Speaker
Description
Statistical shape analysis relies fundamentally on the establishment of correspondence and the definition of suitable shape representations to detect and explain local dissimilarities between groups of objects. Most existing approaches are based on extrinsic or noninvariant properties, requiring alignment and often leading to biased results. Moreover, providing a mathematical interpretation of deformation types such as bending, twisting, or stretching remains challenging. To address these issues, we introduce an intrinsic and invariant framework based on hierarchical, locally parameterized representations using local coordinate systems, enabling reliable detection and interpretation of locational dissimilarities.
Building on this perspective, we focus on slab-shaped objects such as hippocampi and propose a locally parameterized discrete swept skeletal representation that ensures meaningful correspondence across samples. The model fitting procedure is constructed via boundary division and surface flattening, producing skeletal structures that reflect the underlying geometry of swept regions. The quality of the fitted models is evaluated using geometric criteria, including skeletal symmetry, tidiness, and the volume coverage of the implied boundary. This representation supports both visual and statistical analysis and demonstrates improved performance over existing skeletal approaches.
A further challenge is the definition of shape spaces that contain only geometrically valid objects, excluding self-intersections and other inconsistencies. To address this, we study the shape space for tubular objects based on the Elliptical Tube Representation (ETRep), constrained by the Relative Curvature Condition (RCC). The proposed methodology guarantees that geodesic paths remain within the space of valid shapes restricted by the RCC, ensuring that Fréchet means are free of local self-intersections. The framework defines an intrinsic distance based on skeletal coordinate systems and enables consistent comparison of structural variation between groups. Applications to hippocampal data illustrate how the proposed methodology supports both global and localized hypothesis testing within a geometrically valid and interpretable Riemannian framework.