Inference on subspheres model for directional data

Modeling deformations of a real object is an important task in computer vision, biomedical engineering and biomechanics. In this paper, we focus on a situation where a three-dimensional object is rotationally deformed about a fixed axis, and assume that many independent observations are available. Such a problem is generalized to an estimation of concentric, co-dimension 1, subspheres of a polysphere. We formulate least-square estimators as generalized Fr\'{e}chet means, and evaluate the consistency and asymptotic normality.