Spectral Analysis Towards Geometric Auto Encoding of Subcortical Structures

Statistical shape analysis can benefit from algorithms that are intrinsic to the shape; multi-scale and hierarchical; robust to perturbations, yet sensitive to fine-grained content. For this purpose we investigate Deep Spectral Kernels (DSKs), trainable and hierarchical similarity functions based on spectral analysis. DSKs are shape encoders. They are multi-layer and compositional architectures that map semi-structured, high dimensional objects such as meshes to representations fit for machine learning. The encoding generates a sequence of increasingly high-level geometries, augmented with functional maps that summarize relevant details from finer scales. At the core of the procedure, the Spectral Wavelet Transform allow for the encoding of structural and functional data to be done in a shape-intrinsic manner. We experiment with unsupervised clustering of subcortical structures.