A Gaussian process model for data association and a semidefinite programming solution

Area of Science:

• Computer Vision
• Machine Learning
• Statistical Modeling

Background:

• Data association is crucial for tracking objects across frames.
• Existing methods often struggle with complex scenarios and computational complexity.
• Ensuring trajectory smoothness is a key challenge in data association.

Purpose of the Study:

• To propose a novel Bayesian model for the data association problem.
• To enforce trajectory smoothness using Gaussian process priors.
• To frame data association as an optimization problem solvable via MaxCut.

Main Methods:

• Developed a Bayesian model incorporating Gaussian process priors for trajectory smoothness.
• Utilized the evidence framework to score candidate data associations.
• Transformed the problem into a constrained Max K-section problem, specifically MaxCut for K=2.
• Employed Semidefinite Programming (SDP) relaxation for efficient approximate solutions to the MaxCut problem.

Main Results:

• The proposed model efficiently finds optimal data associations.
• The optimization problem is shown to be equivalent to a constrained Max K-section problem.
• For K=2, the problem reduces to MaxCut, solvable with SDP relaxation.
• The resulting clustering is determined by two hyperparameters, selectable via maximum evidence.

Conclusions:

• The Bayesian model provides an effective solution for data association with smooth trajectories.
• The formulation as a MaxCut problem allows for efficient and optimal solutions.
• Hyperparameter selection is streamlined through maximum evidence, enhancing model usability.