Distribution Estimation for Global Data Association via Approximate Bayesian Inference

2025-09-19

AI Summary

In global data association, environmental repetitions or symmetries induce ambiguity, causing conventional single-solution methods—e.g., maximum likelihood or maximum consensus—to fail under multimodal solution distributions. To address this, we introduce approximate Bayesian inference to the problem for the first time, proposing a particle-based multi-hypothesis joint optimization framework. Our approach explicitly models and concurrently evolves the solution distribution by integrating geometric and topological constraints. It combines deterministic and stochastic update rules with GPU acceleration, enabling efficient multimodal inference in point cloud registration and object-to-map matching. Experiments on highly ambiguous real-world and synthetic scenes demonstrate that our method accurately estimates multimodal distributions over transformation parameters, significantly improving association robustness and reliability compared to state-of-the-art single-solution approaches.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG

Abstract

Global data association is an essential prerequisite for robot operation in environments seen at different times or by different robots. Repetitive or symmetric data creates significant challenges for existing methods, which typically rely on maximum likelihood estimation or maximum consensus to produce a single set of associations. However, in ambiguous scenarios, the distribution of solutions to global data association problems is often highly multimodal, and such single-solution approaches frequently fail. In this work, we introduce a data association framework that leverages approximate Bayesian inference to capture multiple solution modes to the data association problem, thereby avoiding premature commitment to a single solution under ambiguity. Our approach represents hypothetical solutions as particles that evolve according to a deterministic or randomized update rule to cover the modes of the underlying solution distribution. Furthermore, we show that our method can incorporate optimization constraints imposed by the data association formulation and directly benefit from GPU-parallelized optimization. Extensive simulated and real-world experiments with highly ambiguous data show that our method correctly estimates the distribution over transformations when registering point clouds or object maps.

Problem

• Estimating multimodal distribution for global data association
• Addressing ambiguity in repetitive or symmetric environments
• Capturing multiple solution modes via Bayesian inference

Innovation

• Approximate Bayesian inference captures multimodal solutions
• Particle evolution covers underlying solution distribution modes
• GPU-parallelized optimization with incorporated constraints