# vim: expandtab:ts=4:sw=4
from __future__ import absolute_import
import numpy as np
from scipy.optimize import linear_sum_assignment
from . import kalman_filter
INFTY_COST = 1e+5
def min_cost_matching(
distance_metric, max_distance, tracks, detections, track_indices=None,
detection_indices=None):
"""Solve linear assignment problem.
Parameters
----------
distance_metric : Callable[List[Track], List[Detection], List[int], List[int]) -> ndarray
The distance metric is given a list of tracks and detections as well as
a list of N track indices and M detection indices. The metric should
return the NxM dimensional cost matrix, where element (i, j) is the
association cost between the i-th track in the given track indices and
the j-th detection in the given detection_indices.
max_distance : float
Gating threshold. Associations with cost larger than this value are
disregarded.
tracks : List[track.Track]
A list of predicted tracks at the current time step.
detections : List[detection.Detection]
A list of detections at the current time step.
track_indices : List[int]
List of track indices that maps rows in `cost_matrix` to tracks in
`tracks` (see description above).
detection_indices : List[int]
List of detection indices that maps columns in `cost_matrix` to
detections in `detections` (see description above).
Returns
-------
(List[(int, int)], List[int], List[int])
Returns a tuple with the following three entries:
* A list of matched track and detection indices.
* A list of unmatched track indices.
* A list of unmatched detection indices.
"""
if track_indices is None:
track_indices = np.arange(len(tracks))
if detection_indices is None:
detection_indices = np.arange(len(detections))
if len(detection_indices) == 0 or len(track_indices) == 0:
return [], track_indices, detection_indices # Nothing to match.
cost_matrix = distance_metric(
tracks, detections, track_indices, detection_indices)
cost_matrix[cost_matrix > max_distance] = max_distance + 1e-5
indices = linear_sum_assignment(cost_matrix)
indices = np.asarray(indices)
indices = np.transpose(indices)
matches, unmatched_tracks, unmatched_detections = [], [], []
for col, detection_idx in enumerate(detection_indices):
if col not in indices[:, 1]:
unmatched_detections.append(detection_idx)
for row, track_idx in enumerate(track_indices):
if row not in indices[:, 0]:
unmatched_tracks.append(track_idx)
for row, col in indices:
track_idx = track_indices[row]
detection_idx = detection_indices[col]
if cost_matrix[row, col] > max_distance:
unmatched_tracks.append(track_idx)
unmatched_detections.append(detection_idx)
else:
matches.append((track_idx, detection_idx))
return matches, unmatched_tracks, unmatched_detections
def matching_cascade(
distance_metric, max_distance, cascade_depth, tracks, detections,
track_indices=None, detection_indices=None):
"""Run matching cascade.
Parameters
----------
distance_metric : Callable[List[Track], List[Detection], List[int], List[int]) -> ndarray
The distance metric is given a list of tracks and detections as well as
a list of N track indices and M detection indices. The metric should
return the NxM dimensional cost matrix, where element (i, j) is the
association cost between the i-th track in the given track indices and
the j-th detection in the given detection indices.
max_distance : float
Gating threshold. Associations with cost larger than this value are
disregarded.
cascade_depth: int
The cascade depth, should be se to the maximum track age.
tracks : List[track.Track]
A list of predicted tracks at the current time step.
detections : List[detection.Detection]
A list of detections at the current time step.
track_indices : Optional[List[int]]
List of track indices that maps rows in `cost_matrix` to tracks in
`tracks` (see description above). Defaults to all tracks.
detection_indices : Optional[List[int]]
List of detection indices that maps columns in `cost_matrix` to
detections in `detections` (see description above). Defaults to all
detections.
Returns
-------
(List[(int, int)], List[int], List[int])
Returns a tuple with the following three entries:
* A list of matched track and detection indices.
* A list of unmatched track indices.
* A list of unmatched detection indices.
"""
if track_indices is None:
track_indices = list(range(len(tracks)))
if detection_indices is None:
detection_indices = list(range(len(detections)))
unmatched_detections = detection_indices
matches = []
for level in range(cascade_depth):
if len(unmatched_detections) == 0: # No detections left
break
track_indices_l = [
k for k in track_indices
if tracks[k].time_since_update == 1 + level
]
if len(track_indices_l) == 0: # Nothing to match at this level
continue
matches_l, _, unmatched_detections = \
min_cost_matching(
distance_metric, max_distance, tracks, detections,
track_indices_l, unmatched_detections)
matches += matches_l
unmatched_tracks = list(set(track_indices) - set(k for k, _ in matches))
return matches, unmatched_tracks, unmatched_detections
def gate_cost_matrix(
kf, cost_matrix, tracks, detections, track_indices, detection_indices,
gated_cost=INFTY_COST, only_position=False):
"""Invalidate infeasible entries in cost matrix based on the state
distributions obtained by Kalman filtering.
Parameters
----------
kf : The Kalman filter.
cost_matrix : ndarray
The NxM dimensional cost matrix, where N is the number of track indices
and M is the number of detection indices, such that entry (i, j) is the
association cost between `tracks[track_indices[i]]` and
`detections[detection_indices[j]]`.
tracks : List[track.Track]
A list of predicted tracks at the current time step.
detections : List[detection.Detection]
A list of detections at the current time step.
track_indices : List[int]
List of track indices that maps rows in `cost_matrix` to tracks in
`tracks` (see description above).
detection_indices : List[int]
List of detection indices that maps columns in `cost_matrix` to
detections in `detections` (see description above).
gated_cost : Optional[float]
Entries in the cost matrix corresponding to infeasible associations are
set this value. Defaults to a very large value.
only_position : Optional[bool]
If True, only the x, y position of the state distribution is considered
during gating. Defaults to False.
Returns
-------
ndarray
Returns the modified cost matrix.
"""
gating_dim = 2 if only_position else 4
gating_threshold = kalman_filter.chi2inv95[gating_dim]
measurements = np.asarray(
[detections[i].to_xyah() for i in detection_indices])
for row, track_idx in enumerate(track_indices):
track = tracks[track_idx]
gating_distance = kf.gating_distance(
track.mean, track.covariance, measurements, only_position)
cost_matrix[row, gating_distance > gating_threshold] = gated_cost
return cost_matrix