Consistent Correspondence of Cone-Beam CT Images Using Volume Functional Maps

Dense correspondence between Cone-Beam CT (CBCT) images is desirable in clinical orthodontics for both intra-patient treatment evaluation and inter-patient statistical shape modeling and attribute transfer. Conventional 3D deformable image registration relies on time-consuming iterative optimization for correspondences. The recent forest-based correspondence methods often require large offline training costs and a separate regularization in the post-processing. In this work, we propose an efficient volume functional map for dense and consistent correspondence between CBCT images. We design a group of volume functions specifically for CBCT images and construct a reduced functional space on supervoxels. The low-dimensional map between the limited spectral bases determines the dense supervoxel-wise correspondence in an unsupervised way. Further, we perform consistent functional mapping in a collection of volume images to handle ambiguous correspondences of craniofacial structures, e.g., those due to the intercuspation. A subset of orthonormal volume functional maps is optimized on a Stiefel manifold simultaneously, which determines the cycle-consistent pairwise functional maps in the volume collection. Benefits of the proposed volume functional maps have been illustrated in label propagation and segmentation transfer with improved performance over conventional methods.