Bayesian Clustering of n-gons

Authors

• Bryn M. Brakefield, The University of Texas at Dallas
• Huimin Li, The University of Texas Rio Grande Valley
• Bencong Zhu, Shenzhen Technology University
• Kevin W. Jin, Yale School of Medicine

Document Type

Article

Publication Date

1-1-2026

Abstract

In statistical shape analysis, transformation-invariant representations are used to quantify structural heterogeneity. Landmark-based methods define shapes via sets of discrete correspondence points, whereas functional approaches model boundaries as continuous curves and are formulated with elastic metrics. However, both treat registration as a separate procedure, decoupling it from statistical inference. We introduce a model-based approach that jointly clusters and registers polygonal chains (n-gons) using their normalized interior angles and side lengths. To account for geometric constraints, we model the data using a weighted composite likelihood constructed from truncated Dirichlet marginal components. Furthermore, we employ a mixture-of-finite-mixtures prior model to infer the number of clusters. Registration is incorporated into the model to align the n-gons and to construct cluster-specific mean shapes. We evaluated our method on a human pose estimation dataset involving gaming actions and on a facial triangular mesh simplification task, demonstrating its applicability in domains involving structured geometric data.

Comments

Copyright © 2026 International Society for Bayesian Analysis  

Recommended Citation

Brakefield, Bryn M., Huimin Li, Bencong Zhu, Kevin W. Jin, Stephen E. McKeown, and Qiwei Li. "Bayesian Clustering of n-gons." Bayesian Analysis 1, no. 1 (2025): 1-26. https://doi.org/10.1214/26-BA1601

First Page

1

Last Page

26

Publication Title

Bayesian Analysis

DOI

10.1214/26-BA1601