Dense correspondence of deformable volumetric images via deep spectral embedding and descriptor learning

Deformable image correspondence plays an essential role in a variety of medical image analysis tasks. Most existing deep learning-based registration and correspondence techniques exploit metric space alignments in the spatial domain and learn a nonlinear voxel-wise mapping function between volumetric images and displacement fields, agnostic to intrinsic structure correspondence. When confronted with high-frequency perturbations of patients' poses and anatomical structural variations, they relied on prior rigid and affine transformations, as well as additional segmentation masks and landmark annotations for reliable registration. This paper presents a data-driven spectral mapping-based correspondence framework to handle the intrinsic correspondence of anatomical structures. At the core of our approach lies a deep convolutional framework that approximates spectral bases and optimizes volumetric descriptors. The multi-path graph convolutional network-based spectral embedding approximation module relieves the computationally expensive eigendecomposition-based embedding of volumetric images. The deep descriptor learning module surpasses the prior hand-crafted descriptors and the descriptor selection. We showcase the efficacy of the core modules, i.e., the spectral embedding approximation and descriptor learning, for volumetric image correspondence and the atlas-based registration on two volumetric image datasets. The proposed method achieves comparable correspondence accuracy with the state-of-the-art deep registration models, resilient to pose and shape perturbations.