Not yet reviewed by Pith; the record is open.

Accurate geometric reconstruction of deformable tissues in monocular endoscopic video remains a fundamental challenge in robot-assisted minimally invasive surgery. Although recent volumetric and point primitive methods based on neural radiance fields (NeRF) and 3D Gaussian primitives have efficiently rendered surgical scenes, they still struggle with handling artifact-free tool occlusions and preserving fine anatomical details. These limitations stem from unrestricted Gaussian scaling and insufficient surface alignment constraints during reconstruction. To address these issues, we introduce Surgical Gaussian Surfels (SGS), which transform anisotropic point primitives into surface-aligned elliptical splats by constraining the scale component of the Gaussian covariance matrix along the view-aligned axis. We also introduce the Fully Fused Deformation Multilayer Perceptron (FFD-MLP), a lightweight Multi-Layer Perceptron (MLP) that predicts accurate surfel motion fields up to 5x faster than a standard MLP. This is coupled with locality constraints to handle complex tissue deformations. We use homodirectional view-space positional gradients to capture fine image details by splitting Gaussian Surfels in over-reconstructed regions. In addition, we define surface normals as the direction of the steepest density change within each Gaussian surfel primitive, enabling accurate normal estimation without requiring monocular normal priors. We evaluate our method on two in-vivo surgical datasets, where it outperforms current state-of-the-art methods in surface geometry, normal map quality, and rendering efficiency, while remaining competitive in real-time rendering performance. We make our code available at https://github.com/aloma85/SurgicalGaussianSurfels