assignTOMHT

Track-oriented multi-hypotheses tracking assignment

Syntax

[assignments,unassignedrows,unassignedcolumns] = assignTOMHT(costmatrix,costThreshold)

Description

[assignments,unassignedrows,unassignedcolumns] = assignTOMHT(costmatrix,costThreshold) returns a table of assignments, assignments, of detections to tracks using a track-oriented multi-hypothesis (TOMHT) algorithm.

The cost of each potential assignment is contained in the cost matrix, 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 costmatrix to 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, unassignedrows, and a list of unassigned detections, unassignedcolumns.

Examples

Assignment Using AssignTOMHT

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 = 4×2 uint32 matrix

   1   1
   1   2
   2   2
   2   3

unassignedTracks = 2×1 uint32 column vector

   2
   3

unassignedDets = 2×1 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.

Input Arguments

costmatrix — Cost matrix

real-valued M-by-N

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 Inf entries to indicate that an assignment is prohibited. The cost matrix cannot be a sparse matrix.

Data Types: single | double

costThreshold — Assignment gates

positive, real-valued 3-element vector

Assignment gates, specified as a positive, real-valued three-element vector [c1gate,c2gate,c3gate] where c1gate <= c2gate <= c3gate.

Example: [0.1,0.3,0.5]

Data Types: single | double

Output Arguments

assignments — Assignment of tracks to detections

integer-valued L-by-2 matrix

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.

Data Types: uint32

unassignedrows — Indices of unassigned tracks

integer-valued P-by-1 column vector

Indices of unassigned tracks, returned as an integer-valued P-by-1 column vector.

Data Types: uint32

unassignedcolumns — Indices of unassigned detections

integer-valued Q-by-1 column vector

Indices of unassigned detections, returned as an integer-valued Q-by-1 column vector.

Data Types: uint32

Algorithms

Assignment Thresholds for Multi-Hypothesis Tracker

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.

Tips:

• 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.

References

[1] 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.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2018b