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).

翻译：图像中物体的形状通常复杂且高维，其变化方式无法被标准欧几里得几何与统计方法所捕捉。统计形状分析包含了一系列方法，用于灵活且可解释地度量几何对象的固有形状及其变异性。弹性形状分析（Elastic Shape Analysis, ESA）是其中之一，它通过轮廓表示物体，并以旋转、尺度、平移和参数化不变的方式度量物体间的形状差异。尽管ESA在众多图像应用中对于量化物体形状非常有用，但基于图像的ESA领域中正式的统计推断方法仍较为有限。本文提出了一种基于经验置信区间的假设检验流程，用于检验所提出的潜在真实形状与估计形状之间的弹性形状距离（Elastic Shape Distance, ESD）。该置信区间采用适用于非光滑泛函的自举法构建，从而考虑了ESD的非可微性。通过数值实验以及来自惯性约束聚变（Inertial Confinement Fusion, ICF）的真实图像示例，验证了该方法的有效性。