Bootstrap-based Hypothesis Test of 2D Contours using Elastic Shape Analysis

2026-06-03

AI Summary

This study addresses the absence of formal statistical inference methods for non-smooth shape distances in elastic shape analysis (ESA). The authors propose a bootstrap-based hypothesis testing framework that, for the first time, introduces a bootstrap procedure tailored to non-smooth functionals into ESA. This approach enables the construction of empirical confidence intervals for elastic shape distances (ESD) between two-dimensional contours, facilitating statistically rigorous assessment of the discrepancy between an estimated shape and its true counterpart. The method explicitly accounts for the non-differentiability inherent in ESD while preserving invariance under rotation, scaling, translation, and reparameterization. Numerical simulations and experiments on real inertial confinement fusion (ICF) image data demonstrate the method’s effectiveness and reliability.

Abstract

Shapes of objects in images are often complex, high-dimensional, and vary in ways not captured by standard Euclidean geometry and statistics. Statistical shape analysis encompasses methods for flexible and interpretable measurement of intrinsic shape and shape variability in geometric objects. Elastic Shape Analysis (ESA) is one such method that measures shape differences between objects, represented by contours, in a way that is invariant to rotation, scale, translation, and parameterization. Although ESA is useful for quantifying shape of objects in many image applications, formal methods for statistical inference in image-based ESA remain limited. This work introduces a hypothesis test procedure based on empirical confidence intervals for the elastic shape distance (ESD) between a proposed underlying true shape and an estimated shape. The confidence intervals are created using a bootstrap procedure for non-smooth functionals, which accounts for the non-differentiability of the ESD. The effectiveness of the method is illustrated through both numerical studies and real world image examples from inertial confinement fusion (ICF).

Problem

• Elastic Shape Analysis
• Hypothesis Test
• Shape Distance
• Statistical Inference
• Bootstrap

Innovation

• Elastic Shape Analysis
• Bootstrap
• Hypothesis Testing
• Elastic Shape Distance
• Non-smooth Functional