PCAsplat: Gaussian Splatting with Local PCA Regularization

Vitor Matias; Filipe Nascimento; Kiyohiro Nakayama; João Paulo Lima; Márcus Lobo; Gordon Wetzstein; Leonidas Guibas; Afonso Paiva

cs.CVOct 7, 2026

PCAsplat: Gaussian Splatting with Local PCA Regularization

Authors: Vitor Matias, Filipe Nascimento, Kiyohiro Nakayama, João Paulo Lima, Márcus Lobo, Gordon Wetzstein, Leonidas Guibas, Afonso Paiva, +1 more

Organizations: Universidade de São Paulo · Stanford University · UFRPE · IMPA

Abstract

Gaussian splatting has emerged as a flexible representation for 3D reconstruction from posed images. However, existing methods are optimized primarily using rasterization-based losses, which supervise a splat only when it contributes to sampled camera rays. Gaussians that are occluded or contribute little to the sampled view therefore receive weak or no geometric gradients and may drift away from the underlying surface, producing undesired floaters. We introduce PCAsplat, a geometry-aware regularization framework for Gaussian splatting based on differentiable local principal component analysis (PCA). Our PCA regularizer acts directly on neighborhoods of Gaussian centers and can therefore update Gaussians that do not contribute to the current training view. We regularize the PCA eigenvalues to encourage Gaussians to move to the underlying surface with isotropic tangent-plane coverage. We also align each Gaussian normal with the PCA-estimated neighborhood normal to enforce consistent orientation. Experiments on DTU, Tanks and Temples, and NeRF Synthetic show that the splats produced by PCAsplat better approximate samples of the reference surface while substantially reducing undesired floaters. These surface-aligned splats enable downstream geometry-processing tasks, including point cloud segmentation, and direct Poisson reconstruction. Additionally, PCAsplat remains competitive under conventional novel view synthesis and mesh extraction tasks. Code will be released.

Figures & tables

Figure 1: We present PCAsplat , a geometric regularization of Gaussian splatting that aligns Gaussians with surfaces through differentiable local PCA. Compared with current methods, PCAsplat substantially reduces floaters (left) and produces cleaner point clouds with better surface coverage (center). This improved point-cloud enables downstream tasks such as instance segmentation (right).

Figure 2: Overview of PCAsplat. We regularize Gaussian neighborhoods directly in scene space. For each Gaussian, we estimate a local neighborhood and compute differentiable PCA statistics that capture the underlying tangent structure. We then regularize the local eigenspectrum to reduce neighborhood thickness and promote isotropic tangent-plane coverage. We also align Gaussian normals with PCA-derived normals, encouraging surface-aligned and well-localized splats. Our formulation is lightweight, differentiable, and directly compatible with existing splatting pipelines.

Figure 3: Balanced coverage with isotropy (left); elongated structures without it (right).

Figure 4: Qualitative comparison on DTU. PCAsplat produces surface-aligned Gaussian centers with substantially fewer floaters, sharper edges, and finer geometric detail than the baselines.

Method	24	37	40	55	63	65	69	83	97	105	106	110	114	118	122	Mean	Time
VGGT- $\Omega$	0.931	1.217	1.502	1.302	1.995	1.468	1.162	5.626	3.363	4.084	2.000	1.263	1.219	2.131	1.754	2.068	63s
COLMAP-D	0.382	0.618	0.336	0.349	0.570	0.837	0.455	1.129	0.650	0.540	0.418	0.468	0.300	0.387	0.348	0.519	26.9m
3DGS	1.056	1.148	1.396	1.035	1.285	1.609	1.354	1.836	1.349	1.005	1.662	1.536	1.037	1.274	1.077	1.311	5.2m
2DGS	0.906	1.879	1.065	0.920	1.261	2.351	1.399	1.377	1.395	0.949	1.231	1.525	1.356	1.308	1.051	1.332	10.9m
GS-Pull	1.243	0.803	1.127	0.719	1.129	1.698	1.554	1.744	1.493	0.954	1.891	1.791	0.806	1.395	1.107	1.297	21.8m
PGSR	0.621	0.651	0.817	0.611	0.804	0.780	0.729	1.020	0.800	0.647	0.801	0.651	0.510	0.666	0.571	0.712	30.5m

Table 1: Quantitative comparison on DTU. We report Chamfer distance (

\downarrow

) between reconstructed and ground-truth point clouds. We highlight the best , second-best , and third-best Gaussian-based results, with PCAsplat achieving the best overall results.

Figure 5: Qualitative comparison of cross-section slices on challenging DTU scenes.

Method	w/o PCA $\rightarrow$	w/ PCA
	Chamfer Dist. ( $\downarrow$ )
2DGS	1.332 $\rightarrow$	1.211
PGSR	0.712 $\rightarrow$	0.667
MILo	0.821 $\rightarrow$	0.754
RaDe-GS	0.662 $\rightarrow$	0.519

Table 2: Effect of local PCA regularization across splatting methods on DTU.

	Tanks and Temples								NeRF Synthetic Mesh
Method	Barn	Cater.	Court.	Igna.	Meet.	Truck	Mean	Time	Chair	Drums	Ficus	Hotdog	Lego	Mats.	Mic	Ship	Mean	Time
VGGT- $\Omega$ *	0.041	0.049	0.033	0.058	0.054	0.116	0.059	2.8	0.112	0.121	0.130	0.168	0.199	0.161	0.091	0.164	0.143	1.5
COLMAP-D	0.555	0.494	0.359	0.712	0.332	0.639	0.515	168.7	0.654	0.543	0.632	0.496	0.489	0.240	0.428	0.409	0.486	25.3
3DGS	0.076	0.080	0.047	0.128	0.056	0.133	0.087	7.9	0.336	0.392	0.543	0.113	0.284	0.161	0.303	0.215	0.293	4.8
2DGS	0.074	0.075	0.032	0.136	0.026	0.144	0.081	12.3	0.253	0.243	0.306	0.051	0.206	0.076	0.221	0.159	0.189	5.5
GSPull	0.071	0.057	0.074	0.105	0.012	0.106	0.071	113	0.119	0.103	0.160	0.009	0.036	0.028	0.077	0.006	0.067	26.4

Table 3: Quantitative comparison on Tanks and Temples and NeRF Synthetic . We report F1-score (

\uparrow

) between reconstructed and ground-truth point clouds. We highlight the best , second-best , and third-best Gaussian-based results. Time is in minutes.

Figure 6: Qualitative comparison on Tanks and Temples. Compared with MILo, RaDe-GS, and GaussianWrapping, PCAsplat concentrates Gaussian centers along scene surfaces, with substantially fewer floaters around objects and below ground. See Fig. 12 and Fig. 11 for additional views of the geometry above and below ground.

$\mathcal{L}_{\mathrm{PCA}}$	$\mathcal{L}_{\mathrm{normal}}$	CD $\downarrow$
		0.655
	✓	0.654
✓		0.520
✓	✓	0.519

Table 4: Ablation study .

Figure 7: Qualitative results of 3D semantic instance segmentation. We apply Mask3D directly to colored point clouds reconstructed by each method on ScanNet++. PCAsplat produces more coherent object masks in the examples shown.

	COLMAP-S	COLMAP-D	RaDe-GS	VGGT- $\Omega$	Ours	Oracle
Top-1 mIoU	0.02%	8.21%	7.77%	10.54%	24.35%	30.41%
Top-3 mIoU	0.21%	8.20%	7.81%	10.58%	24.84%	30.56%

Table 5: Semantic instance segmentation on ScanNet++. We report Top-1 and Top-3 mIoU (

\uparrow

) using Mask3D on point clouds reconstructed by each method.

Figure 8: Using Gaussian centers and normals from PCAsplat, SPSR recovers finer statue details and a smoother ground surface, with substantially fewer spurious mesh components than with RaDe-GS or GaussianWrapping.

Appendix figures & tables9 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 9: Visible meshes from the NeRF Synthetic eight scenes.

Figure 10: Qualitative comparison of object isolation . Previous methods leave floating primitives and subsurface artifacts (red arrows) upon cropping, needing further manual editing to erase them. In contrast, PCAsplat (Ours) achieves clean, artifact-free boundaries, yielding an asset-ready reconstruction without manual cleanup.

Figure 11: “Underworld” geometry comparison on Tanks and Temples. We visualize the Gaussian means of reconstructed scenes from beneath the ground. Baselines fail to control interior floaters in unobserved regions and behind structures. PCAsplat (Ours) suppresses all floaters, resulting in regularized, clean ground and wall boundaries.

Figure 12: Qualitative point cloud detail comparison on Tanks and Temples Across diverse outdoor scenes, baseline methods produce noisy clouds. PCAsplat reconstructs scenes with high geometric fidelity, cleanly resolving intricate structures (e.g., roofs, vehicle contours, and ground details) while removing floating outliers.

	Methods	24	37	40	55	63	65	69	83	97	105	106	110	114	118	122	Mean	Time
Neural	VolSDF ( Yariv et al., 2021 )	1.14	1.26	0.81	0.49	1.25	0.7	0.72	1.29	1.18	0.7	0.66	1.08	0.42	0.61	0.55	0.857	12h¿
	Neus ( Wang et al., 2021 )	1.00	1.37	0.93	0.43	1.10	0.65	0.57	1.48	1.09	0.83	0.52	1.20	0.35	0.49	0.54	0.837	12h¿
	Neuralangelo ( Li et al., 2023 )	0.37	0.72	0.35	0.35	0.87	0.54	0.53	1.29	0.97	0.73	0.47	0.74	0.32	0.41	0.43	0.610	12h¿
Gaussian Based	3DGS ( Kerbl et al., 2023 )	2.14	1.53	2.08	1.68	3.49	2.21	1.43	2.07	2.22	1.75	1.79	2.55	1.53	1.52	1.50	1.966	5.2m
	SuGaR ( Guédon & Lepetit, 2024 )	1.47	1.33	1.13	0.61	2.25	1.71	1.15	1.63	1.62	1.07	0.79	2.45	0.98	0.88	0.79	1.330	52m
	2DGS ( Huang et al., 2024 )	0.50	0.72	0.39	0.39	0.93	0.85	0.78	1.21	1.12	0.67	0.66	1.14	0.43	0.67	0.50	0.731	10.9m

Appendix

Table 6: Quantitative comparison on the DTU dataset . We report the Chamfer Distance (CD)

\downarrow

across 15 scenes and the average optimization time

\downarrow

. Our method achieves the best mean accuracy with a competitive performance.

Figure 13: Qualitative comparison on the DTU Dataset. Our method produces cleaner meshes with more details (e.g. teddy bear plush or house windows) and reduced artifacts (e.g. scissor tip, fruit specularity or skull forehead).

	Methods	Barn	Caterp.	Court.	Ignat.	Meet.	Truck	Mean	Time
Neural	Neus	0.29	0.29	0.17	0.83	0.24	0.45	0.38	12h+
	Geo-Neus	0.33	0.26	0.12	0.72	0.20	0.45	0.35	12h+
	Neuralangelo	0.70	0.36	0.28	0.89	0.32	0.48	0.50	12h+
Gaussian Based	3DGS	0.13	0.08	0.09	0.04	0.01	0.19	0.09	7.9m
	SuGaR	0.14	0.16	0.08	0.44	0.16	0.26	0.21	73m
	2DGS	0.36	0.23	0.13	0.44	0.16	0.26	0.26	12.3m

Appendix

Table 7: Quantitative comparison on the Tanks and Temples dataset . We report F1-score

\uparrow

. We evaluate all results using the scores reported in the papers. PCAsplat achieves competitive results while producing a cleaner underlying point cloud. * The results presented are from RaDe-GS paper. However, due to compute-limiting constraints, we were unable to re-run RaDe-GS TSDF extraction and achieve the same results as they show in their table. As such, we also append here the average results we got from running their code on our end, 0.49 , thus, our 0.50 improves over 0.49, and makes our method competitive with SoTA results.

	Indoor Scenes			Outdoor Scenes
Method	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
3DGS	30.41	0.920	0.189	24.64	0.731	0.234
Mip-Splatting	30.90	0.921	0.194	24.65	0.729	0.245
BakedSDF	27.06	0.836	0.258	22.47	0.585	0.349
SuGaR	29.43	0.906	0.225	22.93	0.629	0.356
2DGS	30.40	0.916	0.195	24.34	0.717	0.246

Appendix

Table 8: Quantitative comparison across indoor and outdoor scenes of the MipNeRF 360 dataset ( Barron et al., 2022 ) . We highlight the best , second-best , and third-best PSNR, SSIM, and LPIPS. Our method maintains competitive performance while significantly improving Gaussian localization.

Figure 14: Curvature (Blue-Red) and Density (Red) splatting. Our method enables local curvature and local density rendering.

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3D Gaussian Splatting 3D Reconstruction Novel View Synthesis Gaussian Splatting

Open paper AskPDF arXiv

3D Gaussians have become a powerful scene representation for real-time splatting and high-quality novel-view synthesis. This has motivated generalizable splatting -- methods that adapt feed-forward geometry prediction networks to produce per-pixel Gaussians from a set of images. However, most generalizable splatting pipelines are supervised primarily through a view-synthesis loss to predict Gaussian orientation, anisotropic scale, opacity, and appearance in addition to their locations. We show that this learning objective is under-constrained. Models trained with view synthesis alone produce splats whose orientations and scales have no geometric connotation. The result is that, while producing decent view-synthesis performance, nearly all generalizable splatting methods produce geometrically inaccurate and misaligned Gaussians. We introduce G3Splat, a geometry-consistent generalizable splatting framework that addresses these degeneracies through differentiable geometric priors on the predicted 3D Gaussians, making the learning problem well-posed. These priors encourage the per-pixel splats to remain on their viewing rays and to orient themselves in accordance with local surfaces. Our priors are architecture-agnostic and can be incorporated into any previously studied geometric backbone for generalizable splatting, as well as different scene representations. We test G3Splat with both DUSt3R-style and VGGT-style backbones to predict pixel-aligned full-rank 3DGS as well as surfel-like 2DGS. Trained on RE10K, G3Splat produces Gaussian splats with significantly higher geometric fidelity than baselines, providing state-of-the-art novel-view depth, mesh reconstruction, and relative pose estimation performance while preserving novel-view synthesis quality, as evaluated on datasets such as ACID and ScanNet. Code and pretrained models are released on our project page.

Abstract

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