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PCAsplat: Gaussian Splatting with Local PCA Regularization

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

arXiv:2610.11011v1cs.CVcs.GR

TL;DR

Rasterization-based supervision can leave occluded or low-contribution Gaussians weakly constrained, allowing floaters that limit geometry processing. PCAsplat regularizes Gaussian neighborhoods with differentiable local PCA; experiments report improved surface alignment and fewer floaters, with competitive novel-view synthesis and mesh extraction.

  • Problem

    Rasterization-based geometric losses provide weak or no gradients to occluded or low-contribution Gaussians, while floaters limit use of the representation for downstream geometry processing.

    Source: §1 · p. 1

  • Method

    PCAsplat applies differentiable local PCA to Gaussian neighborhoods, using eigenvalue-based losses for surface thickness and tangent-plane coverage and aligning Gaussian normals to PCA-derived normals.

    Source: §1 · p. 2

  • Results

    PCAsplat produces surface-aligned splats with fewer floaters and more accurate downstream geometry processing, while remaining competitive in novel view synthesis and mesh extraction.

    Source: §1 · p. 2, §5 · p. 9

  • Takeaways & Limitations

    The surface-aligned Gaussian means can be used directly for downstream geometry-processing tasks, including segmentation and Poisson reconstruction.

    Source: §1 · p. 2, §5 · p. 9

    The PCA derivative formulation assumes fixed neighborhood indices and no repeated eigenvalues.

    Source: §3.2 · p. 5

Abstract

from arXiv · show

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.

1 INTRODUCTION

Gaussian splatting can leave poorly supervised Gaussians off the underlying surface, limiting its use for geometry processing. PCAsplat applies local PCA directly to Gaussian neighborhoods, improving surface alignment while retaining competitive rendering and mesh-extraction performance.

1 INTRODUCTION

  • Rendering-based geometric losses can leave occluded or low-contribution Gaussians weakly supervised, allowing floaters and poorly localized Gaussians to persist and constrain downstream use.Exterior floaters may appear in novel views, while interior ones may remain occluded.Source: §1 · p. 1
  • Local PCA regularizes Gaussian neighborhoods in scene space, providing geometric supervision even to Gaussians that do not contribute to the current training view.It estimates neighborhood covariance eigenvalues to characterize thickness and tangent-plane anisotropy.Source: §1 · p. 2
  • The PCA statistics encourage Gaussian centers toward the surface, isotropic tangent-plane coverage, and alignment of Gaussian normals with PCA-derived normals.The normal alignment is up to sign.Source: §1 · p. 2
  • PCAsplat produces fewer exterior and interior floaters and more accurate instance segmentation than current methods, while remaining competitive in novel view synthesis and TSDF-based mesh extraction.The point-cloud comparison also shows cleaner surface coverage.Source: §1 · p. 2, Figure 1 · p. 2
  • The evaluation treats the splats as surface samples and reports their use in downstream applications, including instance segmentation and Poisson reconstruction.The improved point cloud is presented as enabling downstream instance segmentation.Source: §1 · p. 2, Figure 1 · p. 2

2 RELATED WORK

Prior image-based reconstruction spans classical and neural methods, while Gaussian splatting offers fast explicit primitives but lacks inherent geometry constraints. Related Gaussian methods improve geometry through rendering losses or auxiliary surfaces; PCAsplat instead applies local PCA directly to Gaussian neighborhoods.

2 RELATED WORK

  • Classical reconstruction combines structure from motion and multi-view stereo, while feed-forward models predict cameras, depth maps, and point clouds from unposed images; neural implicit methods jointly learn geometry and view-dependent appearance.Neural implicit methods require repeated neural-field evaluations along rays for volume rendering.Source: §2 · pp. 2–3
  • Gaussian splatting enables fast rasterization of explicit primitives, and later methods use surface-like primitives, rendering losses, surface alignment, or multi-view consistency to improve geometry and mesh extraction.TSDF mesh fusion still relies on ray-Gaussian contributions, so accurate meshes do not necessarily imply surface-aligned Gaussian centers.Source: §2 · p. 3
  • Rendering-based depth and normal losses weight supervision by rendering contributions, so occluded or low-contribution Gaussians may receive weak or no geometric gradients and remain floaters.PCAsplat complements these losses with local 3D neighborhood gradients.Source: §2 · p. 3
  • Hybrid Gaussian–surface approaches couple Gaussians to auxiliary SDFs, distance fields, or extracted meshes, with methods also addressing sparse support, open surfaces, or Gaussian–mesh consistency.Some approaches jointly optimize the auxiliary representation or enforce consistency with the Gaussians.Source: §2 · p. 3
  • PCAsplat adapts local PCA to regularize Gaussian neighborhoods with thickness, tangent-plane coverage, and normal-alignment losses, without learning auxiliary SDFs or extracting meshes during training.Local PCA is used to estimate tangent planes and normals from point clouds.Source: §2 · p. 3

3 METHOD

PCAsplat adds differentiable local PCA losses to Gaussian splatting, regularizing neighborhoods directly in scene space. These losses shape neighborhood thickness and tangent-plane coverage and align Gaussian normals with PCA-derived normals.

3 METHOD

  • Local PCA regularizes Gaussian neighborhoods directly in scene space, including their centers and orientations, alongside the rendering objective.Source: §3 · p. 3, Figure 2 · p. 4

3.1 PROBLEM SETTING

  • The photometric objective combines L1 and structural dissimilarity losses but does not explicitly regularize local Gaussian-neighborhood geometry.Source: §3.1 · p. 4

3.2 LOCAL PCA NEIGHBORHOODS

  • Each Gaussian’s K-nearest-center neighborhood supplies a covariance whose eigendecomposition captures local structure, including an estimated normal and tangent plane.Source: §3.2 · p. 4

3.3 PCA-BASED GEOMETRIC LOSSES

  • The eigenspectrum loss penalizes variance along the estimated normal and promotes balanced spread in the tangent plane, discouraging thick or elongated neighborhoods.Source: §3.3 · p. 5, Figure 3 · p. 5
  • A separate normal-consistency loss aligns each Gaussian normal with the PCA normal, and the final objective adds PCA and normal losses to photometric rendering loss.Source: §3.3 · p. 5

4 EXPERIMENTS

PCAsplat is evaluated for surface alignment, downstream geometry processing, and performance on conventional reconstruction tasks. It improves Gaussian-to-surface alignment across captured and synthetic scenes, with results also reported for plug-in regularization, ablations, segmentation, and Poisson reconstruction.

4 EXPERIMENTS

  • The evaluation covers DTU and Tanks and Temples surface accuracy, ScanNet++ instance segmentation, and F1-score on a visible-surface benchmark constructed from NeRF Synthetic assets.Point-cloud comparisons include Gaussian-based methods, VGGT-Ω, and COLMAP-D.Source: §4 · p. 6

4.1 COMPARISONS

  • 0.519 mm mean Chamfer distance on DTU is 22% lower than RaDe-GS’s 0.662 mm, and PCAsplat matches COLMAP-D’s reported mean CD with lower runtime.Cross-sections also show thinner surface profiles and fewer floaters than RaDe-GS and GaussianWrapping.Source: Table 1 · p. 6, §4.1 · p. 7
  • Adding local PCA regularization lowers Chamfer distance for 2DGS, PGSR, and MILo without additional hyperparameter tuning.The paper describes this as a plug-and-play addition to existing methods.Source: §4.1 · p. 7, Table 2 · p. 7
  • PCAsplat achieves the highest mean F1-score among evaluated Gaussian-based methods on Tanks and Temples and NeRF Synthetic, and is best or second-best on every NeRF Synthetic scene.Figure 6 shows fewer floaters and better surface coverage than the Gaussian-based baselines shown.Source: §4.1 · p. 7, Table 3 · p. 7, Figure 6 · p. 8
  • For TSDF-based mesh extraction and novel view synthesis, PCAsplat achieves the lowest mean Chamfer distance on DTU while remaining competitive on Tanks and Temples..Source: §4.1 · p. 7

4.2 ABLATION STUDY

  • On DTU, the PCA loss reduces Chamfer distance from 0.655 to 0.520, and combining it with normal alignment yields the lowest value, 0.519.The PCA loss penalizes neighborhood thickness and promotes isotropic tangent-plane coverage.Source: §4.2 · p. 8, Table 4 · p. 8

4.3 APPLICATIONS

  • On ScanNet++, PCAsplat has the highest Top-1 and Top-3 mIoU among evaluated reconstructed point clouds, more than doubling the strongest baseline’s scores.Mask3D is applied to each method’s colored point cloud; textureless regions such as white walls remain challenging.Source: §4.3 · p. 8, Table 5 · p. 8, Figure 7 · p. 9
  • For the Tanks and Temples example, SPSR produces cleaner meshes with finer detail and fewer spurious components from PCAsplat centers and normals than from RaDe-GS or GaussianWrapping.Figure 8 shows finer statue details and a smoother ground surface.Source: §4.3 · p. 9, Figure 8 · p. 9

5 CONCLUSION

PCAsplat integrates local PCA regularization into Gaussian splatting to align Gaussians with surfaces. The resulting representation supports downstream geometry processing while remaining competitive in novel view synthesis and mesh extraction.

5 CONCLUSION

  • PCAsplat aligns Gaussians to surfaces by integrating local PCA regularization into training, enabling downstream geometry processing while remaining competitive in novel view synthesis and mesh extraction.The method has modest training overhead and requires a depth-based step for distant floaters and sign disambiguation for normals.Source: §5 · p. 9

A IMPLEMENTATION DETAILS.

Implementation uses an initial rendering-loss training phase followed by PCA regularization, with different total iteration counts for bounded and unbounded scenes. Results use current repositories and dataset-specific hyperparameters, except that NeRF Synthetic uses DTU hyperparameters.

A IMPLEMENTATION DETAILS.

  • Training starts with 7K iterations of LRGB before enabling LPCA and Lnormal, and runs for 20K iterations on bounded scenes or 30K on unbounded scenes.A custom CUDA kernel accelerates batched 3 × 3 eigendecomposition; experiments use an NVIDIA RTX A5500 with 24GB VRAM.Source: A IMPLEMENTATION DETAILS · p. 12
  • Methods use their current GitHub repositories and specified dataset hyperparameters, except that NeRF Synthetic uses DTU hyperparameters.Tab. 1 and Tab. 3 results were generated with the authors’ runs of each method.Source: A IMPLEMENTATION DETAILS · p. 12

B SYNTHETIC MESH DATASET

The NeRF Synthetic scenes lack official surface meshes for reconstruction metrics, so the paper constructs visible reference meshes from the original scene assets. These meshes define the reference for F-score evaluation.

B SYNTHETIC MESH DATASET

  • The visible reference meshes merge scene components, then retain triangles hit first for at least one pixel across training, validation, or test views, yielding a watertight surface.F-score is measured from 106 farthest-point-sampling samples of these meshes.Source: B SYNTHETIC MESH DATASET · p. 12

C ADITIONAL RESULTS

Additional evaluations show that PCAsplat produces asset-ready splats and competitive mesh and novel-view-synthesis results. Its reconstructions also suppress floaters in poorly observed regions and preserve geometric detail.

Asset-ready splats

  • PCAsplat enables object crops with clean, artifact-free boundaries, avoiding the manual cleanup required by previous methods.The comparison highlights floating primitives and subsurface artifacts in prior methods and clean boundaries with PCAsplat.Source: C ADITIONAL RESULTS · p. 13, Figure 10 · p. 13

Overworld and underworld

  • In underworld views, PCAsplat suppresses subsurface floaters and produces clean ground and wall boundaries where baselines leave disorganized Gaussian sprawl.The comparison concerns poorly observed regions beneath the ground and behind structures.Source: C ADITIONAL RESULTS · p. 13, Figure 11 · p. 13

Point cloud detail

  • Across outdoor scenes, PCAsplat produces point clouds that resolve intricate structures and remove floating outliers, while baseline clouds are noisy.Reported details include roofs, vehicle contours, and ground features.Source: Figure 12 · p. 14

Mesh extraction

  • On DTU, PCAsplat obtains a 0.471 mean CD using TSDF extraction; on Tanks and Temples, it matches the best mean F1 among Gaussian-based methods.The DTU comparison covers 15 scenes and reports Chamfer Distance and optimization time; the Tanks and Temples comparison uses F1-score.Source: SURFACE RECONSTRUCTION · p. 14, Table 6 · p. 14, Table 7 · p. 15
  • The authors could not reproduce RaDe-GS TSDF extraction results; their 0.50 result is compared with their own 0.49 rerun.They therefore describe their result as competitive with state of the art.Source: SURFACE RECONSTRUCTION · p. 15

Novel view synthesis

  • On MipNeRF-360, PCAsplat maintains competitive novel-view-synthesis performance across scenes while improving Gaussian localization.The authors state that PCA regularization does not hinder scene appearance.Source: SURFACE RECONSTRUCTION · p. 16, Table 8 · p. 16

Code integration

  • PCAsplat’s PCA regularization is a modular, plug-and-play extension decoupled from the core rasterizer and requires minimal code modification.Its geometric constraints can be integrated into existing optimization loops.Source: SURFACE RECONSTRUCTION · p. 16

D OTHER GEOMETRICAL STATISTICS

The learned PCA eigenspectrum supports local curvature and density estimates for inspecting trained splats, which the paper visualizes in the splatting context.

Other geometrical statistics

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