Data points on Riemannian manifolds are fundamental objects in many applications and fields. Representations include shapes from biology and medical imaging, directions and rotations from robots. This paper addresses the problem of nonparametric regression on shapes when only few observations are available. In particular, we consider the problem of classifying unobserved 3D open parametrized curves using a continuous stochastic process to overcome the discrete nature of observations. The proposed method has a practical objective, characterizing populations of cochlear curves. The numerical solution is geometrically simpler, extensible and can be generalized for other applications. We illustrate and discuss the successful behavior of the proposed approach with various and multiple experimental results.