The Mean Shape under the Relative Curvature Condition
提出椭圆管表示框架，通过相对曲率条件约束形状空间，确保平均形状无局部自交，用于分析结肠和海马等解剖结构，并应用于早期帕金森病的海马结构统计检验。
A key challenge for object representations is defining shape spaces that contain only geometrically valid objects, excluding those that are self-intersecting or otherwise invalid. Such shape spaces inherently ensure that Fréchet means of object populations do not locally self-intersect. We show how to produce a shape space guaranteeing no local self-intersections for specific but important cases where objects are represented by swept elliptical disks. This representation can model a variety of anatomic objects, such as the colon and hippocampus. Our approach for computing geodesic paths in this shape space enables detailed comparisons of structural variations between groups, such as patients and controls. The guarantee is met by constraining the shape space using the Relative Curvature Condition (RCC) of swept regions. This study introduces the Elliptical Tube Representation (ETRep) framework to provide a systematic approach to ensure valid mean shapes, effectively addressing the challenges of complex non-convex spaces while adhering to the RCC. The ETRep shape space incorporates an intrinsic distance metric defined based on the skeletal coordinate system of the shape space. The proposed methodology is applied to statistical shape analysis, facilitating the development of both global and partial hypothesis testing methods, which were employed to investigate hippocampal structures in early Parkinson’s disease.