Nonparametric Bayesian Regression and Classification on Manifolds, With Applications to 3D Cochlear Shapes

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In this paper, we study the cochlear spiral-shaped cavity within the petrous part of the temporal bone. This problem is particularly challenging due to the relationship between the shape and gender, especially for children. We introduce a novel learning-based method that uses advances in shape analysis of curves and statistical modeling to perform regression and classification on cochlear shapes. Advanced shape analysis studies such as regression and classification are performed on curved manifolds which make the standard formulations fail to reach good performances. Focusing on cochlear shapes, we introduce a novel framework to overcome these limitations by avoiding inference on infinite-dimensional spaces when using a Bayesian inference with spherical Gaussian processes decomposition.

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