in data-set")
[docs] def compute_metric(self, manager, **kwargs): r"""Compute metrics: .. math:: \begin{alignat*}{3} \textrm{Name} &\quad \textrm{At Time} &&\quad \textrm{TimeRange}\\ C &\quad \frac{JT({t})}{J({t})} &&\quad \frac{\sum_{t_{start}}^{t_{end}}JT({t})} {\sum_{t_{start}}^{t_{end}}J({t})}\\ A &\quad \frac{N{A}({t})}{JT({t})} &&\quad \frac{\sum_{t_{start}}^{t_{end}} N{A}({t})}{\sum_{t_{start}}^{t_{end}}JT({t})}\\ S &\quad \frac{N({t}) - N{A}({t})}{N({t})} &&\quad \frac{\sum_{t_{start}}^{t_{end}} [N({t}) - N{A}({t})]}{\sum_{t_{start}}^{t_{end}}N({t})}\\ PA &\quad \frac{{\sum_{n\in tracks}PA_{n}(t)}}{NA(t)} &&\quad \frac{\sum_{t_{start}}^{t_{end}}{\sum_{n\in tracks}PA_{n}(t)}} {\sum_{t_{start}}^{t_{end}}{NA(t)}}\\ VA &\quad \frac{{\sum_{n\in tracks}VA_{n}(t)}}{NA(t)} &&\quad \frac{\sum_{t_{start}}^{t_{end}}{\sum_{n\in tracks}VA_{n}(t)}} {\sum_{t_{start}}^{t_{end}}{NA(t)}}\\ R &\quad -- &&\quad \frac{\sum_{j\in truths}NU_j-1}{\sum_{j\in truths}TT_j}\\ LS &\quad -- &&\quad \frac{\sum_{j\in truths}T{L}_{j}}{\sum_{j\in truths}T_{j}}\\ CID &\quad \frac{J{T}({t}) - J{U}({t})}{JT({t})} &&\quad \frac{\sum_{t_{start}}^{t_{end}}[J{T}({t}) - J{U}({T})]} {\sum_{t_{start}}^{t_{end}}J{T}({t})}\\ IDC &\quad \frac{J{C}({t})}{JT({t})} &&\quad \frac{\sum_{t_{start}}^{t_{end}} J{C}({t})}{\sum_{t_{start}}^{t_{end}}J{T}({t})}\\ IDA &\quad \frac{J{A}({t})}{JT({t})} &&\quad \frac{\sum_{t_{start}}^{t_{end}} J{A}({t})}{\sum_{t_{start}}^{t_{end}}J{T}({t})} \end{alignat*} Parameters ---------- manager : MetricManager containing the data to be used to create the metric(s) Returns ------- : list of :class:`~.Metric` objects Generated metrics """ metrics = super().compute_metric(manager, **kwargs) timestamps = manager.list_timestamps() id_completeness_at_times = list() id_correctness_at_times = list() id_ambiguity_at_times = list() JT_sum = JU_sum = JC_sum = JI_sum = JA_sum = 0 for timestamp in timestamps: JTt = self.num_associated_truths_at_time(manager, timestamp) JT_sum += JTt JUt, JCt, JIt = self.num_id_truths_at_time(manager, timestamp) JU_sum += JUt JC_sum += JCt JI_sum += JIt JAt = JTt - JCt - JIt - JUt JA_sum += JAt id_completeness_at_times.append( SingleTimeMetric(title="SIAP ID Completeness at timestamp", value=(JTt - JUt) / JTt if JTt != 0 else 0, timestamp=timestamp, generator=self) ) id_correctness_at_times.append( SingleTimeMetric(title="SIAP ID Correctness at timestamp", value=JCt / JTt if JTt != 0 else 0, timestamp=timestamp, generator=self) ) id_ambiguity_at_times.append( SingleTimeMetric(title="SIAP Ambiguity at timestamp", value=JAt / JTt if JTt != 0 else 0, timestamp=timestamp, generator=self) ) time_range = TimeRange(min(timestamps), max(timestamps)) id_completeness = TimeRangeMetric(title="SIAP ID Completeness", value=(JT_sum - JU_sum) / JT_sum if JT_sum != 0 else 0, time_range=time_range, generator=self) id_correctness = TimeRangeMetric(title="SIAP ID Correctness", value=JC_sum / JT_sum if JT_sum != 0 else 0, time_range=time_range, generator=self) id_ambiguity = TimeRangeMetric(title="SIAP ID Ambiguity", value=JA_sum / JT_sum if JT_sum != 0 else 0, time_range=time_range, generator=self) id_completeness_at_times = TimeRangeMetric(title="SIAP ID Completeness at times", value=id_completeness_at_times, time_range=time_range, generator=self) id_correctness_at_times = TimeRangeMetric(title="SIAP ID Correctness at times", value=id_correctness_at_times, time_range=time_range, generator=self) id_ambiguity_at_times = TimeRangeMetric(title="SIAP ID Ambiguity at times", value=id_ambiguity_at_times, time_range=time_range, generator=self) metrics.extend([id_completeness, id_correctness, id_ambiguity, id_completeness_at_times, id_correctness_at_times, id_ambiguity_at_times]) return metrics
[docs] def find_track_id(self, track, timestamp): """Find `track` ID at `timestamp`. Parameters ---------- track: Track Track object timestamp: datetime.datetime Timestamp to retrieve ID data at Returns ------- any `track` ID at `timestamp` """ state = track[timestamp] index = track.index(state) metadata = track.metadatas[index] return metadata.get(self.track_id)
[docs] def num_id_truths_at_time(self, manager, timestamp): """:math:`JU`, :math:`JC`, :math:`JI`. Calculate the number of true objects that are: Un-identified, correctly identified, incorrectly identified at `timestamp` according to associations held by `manager`. Parameters ---------- manager: MetricManager Containing the data to be used timestamp: datetime.datetime Timestamp at which to consider associations Returns ------- int, int, int Number of true objects: Un-identified, correctly identified, incorrectly identified Note ---- * A true object is considered to be un-identified if all tracks associated with it at `timestamp` have no ID. * A true object is considered to be correctly identified if all tracks associated with it at `timestamp` have the same ID as it. * A true object is considered to be incorrectly identified if all tracks associated with it at `timestamp` have a different ID to it. * A true object is considered to have ambiguous identification if tracks associated with it have differing ID (this value is calculated in the :meth:`~.compute_metric` method). """ unknown_count = 0 correct_count = 0 incorrect_count = 0 assocs = manager.association_set.associations_at_timestamp(timestamp) for truth in manager.groundtruth_paths: truth_id = truth.metadata.get(self.truth_id) track_ids = list() truth_assocs = [assoc for assoc in assocs if truth in assoc.objects] if len(truth_assocs) == 0: continue for assoc in truth_assocs: _, track = self.truth_track_from_association(assoc) track_ids.append(self.find_track_id(track, timestamp)) if all(track_id is None for track_id in track_ids): unknown_count += 1 elif (all(track_id == truth_id and track_id is not None for track_id in track_ids) and truth_id is not None): correct_count += 1 elif all(track_id != truth_id and track_id is not None for track_id in track_ids): incorrect_count += 1 return unknown_count, correct_count, incorrect_count