Gaussian Splatting with Discretized SDF for Relightable Assets
Authors: name: Zuo-Liang Zhu, name: Jian Yang, name: Beibei Wang

3D Gaussian splatting (3DGS) has shown its detailed expressive ability and
highly efficient rendering speed in the novel view synthesis (NVS) task. The
application to inverse rendering still faces several challenges, as the
discrete nature of Gaussian primitives makes it difficult to apply geometry
constraints. Recent works introduce the signed distance field (SDF) as an extra
continuous representation to regularize the geometry defined by Gaussian
primitives. It improves the decomposition quality, at the cost of increasing
memory usage and complicating training. Unlike these works, we introduce a
discretized SDF to represent the continuous SDF in a discrete manner by
encoding it within each Gaussian using a sampled value. This approach allows us
to link the SDF with the Gaussian opacity through an SDF-to-opacity
transformation, enabling rendering the SDF via splatting and avoiding the
computational cost of ray marching.The key challenge is to regularize the
discrete samples to be consistent with the underlying SDF, as the discrete
representation can hardly apply the gradient-based constraints (\eg Eikonal
loss). For this, we project Gaussians onto the zero-level set of SDF and
enforce alignment with the surface from splatting, namely a projection-based
consistency loss. Thanks to the discretized SDF, our method achieves higher
relighting quality, while requiring no extra memory beyond GS and avoiding
complex manually designed optimization. The experiments reveal that our method
outperforms existing Gaussian-based inverse rendering methods. Our code is
available at https://github.com/NK-CS-ZZL/DiscretizedSDF.