Assignment using auction global nearest neighbor
[assignments,unassignedrows,unassignedcolumns] = assignauction(costmatrix,costofnonassignment)
returns a table of
unassignedcolumns] = assignauction(
assignments of detections to tracks derived based on
the forward/reverse auction algorithm. The auction algorithm finds a suboptimal solution to
the global nearest neighbor (GNN) assignment problem by minimizing the total cost of
assignment. While suboptimal, the auction algorithm is faster than the Munkres algorithm for
large GNN assignment problems, for example, when there are more than 50 rows and columns in
the cost matrix.
The cost of each potential assignment is contained in the cost
costmatrix. Each matrix entry represents the cost of a possible
assignments. Matrix rows represent tracks and columns represent detections. All possible
assignments are represented in the cost matrix. The lower the cost, the more likely the
assignment is to be made. Each track can be assigned to at most one detection and each detection
can be assigned to at most one track. If the number of rows is greater than the number of
columns, some tracks are unassigned. If the number of columns is greater than the number of
rows, some detections are unassigned. You can set an entry of
Inf to prohibit an assignment.
costofnonassignment represents the cost of leaving tracks or
detections unassigned. Higher values increase the likelihood that every existing object is
The function returns a list of unassigned tracks,
and a list of unassigned detections,
assignAuction to assign three detections to two tracks.
Start with two predicted track locations in x-y coordinates.
tracks = [1,1; 2,2];
Assume three detections are received. At least one detection will not be assigned.
dets = [1.1, 1.1; 2.1, 2.1; 1.5, 3];
Construct a cost matrix by defining the cost of assigning a detection to a track as the Euclidean distance between them. Set the cost of non-assignment to 0.2.
for i = size(tracks, 1):-1:1 delta = dets - tracks(i, :); costMatrix(i, :) = sqrt(sum(delta .^ 2, 2)); end costofnonassignment = 0.2;
Use the Auction algorithm to assign detections to tracks.
[assignments, unassignedTracks, unassignedDetections] = ... assignauction(costMatrix,costofnonassignment);
Display the assignments.
1 1 2 2
Show that there are no unassigned tracks.
Display the unassigned detections.
Plot detection to track assignments.
plot(tracks(:, 1), tracks(:, 2), '*', dets(:, 1), dets(:, 2), 'o') hold on xlim([0, 4]) ylim([0, 4]) legend('tracks', 'detections') assignStr = strsplit(num2str(1:size(assignments,1))); text(tracks(assignments(:, 1),1) + 0.1, ... tracks(assignments(:, 1),2) - 0.1, assignStr); text(dets(assignments(:, 2),1) + 0.1, ... dets(assignments(:, 2),2) - 0.1, assignStr); text(dets(unassignedDetections(:),1) + 0.1, ... dets(unassignedDetections(:),2) + 0.1, 'unassigned');
The track to detection assignments are:
Detection 1 is assigned to track 1.
Detection 2 is assigned to track 2.
Detection 3 is not assigned.
costmatrix— Cost matrix
Cost matrix, specified as an M-by-N matrix.
M is the number of tracks to be assigned and N
is the number of detections to be assigned. Each entry in the cost matrix contains the
cost of a track and detection assignment. The matrix may contain
entries to indicate that an assignment is prohibited. The cost matrix cannot be a sparse
costofnonassignment— cost of non-assignment of tracks and detections
Cost of non-assignment, specified as a scalar. The cost of
non-assignment represents the cost of leaving tracks or
detections unassigned. Higher values increase the likelihood
that every object is assigned. The value cannot be set to
assignments— Assignment of tracks to detections
Assignment of detections to track, returned as an integer-valued L-by-2 matrix where L is the number of assignments. The first column of the matrix contains the assigned track indices and the second column contains the assigned detection indices.
unassignedrows— Indices of unassigned tracks
Indices of unassigned tracks, returned as an integer-valued P-by-1 column vector.
unassignedcolumns— Indices of unassigned detections
Indices of unassigned detections, returned as an integer-valued Q-by-1 column vector.
 Samuel S. Blackman and Popoli, R. Design and Analysis of Modern Tracking Systems. Artech House: Norwood, MA. 1999.