The relative curvature condition (RCC) serves as a crucial constraint, ensuring the avoidance of self-intersection problems in calculating the mean shape over a sample of swept regions. By considering the RCC, this work discusses estimating the mean shape for a class of swept regions called elliptical slabular objects based on a novel shape representation, namely elliptical tube representation (ETRep). The ETRep shape space equipped with extrinsic and intrinsic distances in accordance with object transformation is explained. The intrinsic distance is determined based on the intrinsic skeletal coordinate system of the shape space. Further, calculating the intrinsic mean shape based on the intrinsic distance over a set of ETReps is demonstrated. The proposed intrinsic methodology is applied for the statistical shape analysis to design global and partial hypothesis testing methods to study the hippocampal structure in early Parkinson's disease.

翻译：相对曲率条件（RCC）作为一项关键约束，可确保在计算扫掠区域样本的平均形状时避免自相交问题。本研究通过引入RCC，基于一种新型形状表示——椭圆管表示（ETRep），探讨了一类名为椭圆板状物体的扫掠区域的平均形状估计方法。阐述了ETRep形状空间如何依据物体变换配备外在距离与内在距离，其中内在距离由形状空间的内在骨骼坐标系决定。进一步地，展示了基于一组ETRep的内在距离计算内在平均形状的方法。所提出的内在方法论被应用于统计形状分析，以设计全局和局部假设检验方法，研究早期帕金森病中海马体的结构变化。