Dynamic Gaussian Re-classifier (DGR)

• DGR is an adaptive optimization procedure that dynamically reclassifies planar Gaussians by monitoring gradient magnitudes to correct misassignments.
• It systematically reverts incorrectly constrained Gaussians to unconstrained xyz parameterization, thereby enhancing convergence and geometric fidelity.
• Integrated with GSPlane, DGR improves mesh extraction precision with measurable gains in F-score and significant vertex reduction in planar regions.

The Dynamic Gaussian Re-classifier (DGR) is an adaptive optimization procedure introduced in the GSPlane framework to improve planar reconstruction using structured Gaussian models. It systematically monitors the per-Gaussian gradient behavior, correcting misclassified planar Gaussians by reverting their parameterizations, thus promoting robust convergence and high-fidelity mesh extraction. Designed to address errors propagated from off-the-shelf normal and mask estimators used for planar prior assignments—such as Metric3Dv2 and SAM—DGR ensures stable optimization and enhanced geometric reconstruction in both indoor and outdoor scenes (Gan et al., 20 Oct 2025).

1. Context and Motivation

In Gaussian Splatting-based surface reconstruction, the use of explicit planar priors enables accurate, structured scene representations, particularly of man-made environments with prominent planar regions. The GSPlane method leverages convex combinations of three basis points to reparameterize certain Gaussian 3D centers, effectively instilling planar constraints. However, the automated nature of prior assignment—based on external segmentation and normal prediction—can introduce false-positive planar Gaussians. These erroneously assigned Gaussians cannot adhere to the strict planar constraint, resulting in persistently high gradient magnitudes with respect to their positional encoding, ultimately compromising both convergence speed and mesh quality. The DGR mechanism directly addresses these failures by dynamically identifying such Gaussians and restoring them to unconstrained (xyz) optimization, thereby stabilizing the learning process and mesh extraction fidelity (Gan et al., 20 Oct 2025).

2. Mathematical Formulation

Let $L$ denote the total loss function, encompassing photometric, regularizer, and planar prior terms. The population of Gaussians is divided into two sets:

• $\mathcal{P}$: planar Gaussians using convex-combination ($\omega$) parameterization,
• $\mathcal{N}$: non-planar Gaussians retaining direct $(x, y, z)$ coordinates.

For each Gaussian $i$, the magnitude of its gradient with respect to its coordinate parameters is computed as

$\|g_i\| \triangleq \|\nabla_{p_i} L\|$

where $p_i \in \{\omega_{i1}, \omega_{i2}, \omega_{i3}\}$ for $i \in \mathcal{P}$, or $p_i \in \{x_i, y_i, z_i\}$ for $i \in \mathcal{N}$. The current planar and non-planar gradient sets are $G_\mathcal{P}$ and $G_\mathcal{N}$, respectively. DGR operates by:

• Selecting the top $\alpha\%$ (default: 5%) of planar Gaussians with the largest gradients: $P_{high}$.
• Computing a reclassification threshold $T$ as the mean of the top $\beta\%$ (default: 20%) of non-planar gradient magnitudes in $G_\mathcal{N}$.
• Reclassifying any $i \in P_{high}$ with $\|g_i\| > T$ to non-planar status: i.e., reverting its parameterization from the planar prior-based coordinates back to unconstrained $(x, y, z)$. The affected Gaussian is then excluded from future planar prior loss calculations.

This dynamic rule can be summarized as:

$$i \to \mathcal{N} \;\text{if}\; i \in P_{high} \; \text{and} \; \|\nabla_{\omega_{i}} L\| > T$$

3. Algorithmic Workflow and Scheduling

DGR is tightly integrated with the GSPlane training loop, which comprises iterative densification and Gaussian parameter optimization. The DGR phase periodically intervenes after densification events and during late-stage training to enforce adaptive reclassification. Algorithmically:

1. Gaussians are initialized and some are assigned planar priors using segmentation and normal-prediction outputs.
2. Each training iteration comprises rendering, loss evaluation, back-propagation, and parameter updates (including either $\omega$ or $(x, y, z)$ for position).
3. DGR is activated in scheduled windows:
   • After each densification (every 1,000 iterations between 500 and 15,000), DGR runs for 50 steps.
   • A final DGR application runs for 100 iterations at step 20,000.
   • DGR is only enabled after the initial 500 iterations to allow initial representation stabilization and ceases before the final fine-tuning phase.

Within each DGR window, the gradient-based selection and reparameterization are performed as described, with newly liberated Gaussians initialized by projecting from their previous planar representation.

4. Implementation Parameters and Practical Considerations

Key hyperparameters for DGR include:

• $\alpha = 5\%$ (planar top-percentile for reclassification consideration)
• $\beta = 20\%$ (non-planar percentile for reference threshold computation)
• DGR window duration: 50 iterations (post-densification), 100 iterations (final pass at 20,000)
• Plane-basis points for convex combinations are trainable but updated with a learning rate reduced by an order of magnitude relative to core Gaussian parameters, accommodating gentle plane adaptations.

Once a Gaussian is reclassified as non-planar, it immediately ceases to augment the planar prior term:

$$L_{planar} = \sum_{i \in \mathcal{P}} \| (\omega_{i1}F_1 + \omega_{i2}F_2 + \omega_{i3}F_3) - x_i \|^2$$

and the respective $x_i, y_i, z_i$ become trainable directly. DGR scheduling avoids the early unstable phase and late fine-tuning to maximize its corrective effect.

5. Empirical Evaluation and Impact

Ablation studies in the GSPlane project demonstrate measurable benefits of DGR. The addition of DGR atop a structured planar basis yields further improvements over planar basis alone:

• Baseline 2DGS F-score: ≈ 0.583
• With structured basis: ≈ 0.633
• With structured basis and DGR: ≈ 0.636

This constitutes a ≈ 0.3 percentage point F-score increase, indicating effective mitigation of false-positive planar Gaussians and improved planar fitting. Post-DGR, the distributions of planar Gaussian gradients exhibit reduced heterogeneity and reduced oscillations in the planar-prior loss term.

Mesh extraction metrics further confirm improved mesh precision and recall rates (by 1–3% over baseline GS), even prior to mesh-layout refinement. For outdoor scenes, DGR also contributes to F-score increases and achieves over 90% reduction in vertex counts within planar regions, emphasizing the dual impact on accuracy and compactness (Gan et al., 20 Oct 2025).

6. Significance and Implications

DGR exemplifies an adaptive correction strategy for structured representations, dynamically negotiating the boundary between constraint expressivity and model flexibility. By continuously monitoring gradient behaviors, DGR mitigates the long-term impact of initial prior misassignments, resulting in more stable reconstructions. A plausible implication is that similar gradient-driven reclassification could be applied in other problems that leverage prior-driven structured latent spaces, where automatic segmentation is imperfect. The approach demonstrates that careful monitoring and responsive relaxation of constraints are instrumental in achieving both geometric accuracy and topological simplicity in structured scene reconstructions.