GaussianRoom: Gaussian Modeling in Indoor Scenes

• GaussianRoom is a set of frameworks that use Gaussian modeling techniques to perform comprehensive indoor scene reconstruction, rendering, and occupancy estimation.
• It integrates explicit 3D Gaussian splatting with implicit neural SDFs, leveraging monocular cues and SDF-guided densification to achieve accurate surface reconstruction.
• The framework extends to realistic glass and mirror rendering using mirrored Gaussians and Fresnel-based blending, and applies GMM-HMM models for audio-based occupancy analysis.

GaussianRoom refers to multiple prominent frameworks leveraging different forms of Gaussian modeling in the context of indoor scene analysis and processing. Most notably, the term encompasses: (1) a unified 3D reconstruction and rendering framework that integrates 3D Gaussian Splatting (3DGS) with a neural signed distance field (SDF) for state-of-the-art surface reconstruction and real-time rendering of indoor scenes, (2) an extension of Gaussian splatting for accurate rendering of transmission and reflection phenomena in room environments with planar glass, and (3) an audio-based occupancy estimation system utilizing Gaussian Mixture Models (GMMs) coupled with a Hidden Markov Model (HMM). The following provides a comprehensive account of each GaussianRoom variant, their mathematical formulations, methodological innovations, experimental validations, and research context.

1. Integrated 3D Gaussian Splatting and Neural Signed Distance Fields for Scene Reconstruction

GaussianRoom, as introduced by Luo et al., targets the challenge of reconstructing and rendering large indoor scenes from posed RGB images—specifically addressing limitations of existing 3DGS and neural SDF methodologies when applied to textureless or poorly-featured environments (Xiang et al., 30 May 2024).

Coupled Representation

The GaussianRoom framework tightly couples an explicit 3DGS surface representation with an implicit neural SDF:

• SDF → 3DGS: A neural SDF field $f_g: \mathbb{R}^3 \to \mathbb{R}$ is trained to approximate scene geometry, with its zero level set representing the surface. This field guides the spatial distribution of Gaussians via global and local densification/pruning, ensuring surface adherence even when photometric cues are weak or initial point clouds are sparse.
• 3DGS → SDF: The current set of Gaussians is rasterized to produce coarse depth maps, which in turn concentrate SDF ray samples near surfaces, enhancing SDF convergence and efficiency.

Regularization with Monocular Cues

The framework incorporates monocular normal priors and image edge maps, serving as additional loss terms and sampling weights. This resolves ambiguities in flat, textureless regions and enhances detail recovery.

2. Mathematical Formulation and Coupling Mechanisms

3D Gaussian Splatting

Each Gaussian $G_i$ is defined by:

• Mean $\mu_i \in \mathbb{R}^3$
• Covariance $\Sigma_i = R_i S_i^2 R_i^T$ (with $R_i$ orthogonal, $S_i$ diagonal)
• Color $c_i \in \mathbb{R}^3$
• Opacity $\alpha_i \in [0,1]$

The unnormalized 3D density is $$G_i(\mathbf{x}) = \exp\left( -\frac{1}{2} (\mathbf{x} - \mu_i)^T \Sigma_i^{-1} (\mathbf{x} - \mu_i) \right)$$. Rendering proceeds by projecting each 3D Gaussian to 2D, and α-blending colors and normals across sorted splats (closest-to-farthest) to each pixel.

Neural SDF Field

The scene surface is the zero-level set $\{\mathbf{x} \mid f_g(\mathbf{x}) = 0\}$ of a multi-layer perceptron (MLP). Using the NeuS formula, SDF values are converted to differential opacity, and final color/normals are similarly blended per ray.

SDF-Guided Densification and Pruning

Two key mechanisms redistribute Gaussian primitives:

• Global Densification: The scene is partitioned into voxels; those near the SDF surface and underpopulated receive $K$ new Gaussians (cloned from local neighbors).
• Local Densification/Pruning: Each Gaussian’s proximity to the surface (modulated by $f_g$ and its current opacity) determines whether it is split (densified) or pruned. The indicator $\eta = \exp(-S^2 / (\lambda_\sigma \sigma^2))$ (with $S = f_g(\mu)$, $\sigma$ the Gaussian’s opacity) controls these decisions.

Losses and Optimization

The total loss is $L = L_{gs} + L_{sdf}$ where:

• $L_{gs}$ combines photometric, D-SSIM, and normal map losses, with weights adjusted by edge strength.
• $L_{sdf}$ extends these with an Eikonal loss for SDF regularity.

Typical hyperparameters are $\lambda_1 = 0.8$, $\lambda_2 = 0.01$, $\lambda_{eik} = 0.1$.

3. Optimization Pipeline and Implementation Details

GaussianRoom employs a three-stage optimization:

1. 3DGS Pre-training (15K iterations): Minimizes photometric losses to produce an initial Gaussian cloud.
2. Joint 3DGS+SDF Optimization (80K iterations): Begins with coarse geometry learning (no mutual densification for 6K iterations), then alternates SDF-guided global (every 2K iterations) and local densification/pruning (every 100 iterations). Gaussian-generated depth maps define SDF sampling windows along each ray.
3. Mesh Extraction: After training, final geometry is extracted from the SDF via Marching Cubes on a $512^3$ grid.

• Codebase is based on 3DGS (Kerbl et al.) and NeuS (Wang et al.).
• The SDF MLP uses 8 hidden layers with 256 channels.
• Training times are approximately 4 hours per scene on a single V100 GPU.

4. Experimental Validation and Quantitative Results

Experiments on ScanNet V2 and ScanNet++ evaluate reconstruction and rendering quality.

• Surface reconstruction metrics: F-score @ 5cm: 0.768 (ScanNet), 0.872 (ScanNet++).
• Novel view metrics: SSIM: 0.758 / 0.844; PSNR: 23.60 / 22.00; LPIPS: 0.391 / 0.296.

Comparisons indicate state-of-the-art performance, significantly outperforming MonoSDF and prior Gaussian/NeRF baselines. Ablation studies confirm critical contributions from SDF-driven densification, local split/prune, and monocular priors.

Module removed	F-score Δ	PSNR Δ	Effect summary
SDF-guided global densif.	–	–1dB	More floaters, lower PSNR
Local split/prune	~–1%	–	Degraded geometric accuracy
Gaussian-guided sampling	–	–10%	Slowed SDF convergence
Normal prior	–0.380	–	Major geometric breakdown
Edge prior	–	↑LPIPS	Blurrier details

5. Extensions for Realistic Glass and Mirror Rendering

In the context of planar transmission/reflection (e.g., glass panes in rooms), the “GaussianRoom” methodology is extended as TR-Gaussians (Liu et al., 17 Nov 2025). This approach augments splatting with:

• Learnable planar reflection planes: Each glass/mirror pane is parameterized by center, normal, size, and base reflectance ($R_0$).
• Mirrored Gaussians: Reflection is handled by creating mirrored copies of all Gaussians with respect to the plane.
• Fresnel-based blending: Transmission and reflection images are blended per-pixel with a Schlick-model reflectance $$F(\mathbf{u}) = R_0 + (1-R_0)(1-\mathbf{n}_p\cdot\mathbf{d})^5$$.
• Masking and regularization: Glass regions use a learned mask; geometric losses and opacity perturbation further regularize optimization.

Empirical results on the "GaussianRoom" dataset demonstrate real-time synthesis (225 FPS), high fidelity (PSNR 31.21 dB, SSIM 0.951), and superior performance over NeRF-based reflectance models.

6. Audio-Based Occupancy Estimation with GMM-HMM

An unrelated but similarly named framework, “GaussianRoom,” applies Gaussian mixture models for real-time room-occupancy analysis from audio (Valle, 2016). The procedure involves:

• Feature extraction: 60-D MFCC+deltas from short-time audio frames.
• State binning: Occupancy is binned via integer square root across 15 labels.
• GMM modeling: One diagonal-covariance GMM per occupancy bin, trained by EM with model order chosen by BIC.
• Temporal modeling: A 15-state HMM with uniform or heuristic transition prior, and MAP sequence decoding via Viterbi.
• Performance: Evaluated on ~386 15-min samples from a retail store, the approach achieves lowest RMSE among tested methods (slight underprediction bias, robust up to ~200 people).

7. Strengths, Limitations, and Research Directions

Strengths

• Robust recovery of textureless and ambiguous geometry (SDF-coupled 3DGS).
• Real-time rendering for both standard and reflective/transmissive room scenes.
• Sample- and computation-efficient convergence via mutual guidance between explicit and implicit representations.
• Lightweight, non-invasive occupancy estimation from audio (GMM-HMM).

Limitations

• SDF evaluation remains slower than pure splatting; global densification frequency may miss small features (Xiang et al., 30 May 2024).
• Glass modeling supports only planar or piecewise-planar geometry; non-planar glass requires patch approximations or additional rendering steps (Liu et al., 17 Nov 2025).
• Audio-occupancy approach is limited by ambient noise and sparse data at occupancy extremes (Valle, 2016).

Future Directions

• SDF acceleration: Replacing the SDF-MLP with multi-resolution hash or tri-plane encoders.
• Dynamic scene modeling: Incorporating time-varying SDF and Gaussian parameters.
• Adaptive refinement: Integrating uncertainty estimation for targeted densification.
• Reflective/transmissive generalization: Patch-based approximations for curved glass/mirrors, environment map-based lighting, and dynamic view/BRDF estimation.

Integration of explicit splatting with implicit SDFs, extended by physically-informed reflection/transmission models and cross-modal GMM inference, situates GaussianRoom as a diverse, evolving paradigm in indoor scene modeling and analysis (Xiang et al., 30 May 2024, Liu et al., 17 Nov 2025, Valle, 2016).