H-2DGS: Height-Field Gaussian Splatting for Sharp and Deformable Neurosurgical Surface Reconstruction
Neurosurgical navigation commonly presents magnetic resonance imaging (MRI) as 2D slices, making it difficult to relate the anatomy in those slices to the cortical surface observed through the surgical microscope. We seek a common 3D visualization that combines a photorealistic reconstruction of the exposed cortex during tumor surgery with whole-brain MRI context and diffusion tractography pathways. This requires the reconstructed cortex to form a clear boundary around the brain anatomy rather than a diffuse volume that obscures internal structures. Conventional 3D Gaussian Splatting (3DGS) can reproduce observed views but, under limited surgical view coverage, may distribute opacity through a thick and geometrically ambiguous band. We introduce height-field 2D Gaussian Splatting (H-2DGS), a three-stage pipeline that concentrates a robust 3DGS reconstruction, fuses its depth into a shared truncated signed distance field (TSDF) surface, and represents that surface with curved, surface-oriented Gaussian primitives. Separate height, color, and opacity bases provide local geometry and appearance, while a neighbor-transition objective coordinates overlapping patches. The explicit surface further supports postoperative alignment: MRI-derived depth deforms the reconstruction, and tracked-color supervision with alternating optimization preserves its appearance. Across five real neurosurgical cases, H-2DGS gives low multi-view depth inconsistency, a compact 7.97MB representation, and interactive rendering at 29--42ms per frame. The resulting sharp, deformable surface integrates clearly with tractography and MRI anatomy, including a postoperative resection cavity.