Deformable 2D Gaussian Splatting

Building upon the real-time rendering capability of 3D Gaussian Splatting (3DGS), 2D Gaussian Splatting (2DGS) achieves improved surface reconstruction and geometric fidelity for novel view synthesis through explicit planar Gaussian primitives. However, the smooth falloff inherent to Gaussian kernels fundamentally limits the reconstruction of high-frequency shape signals, causing over-smoothed edges and loss of fine geometric detail. Prior works have explored alternative kernel functions to address this limitation, yet through systematic evaluation across signal fitting tasks, we find that all existing kernels suffer from the Gibbs phenomenon — producing oscillatory artifacts near sharp discontinuities. This observation motivates a fundamentally different strategy: rather than replacing the kernel, we make it deformable. This study presents Deformable 2D Gaussian Splatting, which augments each Gaussian surfel with a learnable, monotonic coordinate remapping in its local tangent plane. With only a single free control point per axis (two extra parameters), the remapping enables asymmetric radial profiles, allowing each primitive to reliably capture sharp edges and irregular structures that symmetric kernels inherently cannot represent. The deformation operates on the 2D tangent plane of 2DGS, preserving the differentiable rasterization pipeline with negligible overhead, and is optimized end-to-end through rendering loss alone. Experiments on MipNeRF 360 and Tanks&Temples demonstrate that our method effectively suppresses Gibbs artifacts at sharp boundaries and achieves state-of-the-art performance among 2DGS-based approaches in PSNR, SSIM, and LPIPS.