Nonparametric Multi-shape Modeling with Uncertainty Quantification
This work addresses the challenge of incorporating between-curve dependence in shape analysis, which is important for statistical tasks in fields like medical imaging or computer vision, though it appears incremental as it extends existing Gaussian process methods.
The authors tackled the problem of modeling multiple closed curves with structural similarities by proposing a multi-output, multi-dimensional Gaussian process framework, which provides meaningful uncertainty quantification for shape analysis tasks.
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.