Atlas-Based Shared-Boundary Deformable Multi-Surface Models through Multi-Material and Two-Manifold Dual Contouring

Abstract

This paper presents a multi-material dual “contouring” method used to convert a digital 3D voxel-based atlas of basal ganglia to a deformable discrete multi-surface model that supports surgical navigation for an intraoperative MRI-compatible surgical robot, featuring fast intraoperative deformation computation. It is vital that the final surface model maintain shared boundaries where appropriate so that even as the deep-brain model deforms to reflect intraoperative changes encoded in ioMRI, the subthalamic nucleus stays in contact with the substantia nigra, for example, while still providing a significantly sparser representation than the original volumetric atlas consisting of hundreds of millions of voxels. The dual contouring (DC) algorithm is a grid-based process used to generate surface meshes from volumetric data. The DC method enables the insertion of vertices anywhere inside the grid cube, as opposed to the marching cubes (MC) algorithm, which can insert vertices only on the grid edges. This multi-material DC method is then applied to initialize, by duality, a deformable multi-surface simplex model, which can be used for multi-surface atlas-based segmentation. We demonstrate our proposed method on synthetic and deep-brain atlas data, and a comparison of our method’s results with those of traditional DC demonstrates its effectiveness.