Pseudo-Rendering for Resolution and Topology-Invariant Cortical Parcellation

Parcellation of mesh models for cortical analysis is a central problem in neuroimaging. Most classical and deep learning methods have requisites in terms of mesh topology, requiring inputs that are homeomorphic to a sphere (i.e., no holes or handles). Topology correction algorithms do exist, but their computational complexity is quadratic with the size of the topological defects - sometimes hours, effectively precluding segmentation of incorrect meshes, including those derived from imperfect segmentations or obtained from inherently noisy modalities like surface scanning. Furthermore, deep learning mesh segmentation also struggles surface scans of brains because they are relatively nondescript and require modeling of longer-range dependencies. Here we propose "pseudo-render-inverse-render" (PRIR), a novel perspective on cortical mesh parcellation that effectively reframes the problem as a 2D segmentation task using an direct-inverse rendering framework. Our approach: (i) renders the mesh from a number of perspectives, projecting the three components of the face normal vectors to a three-channel image; (ii) segments these images with U-Nets; (iii) maps the 2D segmentations back to vertices (inverse rendering); and (iv) aggregates the information from multiple views, postprocessing the output with a Markov Random Field to ensure smoothness and segmentation of occluded areas. PRIR is not affected by mesh topology and easily captures long-range dependencies with the U-Nets. Our results demonstrate: state-of-the-art accuracy on topologically correct white matter meshes; equally accurate performance on simulated surface scans; and robust segmentation of real surface scans.