Nonparametric Multi-shape Modeling with Uncertainty Quantification

TL;DR

This paper introduces a nonparametric Gaussian process framework for modeling multiple closed curves with uncertainty quantification, capturing complex dependencies and enabling advanced shape analysis.

Contribution

It presents a novel multi-output Gaussian process approach for nonparametric shape modeling, addressing dependence and uncertainty in collections of closed curves.

Findings

Effective modeling of multiple closed curves with uncertainty quantification.

Demonstrated utility on shape-related tasks.

Addresses multi-level dependence in functional data.

Abstract

The modeling and uncertainty quantification of closed curves is an important problem in the field of shape analysis, and can have significant ramifications for subsequent statistical tasks. Many of these tasks involve collections of closed curves, which often exhibit structural similarities at multiple levels. Modeling multiple closed curves in a way that efficiently incorporates such between-curve dependence remains a challenging problem. In this work, we propose and investigate a multiple-output (a.k.a. multi-output), multi-dimensional Gaussian process modeling framework. We illustrate the proposed methodological advances, and demonstrate the utility of meaningful uncertainty quantification, on several curve and shape-related tasks. This model-based approach not only addresses the problem of inference on closed curves (and their shapes) with kernel constructions, but also opens doors to nonparametric modeling of multi-level dependence for functional objects in general.