Planar Gaussian Splatting Methods

• Planar Gaussian Splatting is a neural 3D reconstruction technique that incorporates explicit planar constraints to regularize geometry and enhance rendering.
• It models scenes using flattened Gaussian primitives grouped into planar clusters, which improves segmentation and overall scene accuracy.
• The method supports robust rendering pipelines with efficient optimization, offering enhanced performance in low-texture and ambiguous regions.

Planar Gaussian Splatting refers to a class of neural 3D reconstruction and rendering methods that generalize the standard Gaussian Splatting (GS) framework by integrating explicit planar constraints, groupings, or priors into the representation and optimization of Gaussian primitives. These approaches enable structured modeling of 3D scenes dominated by planes (e.g., indoor environments, building facades, dynamic surfaces), yield more accurate and regularized geometry, and often support explicit plane instance parsing or improved generalization across image domains.

1. Mathematical Foundations and Primitive Representation

Planar Gaussian Splatting models a 3D scene as a collection of $N$ Gaussian primitives (“splats”). Each primitive $i$ is parameterized by a spatial mean $\mu_i \in \mathbb{R}^3$, a positive-definite covariance matrix $\Sigma_i \in \mathbb{R}^{3 \times 3}$, color $c_i \in \mathbb{R}^3$, opacity $\alpha_i \in \mathbb{R}^+$, and additional plane-structural attributes such as a $k$-dimensional plane descriptor $d_i$ and surface normal $n_i$:

$$G_i(x) = w_i \exp\left(-\tfrac{1}{2} (x - \mu_i)^\top \Sigma_i^{-1} (x - \mu_i)\right)$$

where in practice $w_i$ is absorbed into $\alpha_i$ (Zanjani et al., 2 Dec 2024).

A defining feature of planar Gaussian variants is the deformation of some principal axis of $\Sigma_i$ toward zero, enforcing that the primitive lies close to a 2D manifold. This can be written as:

$$\Sigma_i = R_i\,\mathrm{diag}(s_{i,1}^2, s_{i,2}^2, \epsilon)\,R_i^\top, \quad \epsilon \to 0$$

where $R_i \in SO(3)$ is a rotation and $s_{i,1}, s_{i,2}$ are in-plane scales, thus producing a “flattened” Gaussian disc (Zanjani et al., 2 Dec 2024, Chen et al., 10 Jun 2024, Wu et al., 21 Nov 2025).

The planar descriptor $d_i$ typically summarizes local appearance and plane semantics, often derived from 2D segmentation masks or normal predictions that are lifted from image space using camera geometry (Zanjani et al., 2 Dec 2024). The primitive normal $n_i$ is either learned directly, computed as an eigenvector of $\Sigma_i$, or obtained from average normals across projected views.

2. Rendering Pipeline and Volume Compositing

Planar Gaussian Splatting employs a neural rendering pipeline akin to standard GS, where each pixel is synthesized by casting a ray and compositing contributions from the ordered list of intersected splats.

For each camera ray $r(t) = o + t d$, the predicted color is:

$$C_{\mathrm{pred}}(r) = \sum_{i=1}^N T_i\,\alpha_i\,c_i$$

where

$T_i = \exp\left(-\sum_{j < i} \alpha_j \right)$

and the splats are sorted by increasing mean-ray distance (Zanjani et al., 2 Dec 2024).

The pipeline supports rendering not only color but also unbiased depth and normal maps. Unbiased per-pixel depth can be computed by dividing the $\alpha$-weighted sum of plane-to-camera distances by the $\alpha$-weighted sum of normals projected onto the camera ray, enforcing that the output depth exactly intersects the estimated plane (Chen et al., 10 Jun 2024, Cai et al., 26 Aug 2024, Wu et al., 21 Nov 2025). This yields depth and normal maps that are more free from multi-view inconsistencies than in naïve 3DGS.

Alpha compositing in the planar setting is closed-form for both color and plane attributes, and facilitates subsequent operations such as TSDF fusion and mesh extraction.

3. Plane Grouping, Priors, and Structural Segmentation

A central innovation in Planar Gaussian Splatting is the explicit grouping of primitives into planar clusters, often corresponding to semantically meaningful or geometrically consistent planes. This is operationalized by constructing a hierarchical tree-structured mixture of Gaussians, wherein similar splats are merged based on the plane descriptor, normal, and spatial proximity:

$$P_{\mathrm{merge}}(i, j) \propto \exp\left(-\frac{\|d_i - d_j\|^2}{\sigma_d^2}\right) \exp\left(-\frac{\|n_i - n_j\|^2}{\sigma_n^2}\right) \exp\left(-\frac{\|\mu_i - \mu_j\|^2}{\sigma_s^2}\right)$$

(Zanjani et al., 2 Dec 2024).

Merging proceeds greedily or via EM-like schedules until a threshold is reached, and surviving clusters yield plane hypotheses whose 3D equations are determined by robust estimation (e.g., PCA) (Zanjani et al., 2 Dec 2024, Jin et al., 27 Oct 2025).

Planar priors can also be integrated via external semantic detectors (e.g., vision-LLMs, LoD2 semantic building models), providing strong geometric and mask supervision for plane detection, instance splitting, and overall scene regularization (Jin et al., 27 Oct 2025, Zhang et al., 10 Aug 2025). Planar constraints have been shown to be critical in low-texture or ambiguous regions.

4. Loss Functions and Training Objectives

Planar GS frameworks optimize a composite loss comprising multiple terms:

• Photometric rendering loss (e.g., $L_2$ or $L_1$ color residuals, D-SSIM) over all pixels and views:

$$L_{\mathrm{photo}} = \sum_p \|C_{\mathrm{pred}}(p) - I_{\mathrm{gt}}(p)\|_2^2$$

• Planarity regularization, e.g., penalizing the minimum axis of the splat covariance or enforcing all splats in a plane cluster to be coplanar:

$$L_{\mathrm{planar}} = \sum_{i\in\mathcal{P}} w_i \|n^\top_i (\mu_i - p_i)\|^2$$

• Geometric supervision using priors from multi-view depth, normals, or known mesh geometry:

$$L_{\mathrm{geo}} = \lambda_\mathrm{rd} L_\mathrm{rd} + \lambda_\mathrm{rn} L_\mathrm{rn} + \lambda_\mathrm{dn} L_\mathrm{dn}$$

where $L_\mathrm{rd}$ enforces depth alignment, $L_\mathrm{rn}$ aligns rendered and prior normals, and $L_\mathrm{dn}$ encourages depth-normal consistency (Jin et al., 27 Oct 2025, Chen et al., 10 Jun 2024, Zhang et al., 10 Aug 2025).

• Regularization terms for smoothness ($\sum_{i\sim j}\|c_i - c_j\|^2$), sparsity ($\sum_i \alpha_i$), and overlap separation ($$\exp\{-\|\mu_i - \mu_j\|^2 / \sigma_{\mathrm{sep}}^2\}$$) (Zanjani et al., 2 Dec 2024).
• Motion-specific and dynamic scene constraints (e.g., ARAP, temporal geometry) when reconstructing articulated or dynamic scenes (Cai et al., 26 Aug 2024, Wu et al., 21 Nov 2025).

These terms are weighted according to dataset and optimization stage, and optimization is performed on all Gaussian parameters, clustering structure, and other scene-specific variables.

5. Extracting Planar Geometry and Scene Structure

After optimization, plane clusters can be post-processed to yield explicit plane equations, instance labels, and structural segmentation of the 3D scene. Principal component analysis or robust regression yields the normal and offset for each plane instance (Zanjani et al., 2 Dec 2024). The resulting clusters can be used to generate interpretable geometry (e.g., wall, floor, façade surfaces), enable object/part-level parsing, or facilitate further downstream tasks (e.g., building-focused reconstruction, articulated object tracking) (Jin et al., 27 Oct 2025, Wu et al., 21 Nov 2025).

For dynamic or articulated scenes, the explicit planar modeling enables temporally consistent prediction of normals, part motion, and joint parameters, coupled via temporally-aware geometric losses (e.g., Taylor expanded normal-velocity consistency) (Wu et al., 21 Nov 2025).

6. Empirical Performance and Applications

Planar Gaussian Splatting methods demonstrate substantial empirical advantages across benchmarks:

• On ScanNet, PGS achieves voxel-IoU of 3.024, Rand Index of 0.919, and Segmentation Consistency of 0.415, surpassing ablated variants and prior GS-based frameworks (Zanjani et al., 2 Dec 2024).
• PlanarGS achieves significantly lower Chamfer distances (e.g., 4.49 cm vs. 11.92 cm for 3DGS baseline) and higher F1 scores (77.1% vs. 38.5%) for indoor scene surface reconstruction, while also improving PSNR and SSIM for novel-view synthesis (Jin et al., 27 Oct 2025).
• PGSR and 2DGS report state-of-the-art surface accuracy in terms of Chamfer and F1 on DTU and Tanks & Temples, with PGSR training converging within 1 hour and 2DGS within minutes (Chen et al., 10 Jun 2024, Huang et al., 26 Mar 2024).
• GS4Buildings, leveraging LoD2 semantic priors, increases geometric accuracy by 32.8% and completeness by 20.5% over vanilla 2DGS for urban building reconstruction (Zhang et al., 10 Aug 2025).

Planar GS approaches exhibit robustness to domain shift, effective handling of low-texture or ambiguous regions, efficient training and inference (on the order of minutes), and scalability to large-scale or dynamic scenes (as in StreetSurfGS and DynaSurfGS) (Cui et al., 6 Oct 2024, Cai et al., 26 Aug 2024).

Applications include high-fidelity scene reconstruction, mesh extraction for robotics and digital twins, real-time viewport synthesis, articulated geometry tracking, and explicitly modeled surface parsing.

7. Extensions, Variants, and Research Directions

Recent work extends the planar GS formalism to dynamic surface reconstruction (DynaSurfGS), articulated object modeling (REArtGS++), urban-scale environments (StreetSurfGS), and building-focused scenarios with strong priors (GS4Buildings).

Variants also tackle domain-specific effects, such as view-dependent planar reflection and transmission via explicit plane-anchored mirrored Gaussians (TR-Gaussians), blending physically-based appearance modeling into the splatting framework (Liu et al., 17 Nov 2025).

The field continues to address open challenges, including handling scene transparency, thin structures, and occlusion robustness, as well as enhancing the fidelity of plane detection and segmentation by integrating stronger geometric or semantic priors.

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References

• Planar Gaussian Splatting (Zanjani et al., 2 Dec 2024)
• PlanarGS: High-Fidelity Indoor 3D Gaussian Splatting Guided by Vision-Language Planar Priors (Jin et al., 27 Oct 2025)
• PGSR: Planar-based Gaussian Splatting for Efficient and High-Fidelity Surface Reconstruction (Chen et al., 10 Jun 2024)
• 2D Gaussian Splatting for Geometrically Accurate Radiance Fields (Huang et al., 26 Mar 2024)
• GS4Buildings: Prior-Guided Gaussian Splatting for 3D Building Reconstruction (Zhang et al., 10 Aug 2025)
• DynaSurfGS: Dynamic Surface Reconstruction with Planar-based Gaussian Splatting (Cai et al., 26 Aug 2024)
• REArtGS++: Generalizable Articulation Reconstruction with Temporal Geometry Constraint via Planar Gaussian Splatting (Wu et al., 21 Nov 2025)
• StreetSurfGS: Scalable Urban Street Surface Reconstruction with Planar-based Gaussian Splatting (Cui et al., 6 Oct 2024)
• TR-Gaussians: High-fidelity Real-time Rendering of Planar Transmission and Reflection with 3D Gaussian Splatting (Liu et al., 17 Nov 2025)