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A Graph Neural Network Approach for Solving the Ranked Assignment Problem in Multi-Object Tracking

Robin Dehler, Martin Herrmann, Jan Strohbeck, Michael Buchholz

Abstract

Associating measurements with tracks is a crucial step in Multi-Object Tracking (MOT) to guarantee the safety of autonomous vehicles. To manage the exponentially growing number of track hypotheses, truncation becomes necessary. In the $δ$-Generalized Labeled Multi-Bernoulli ($δ$-GLMB) filter application, this truncation typically involves the ranked assignment problem, solved by Murty's algorithm or the Gibbs sampling approach, both with limitations in terms of complexity or accuracy, respectively. With the motivation to improve these limitations, this paper addresses the ranked assignment problem arising from data association tasks with an approach that employs Graph Neural Networks (GNNs). The proposed Ranked Assignment Prediction Graph Neural Network (RAPNet) uses bipartite graphs to model the problem, harnessing the computational capabilities of deep learning. The conclusive evaluation compares the RAPNet with Murty's algorithm and the Gibbs sampler, showing accuracy improvements compared to the Gibbs sampler.

A Graph Neural Network Approach for Solving the Ranked Assignment Problem in Multi-Object Tracking

Abstract

Associating measurements with tracks is a crucial step in Multi-Object Tracking (MOT) to guarantee the safety of autonomous vehicles. To manage the exponentially growing number of track hypotheses, truncation becomes necessary. In the -Generalized Labeled Multi-Bernoulli (-GLMB) filter application, this truncation typically involves the ranked assignment problem, solved by Murty's algorithm or the Gibbs sampling approach, both with limitations in terms of complexity or accuracy, respectively. With the motivation to improve these limitations, this paper addresses the ranked assignment problem arising from data association tasks with an approach that employs Graph Neural Networks (GNNs). The proposed Ranked Assignment Prediction Graph Neural Network (RAPNet) uses bipartite graphs to model the problem, harnessing the computational capabilities of deep learning. The conclusive evaluation compares the RAPNet with Murty's algorithm and the Gibbs sampler, showing accuracy improvements compared to the Gibbs sampler.

Paper Structure

This paper contains 16 sections, 8 equations, 3 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. Multi-Object Generalized Labeled Multi-Bernoulli Filter
  4. Ranked Assignment Problem
  5. Graph Neural Networks
  6. Related Work
  7. Ranked Assignment Prediction
  8. Graph Creation
  9. Ranked Assignment Prediction Graph Neural Network
  10. Post-processing Module
  11. Experiments
  12. Training Setup
  13. Evaluation Setup
  14. Performance Evaluation
  15. Computational Complexity
  16. ...and 1 more sections

Figures (3)

  • Figure C1: Architecture of the RAPNet. Left part: Encoding of the node and edge features. Before the multiplication step of $x_s$ and $x_t$, the feature vectors are indexed with the respective edge index vectors to fit the dimensions. Right part: Decoding using LSTM layers and creation of predicted assignments. The channel sizes $C_{\text{enc}}=32$, $C_{\text{lstm}}=128$ and $C_{\text{dec}}=32$ are shown above each neural network layer. The final output $y_{\text{pred}}$ is of shape $|\mathcal{E}|\times k_{\text{max}}$.
  • Figure D1: Plots of the two sweeps of the parameters $k_{\text{max}}$ and $\nu_s$ evaluated with the scores accuracy, wp and cost. For readability reasons in the accuracy plots, only the accuracies of the first $4$ solutions for the RAPNet with the post-processing and the Gibbs sampler are shown. The legends on the right are also valid for the left plots. In the legends, RAPNet-PP and RAPNet-a indicate the versions with and without post-processing, respectively.
  • Figure D2: Distribution of matrix sizes in the simulation data.