[Paper Review] Object-based World Modeling in Semi-Static Environments with Dependent Dirichlet-Process Mixtures

Lawson L. S. Wong, Thanard Kurutach+2 more|arXiv (Cornell University)|Dec 2, 2015

Bayesian Methods and Mixture Models16 references3 citations

TL;DR

This paper proposes a dependent Dirichlet process mixture model (DDPMM) for object-based world modeling in semi-static environments, where objects remain mostly stationary between observations. By extending static clustering with temporal dependencies via DDPMM and deriving a MAP inference algorithm with data association constraints, the method improves computational efficiency over traditional multiple-target tracking while maintaining accuracy in object tracking and attribute estimation under noisy, partial observations.

ABSTRACT

To accomplish tasks in human-centric indoor environments, robots need to represent and understand the world in terms of objects and their attributes. We refer to this attribute-based representation as a world model, and consider how to acquire it via noisy perception and maintain it over time, as objects are added, changed, and removed in the world. Previous work has framed this as multiple-target tracking problem, where objects are potentially in motion at all times. Although this approach is general, it is computationally expensive. We argue that such generality is not needed in typical world modeling tasks, where objects only change state occasionally. More efficient approaches are enabled by restricting ourselves to such semi-static environments. We consider a previously-proposed clustering-based world modeling approach that assumed static environments, and extend it to semi-static domains by applying a dependent Dirichlet-process (DDP) mixture model. We derive a novel MAP inference algorithm under this model, subject to data association constraints. We demonstrate our approach improves computational performance in semi-static environments.

Motivation & Objective

• To address the challenge of maintaining an accurate, attribute-based world model in human-centric indoor environments where objects change infrequently.
• To reduce computational cost by exploiting semi-static dynamics, where objects remain stationary between observation epochs, rather than assuming full dynamical motion.
• To extend static clustering-based world modeling to dynamic, semi-static domains by modeling temporal dependencies between object attributes across time.
• To develop a novel MAP inference algorithm under a DDPMM framework that respects data association constraints and handles missing or noisy observations.
• To demonstrate improved computational performance over traditional multiple-target tracking methods in semi-static settings.

Proposed method

• The method employs a dependent Dirichlet process mixture model (DDPMM) to model temporal dependencies between clusters of object detections across time, allowing for object persistence and attribute evolution.
• It uses a collapsed Gibbs sampling inference scheme with predictive likelihoods derived from Kalman filtering dynamics for pose prediction and observation likelihoods.
• Three cases are modeled for observation assignment: (1) existing and instantiated clusters, (2) existing but uninstantiated clusters (future prediction), and (3) new clusters using a noninformative base distribution.
• The predictive distribution for future poses is derived using a generalized transition model that propagates the last observed state forward with process noise, modeled as $\mathcal{N}(\mu^{k\tau}, \Sigma^{k\tau} + (t-\tau)R(a^k))$.
• For new clusters, the method uses a uniform prior over the world volume to avoid improper posterior evaluations, replacing the improper normal prior with a proper uniform distribution.
• The observation likelihood integrates over latent parameters (attribute $a^k$ and pose $x^{kt}$), combining categorical likelihoods for attributes and Gaussian likelihoods for spatial poses.

Experimental results

Research questions

• RQ1 Can a Bayesian nonparametric model effectively model object persistence and attribute changes in semi-static environments without assuming full dynamical motion?
• RQ2 How can temporal dependencies between object clusters across time be modeled to improve data association and reduce computational cost?
• RQ3 What inference strategy enables efficient, scalable world modeling under noisy, partial observations with unknown object counts?
• RQ4 How does the proposed DDPMM-based approach compare to traditional multiple-target tracking in terms of accuracy and computational efficiency in semi-static domains?
• RQ5 Can the model handle object birth, death, and attribute changes while maintaining consistent identity tracking across time?

Key findings

• The proposed DDPMM-based world modeling approach achieves significant computational efficiency gains over traditional multiple-target tracking methods in semi-static environments.
• The method successfully models object persistence, attribute changes, and object appearance/disappearance through a principled Bayesian nonparametric framework with temporal dependencies.
• The collapsed Gibbs sampling inference with predictive likelihoods enables robust data association even under high noise and occlusion, as shown by the likelihood expressions in Equations 37–41.
• The use of a uniform prior over the world volume for new cluster creation avoids improper posterior evaluations and enables stable inference without requiring improper densities.
• The model outperforms static clustering approaches by incorporating temporal dynamics, allowing for accurate tracking of object attributes and poses over time.
• The MAP inference algorithm with data association constraints effectively balances model complexity and accuracy, particularly in scenarios with false positives and negatives.