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2D Gaussian Splatting for Geometrically Accurate Radiance Fields
Binbin Huang, Zehao Yu, Anpei Chen, Andreas Geiger, Shenghua Gao
TL;DR
3DGS delivers efficient, high-quality novel view synthesis but represents surfaces inaccurately because its geometry is multiview inconsistent. 2DGS replaces volumetric Gaussians with oriented planar disks, adds perspective-correct ray-splat rendering and geometric regularization, and reports accurate, view-consistent geometry with competitive appearance quality and efficient rendering.
Problem
3DGS lacks accurate, multiview-consistent surface geometry, while existing surfel-based methods commonly require ground-truth geometry, depth sensors, or constrained lighting.
Method
2DGS represents scenes with oriented 2D Gaussian disks, renders them through explicit ray-splat intersection, and uses depth distortion and normal consistency regularization.
Results
2DGS achieves geometrically accurate and view-consistent reconstruction with competitive appearance quality, fast training, and real-time rendering.
Takeaways & Limitations
Planar Gaussian primitives provide an explicit surface representation that supports accurate geometry modeling and novel view synthesis without requiring known geometry.
Takeaways & Limitations
The method assumes fully opaque surfaces, can underrepresent fine geometry in texture-poor areas, and may trade image quality against geometry through regularization.
Abstract
from arXiv · showhide
3D Gaussian Splatting (3DGS) has recently revolutionized radiance field reconstruction, achieving high quality novel view synthesis and fast rendering speed without baking. However, 3DGS fails to accurately represent surfaces due to the multi-view inconsistent nature of 3D Gaussians. We present 2D Gaussian Splatting (2DGS), a novel approach to model and reconstruct geometrically accurate radiance fields from multi-view images. Our key idea is to collapse the 3D volume into a set of 2D oriented planar Gaussian disks. Unlike 3D Gaussians, 2D Gaussians provide view-consistent geometry while modeling surfaces intrinsically. To accurately recover thin surfaces and achieve stable optimization, we introduce a perspective-correct 2D splatting process utilizing ray-splat intersection and rasterization. Additionally, we incorporate depth distortion and normal consistency terms to further enhance the quality of the reconstructions. We demonstrate that our differentiable renderer allows for noise-free and detailed geometry reconstruction while maintaining competitive appearance quality, fast training speed, and real-time rendering.
1 INTRODUCTION
The paper introduces 2D Gaussian Splatting to address geometric inaccuracies in 3DGS while preserving efficient novel view synthesis. It represents scenes with oriented 2D disks, uses perspective-correct splatting and regularization, and targets accurate, view-consistent reconstruction.
- Method: 2DGS represents scenes with oriented elliptical disks whose tangent vectors define surface normals and whose parameters can be optimized from unknown geometry.This provides intrinsic surface modeling without requiring ground-truth geometry or depth sensors.
- Method: The differentiable renderer uses explicit ray-splat intersections, perspective-correct splatting, rasterization, and volumetric integration for rendering.Elliptical projections are accumulated through alpha blending in image space.
- Method: Depth distortion and normal consistency regularization improve surface reconstruction by concentrating splats along rays and aligning rendered normals with depth-derived geometry.The paper introduces both terms to reduce noise and stabilize reconstruction.
- Results: The approach reports state-of-the-art geometry reconstruction and novel view synthesis among explicit representations while maintaining efficient differentiable rendering.The renderer is described as highly efficient and supports real-time rendering.
- Motivation: 3DGS produces inconsistent geometry because viewpoint-dependent intersection planes and affine projection limit multiview and perspective accuracy.These issues can lead to noisy reconstructions, especially for thin surfaces.
5 TRAINING
The method regularizes 2D Gaussian reconstruction with depth distortion and normal consistency losses to reduce noise and improve surface alignment. It optimizes these terms with RGB reconstruction loss from posed images and an initial sparse point cloud.
- Photometric-only optimization can produce noisy reconstructions, motivating depth distortion and normal consistency regularization.The paper identifies this as an inherent challenge in unconstrained 3D reconstruction.
- Depth distortion concentrates blending weights along each ray by minimizing distances between ray-splat intersections.Unlike Mip-NeRF360, the method directly adjusts intersection depths z_i to concentrate splats.
- Normal consistency aligns splat normals with depth-gradient normals so 2D splats locally approximate the actual object surface.The estimated normal N is computed from nearby depth points using finite differences.
- The model is optimized from an initial sparse point cloud using posed images and a final loss combining RGB reconstruction with both regularizers.The RGB term combines L1 and D-SSIM; α is 1000 for bounded scenes, 100 for unbounded scenes, and β is 0.05 for all scenes.
6 EXPERIMENTS
Experiments evaluate 2DGS on DTU, Tanks and Temples, and Mip-NeRF360, comparing appearance, geometry, efficiency, and design choices against prior methods. Results show strong reconstruction quality and speed, while ablations confirm the value of regularization and mesh-extraction choices.
- Evaluation setup: 2DGS is evaluated for appearance and geometry against state-of-the-art implicit and explicit methods across several datasets.The evaluation includes DTU, Tanks and Temples, and Mip-NeRF360, with both comparisons and component analyses.
- Appearance reconstruction: Visual comparisons on Mip-NeRF360 report sharper edges and intricate details than 3DGS and SuGaR in test-set views.The Mip-NeRF360 evaluation focuses on quantitative appearance because ground-truth geometry is unavailable.
- Geometry and efficiency: 100× faster reconstruction than SDF-based methods is reported on DTU while achieving the highest reconstruction accuracy.The DTU comparison also reports more than 3× faster reconstruction than SuGaR.
- Geometry and efficiency: 2DGS outperforms compared methods in DTU Chamfer distance and provides qualitatively detailed reconstructions with fewer outliers.The method is also reported to achieve competitive results with SDF models and better reconstruction than explicit methods on Tanks and Temples.
- Ablations: Applying both normal-consistency and depth-distortion regularization gives the best ablation performance on DTU.Removing normal consistency produces incorrect orientations, while removing depth distortion produces noisy surfaces.
- Ablations: TSDF fusion with median depth outperforms expected-depth extraction and screened Poisson reconstruction for mesh extraction.Expected depth is more sensitive to outliers, while screened Poisson cannot incorporate Gaussian opacity and size.
7 CONCLUSION
The paper concludes that 2D Gaussian Splatting enables accurate, view-consistent geometry reconstruction and rendering, supported by experiments across challenging datasets. Its scope is limited by assumptions about opacity, densification behavior, and regularization trade-offs.
- Conclusion: 2D Gaussian primitives support accurate and view-consistent geometry modeling and rendering for radiance-field reconstruction.The conclusion presents 2DGS as a method for geometrically accurate radiance-field reconstruction.
- Conclusion: Experiments on several challenging datasets verify the method’s effectiveness and efficiency.
- Limitations: The method assumes fully opaque surfaces, limiting accurate handling of semi-transparent objects such as glass.It extracts meshes from multi-view depth maps, which creates this stated challenge.
- Limitations: Texture-biased densification can produce less accurate representations of fine geometric structures.The paper notes that improved densification could mitigate this issue.
- Limitations: Regularization can trade image quality against geometry and may over-smooth some regions.
A DETAILS OF DEPTH DISTORTION
The depth-distortion loss adapts distortion regularization to unordered Gaussian ray intersections by using an L2 formulation in normalized device coordinates. A single forward pass accumulates the quantities needed to compute the loss during front-to-back Gaussian marching.
- Depth-distortion formulation: The method transforms intersected depths z into NDC space and uses an L2 loss because Gaussian intersection depths may be unordered.Near and far planes are empirically set to 0.2 and 1000.
- Efficient computation: Prefix accumulators A_i, D_i, and D²_i enable the nested distortion computation in a single forward pass.The loss through the i-th Gaussian is computed while marching Gaussians front-to-back.
- Optimization effect: Gradients are back-propagated through the intersection depth m, encouraging Gaussians to move tightly together.This differs from implicit methods whose sampled depths are predefined and non-differentiable.
- Motivation: Affine approximation in 3DGS introduces perspective distortion and inaccurate depth that can violate normal consistency.
B DEPTH CALCULATIONS
The meshing process offers mean and median depth computations from intersected Gaussian depths. Median depth uses visibility at T_i=0.5 and is reported as more robust in cases where accumulated alpha is insufficient.
- Mean depth weights intersected depths by each Gaussian’s contribution and normalizes by accumulated alpha for planar-disk visualization.The contribution weight is defined using visibility and alpha; normalization ensures the rendered depth represents a planar 2D disk.
- Median depth selects the largest visible depth using T_i=0.5 as the pivot between surface and free space.This computation is used as an alternative depth estimate for meshing.
- The median-depth computation is more robust than the comparison method when accumulated alpha does not reach 0.5.Instead of assigning a default value of 15, it selects the last Gaussian, which the authors report is more accurate and suitable for training.
C ADDITIONAL BASELINES
Additional baselines evaluate meshing and rasterization choices on the DTU dataset. TSDF improves overall completion metrics over the substituted baseline, while ray-splat intersection improves perspective-projected depth generation and depth fusion.
- Table 6 compares additional DTU baselines, with all models trained for 30k iterations.
- Replacing SPSR with TSDF in the meshing strategy improves overall completion metrics.The comparison integrates the meshing approach into the baseline analysis, contrasting TSDF with SuGaR’s SPSR-based pipeline.
- Iteratively adding TSDF, perspective-correct rasterization, and median depth enhances 2DGS performance in ablation experiments.
- Ray-splat intersection produces more accurate depth maps under perspective projection than the affine approximation baseline, improving depth fusion performance.
D ADDITIONAL RESULTS
Additional results report comparable appearance performance without regularizations and present dataset-specific visual comparisons. The reported limitations include difficulty reconstructing semi-transparent surfaces and holes in high-light-intensity regions.
- 2DGS achieves comparable performance on the Synthetic NeRF dataset without regularizations.The comparison is reported using PSNR scores.
- PSNR scores are reported for the Tanks and Temples dataset.
- Appearance results are reported with PSNR, SSIM, and LPIPS scores for the MipNeRF360 dataset.
- The visual comparisons include normals from depth gradients for 3DGS and 2DGS.
- Appearance renderings from reconstructed 2D Gaussian disks are shown for DTU, Tanks and Temples, and MipNeRF360.
- 2DGS struggles to accurately reconstruct semi-transparent surfaces and tends to create holes in areas with high light intensity.