  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.
