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

Thomas M. Menino Convention & Exhibition Center 

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 with flexible and interpretable measures of the intrinsic shape and variability of shape in geometric objects. One such
method called Elastic Shape Analysis (ESA) measures differences in the shape of two objects invariant to transformations, such as rotation, scale, translation, and parameterization. While useful for many image applications, formal statistical inference methods applying ESA to an image are limited. In this paper we introduce a hypothesis testing method that computes empirical confidence intervals of the elastic shape distance (ESD) between the true shape and the estimated shape. This methodology enables testing whether a prespecified null shape of the latent structure could plausibly have generated the empirical data distribution. The effectiveness of the method is illustrated through several numerical studies and real world image examples in inertial confinement fusion (ICF).

Bootstrap confidence Intervals

Elastic Shape Analysis

Hypothesis Test

Image Processing 

Section on Statistics in Imaging