CLONE: Continuous Latent Optimization for Normal Estimation via 3D Gaussian Splatting

Abstract

We propose CLONE, a Continuous Latent Optimization framework for Normal Estimation via 3D Gaussian splatting. The core idea is to construct an image-geometry-image consistency loop that unifies explicit geometric representation with differentiable rendering, thereby enabling weakly supervised learning without normal ground truth. Specifically, CLONE comprises four components. First, by introducing a differentiable light interaction model with a learnable modulation kernel, we perform a unified reparameterization of the 3DGS parameter space, establishing an explicit and stable mapping between 3DGS geometric parameters and surface normals and turning the photometric loss into an internal supervision signal. Second, the conditional single-step deterministic refinement network integrates denoising architectures with differentiable reprojection constraints to refine the initial normals, thereby adaptively recovering the high-frequency details erased by the inherently smooth Gaussian primitives. Third, the cross-domain gating fusion mechanism adaptively combines the two complementary normal estimates while imposing multi-view reprojection consistency and implicit geometric regularization, reconciling the geometrically consistent yet over-smooth 3DGS estimate with the detailed yet potentially geometry-inconsistent refinement. Finally, all components are jointly optimized under a unified photometric reprojection objective with geometric consistency regularizations in a fully differentiable pathway, and the directional regularization aligns the learnable principal directions with the geometric normals, achieving an end-to-end optimization closed loop without relying on external normal labels.