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

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).