Track-oriented multi-hypotheses tracking assignment
returns a table of assignments,
unassignedcolumns] = assignTOMHT(
assignments, of detections to tracks
using a track-oriented multi-hypothesis algorithm (TOMHT).
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.
costThreshold represents the set of three gates used for assigning
detections to tracks.
The function returns a list of unassigned tracks,
and a list of unassigned detections,
Find the assignments from a cost matrix using
assignTOMHT with a nonzero C1 gate and a nonzero C2 gate.
Create a cost matrix that assigns:
Track 1 to detection 1 within the C1 gate and detection 2 within the C2 gate.
Track 2 to detection 2 within the C2 gate and detection 3 within the C3 gate.
Track 3 is unassigned.
Detection 4 is unassigned.
costMatrix = [4 9 200 Inf; 300 12 28 Inf; 32 100 210 1000]; costThresh = [5 10 30];
Calculate the assignments.
[assignments, unassignedTracks, unassignedDets] = assignTOMHT(costMatrix,costThresh)
assignments = 4x2 uint32 matrix 1 1 1 2 2 2 2 3
unassignedTracks = 2x1 uint32 column vector 2 3
unassignedDets = 2x1 uint32 column vector 3 4
Tracks that are assigned detections within the C1 gate are not considered as unassigned. For example, track 1. Detections that are assigned to tracks within the C2 gate are not considered as unassigned. For example, detections 1 and 2.
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
costThreshold— Assignment gates
Assignment gates, specified as a positive, real-valued three-element vector
c1gate <= c2gate <=
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.
Three assignment thresholds, C1 , C2, and C3, control (1) the assignment of a detection to a track, (2) the creation of a new branch from a detection, and (3) the creation of a new branch from an unassigned track. The threshold values must satisfy: C1 <= C2 <= C3.
If the cost of an assignment is
C = costmatrix(i,j), the following
hypotheses are created based on comparing the cost to the values of the assignment
thresholds. Below each comparison, there is a list of the possible hypotheses.
Increase the value of C3 if there are detections that should be assigned to tracks but are not. Decrease the value if there are detections that are assigned to tracks they should not be assigned to (too far away).
Increasing the values C1 and C2 helps control the number of track branches that are created. However, doing so reduces the number of branches (hypotheses) each track has.
To allow each track to be unassigned, set C1 = 0.
To allow each detection to be unassigned, set C2 = 0.
 Werthmann, John R. "Step-by-step description of a computationally efficient version of multiple hypothesis tracking." In Signal and Data Processing of Small Targets 1992, vol. 1698, pp. 288-300. International Society for Optics and Photonics, 1992.