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We present CortexODE, a deep learning framework for cortical surfacereconstruction. CortexODE leverages neural ordinary differential equations(ODEs) to deform an input surface into a target shape by learning adiffeomorphic flow. The trajectories of the points on the surface are modeledas ODEs, where the derivatives of their coordinates are parameterized via alearnable Lipschitz-continuous deformation network. This provides theoreticalguarantees for the prevention of self-intersections. CortexODE can beintegrated to an automatic learning-based pipeline, which reconstructs corticalsurfaces efficiently in less than 5 seconds. The pipeline utilizes a 3D U-Netto predict a white matter segmentation from brain Magnetic Resonance Imaging(MRI) scans, and further generates a signed distance function that representsan initial surface. Fast topology correction is introduced to guaranteehomeomorphism to a sphere. Following the isosurface extraction step, twoCortexODE models are trained to deform the initial surface to white matter andpial surfaces respectively. The proposed pipeline is evaluated on large-scaleneuroimage datasets in various age groups including neonates (25-45 weeks),young adults (22-36 years) and elderly subjects (55-90 years). Our experimentsdemonstrate that the CortexODE-based pipeline can achieve less than 0.2mmaverage geometric error while being orders of magnitude faster compared toconventional processing pipelines.

CortexODE: Learning Cortical Surface Reconstruction by Neural ODEs