Nonlinear Probabilistic Latent Variable Models for Groupwise Correspondence Analysis in Brain Structures

Neuroimage correspondence analysis is critical in applications that model neurodegenerative disease progression. Establishing meaningful relations between non-rigid objects such as brain structures poses a challenging topic in the bio-imaging signal processing field. In this paper, we introduce a novel nonlinear probabilistic latent variable model approach to infer shape correspondences of brain structures. To this end, we perform an unsupervised clustering process that is automatically carried out by a nonlinear kernelized probabilistic latent variable model. The kernel embeddings are accomplished by using random Fourier features as nonlinear mappings of 3D shape descriptors. We experimentally show how the model proposed can accurately establish meaningful relations between any pair of non-rigid shapes such as those brain structures related to the Alzheimer's disease.