Incremental Surfel Fusion with Information Filter

• The paper introduces an incremental surfel fusion method that leverages information filters to update uncertainty-aware, probabilistic maps in real time.
• It details an additive update mechanism that efficiently incorporates new 3D sensor measurements from LiDAR or RGB-D inputs to refine surfel states.
• Experiments show enhanced reconstruction fidelity and computational efficiency, achieving up to 24 FPS with significant frame reduction.

Incremental surfel fusion with information filter is a class of algorithms aimed at efficient, real-time dense surface reconstruction by maintaining and updating a probabilistic map of surface elements—surfels—using the information form (inverse covariance) of Gaussian estimation. These techniques are designed for systems receiving continuous 3D sensor input, such as LiDAR or RGB-D, with the goal of producing high-fidelity, uncertainty-aware maps as sensor data arrives and with real-time performance. The core paradigm is to represent each surfel by its geometric and, in some cases, radiometric attributes and explicitly track their uncertainty; measurements from new frames are incrementally fused through additive updates to each surfel’s information (precision) and information vector, leveraging the efficiency and robustness of information filters. This framework enables principled exploitation of spatial redundancy, effective denoising, and flexible fusion rules, all while ensuring tractable computational pipelines for large-scale mapping and SLAM.

1. Surfel State, Uncertainty, and Information Formulation

A surfel is parameterized by its centroid position $\mathbf{p} \in \mathbb{R}^3$, normal vector $\mathbf{n} \in \mathbb{R}^3$ (subject to $\|\mathbf{n}\|=1$), and optionally a scale/radius $r$ or additional attributes such as in-plane Gaussian scales, a quaternion rotation, color coefficients, and opacity. The full state vector takes the form $$\mathbf{x} = [\mathbf{p}^\top\ \mathbf{n}^\top\ r]^\top \in \mathbb{R}^7$$ (for LiDAR), or $$\mathbf{x}_i = [\mathbf{p}_i; \mathbf{n}_i] \in \mathbb{R}^6$$ (for RGB-D/geometry-aware Gaussian surfels). Gaussian uncertainty over the state is maintained either as a covariance $\Sigma \in \mathbb{R}^{d \times d}$ or, more frequently for efficiency and fusion, as its inverse: the information matrix $Y = \Sigma^{-1}$ (or $\Lambda$), along with the information vector $y = Y \hat{x}$. The mean can always be recovered as $\hat{x} = Y^{-1}y$ (Park et al., 2017, Pan et al., 1 Dec 2025).

2. Information Filter-Based Incremental Fusion

The core of incremental surfel fusion with information filter is the additive nature of the information filter update. Given a prior surfel (information matrix $Y$, vector $y$, mean $\hat{x}$) and a new measurement $z$ with noise covariance $R$, the update is: $Y^+ = Y^- + R^{-1}, \qquad y^+ = y^- + R^{-1}z$ resulting in an updated mean $\hat{x}^+ = (Y^+)^{-1}y^+$. This additive property extends naturally to fusing multiple independent surfel estimates: $$Y_\mathrm{fused} = Y_1 + Y_2,\qquad y_\mathrm{fused} = y_1 + y_2$$ The measurement model is typically linear, with $z = Hx + v$, $H = I$, and $v \sim \mathcal{N}(0, R)$ in the standard case. For geometry-aware fusion, observation covariances $R$ depend on both sensor range and angle, or depth for RGB-D, often assumed block-diagonal or diagonal for computational economy (Park et al., 2017, Pan et al., 1 Dec 2025).

3. Data Association, Gating, and Redundancy Filtering

Data association between incoming measurements and existing surfels employs a geometry-aware, uncertainty-gated strategy, typically using the Mahalanobis distance: $\nu = z - \hat{x}, \qquad S = \Sigma + R$ Measurement-surfel pairs are accepted for fusion if $\nu^\top S^{-1} \nu < \chi^2_{d,\alpha}$. Some systems accelerate this by first gating only on 3D centroid before considering normal alignment. In addition, information-theoretic approaches such as the Normalised Information Distance (NID) compute a scalar novelty score between predicted and live RGB-D appearance: $$\mathrm{NID}(\mathcal{F}_t^p, \mathcal{F}_t^l) = \frac{H(\mathcal{F}_t^p, \mathcal{F}_t^l) - I(\mathcal{F}_t^p;\mathcal{F}_t^l)}{H(\mathcal{F}_t^p, \mathcal{F}_t^l)}$$ Fusion is triggered only when NID exceeds a configurable threshold $\tau$, yielding up to ~50% reduction in fused frames with minor loss in accuracy (Gallagher et al., 2021).

4. Practical Algorithms and Pipeline Integration

The overall processing pipeline for incremental surfel fusion with information filtering involves the following steps for each input frame:

1. Measurement Extraction: Obtain surfel measurements by local plane fitting (LiDAR) or image-based vertex/normal maps (RGB-D).
2. Prediction and Association: For each measurement, retrieve predicted surfel info, and search for candidate matches using spatial indexes (e.g., k-d tree, voxel grid).
3. Gated Fusion: For accepted pairs, compute and add information update; otherwise, create new surfel.
4. Surfel State Update: Update surfel mean, enforce normal normalization (with minimal rotation in quaternion-based representations), and update associated statistics.
5. Pruning: Remove surfels with low confidence or low information gain for map sparsity.
6. Global Consistency: In some systems, periodic differentiable rendering-based optimization is applied to jointly refine surfels over a batch of frames; a geometric regularizer keeps them near their incremental fusion state (Pan et al., 1 Dec 2025).

These steps are accelerated by choosing sparse or block-diagonal information representations and GPU backends for core computations, enabling throughput up to 24 FPS in state-of-the-art systems (Pan et al., 1 Dec 2025).

5. Experimental Performance and Trade-offs

Incremental information-filtered surfel fusion achieves substantial improvements in reconstruction fidelity and computational efficiency:

System	RMSE / Acc.	Fused Frames Reduction	Throughput
NID-EF ($\tau=0.9$)	$4.9$ mm	$-51\%$	Comparable EF
EGG-Fusion (Replica)	$0.90$ cm	-	$24.2$ FPS
EGG-Fusion (ScanNet++)	$0.67$ cm	-	$24.2$ FPS
RTG-SLAM	$1.30$ cm	-	$15.7$ FPS

Where RMSE/Acc are reconstruction errors, and fused frame reduction shows how many sensor frames are skipped with negligible impact on quality (Pan et al., 1 Dec 2025, Gallagher et al., 2021). A plausible implication is that information-filtering combined with information-theoretic novelty gating bounds computational growth in long-term mapping while maintaining geometric fidelity. Experiments show that up to 60% of frames can be skipped, cutting surfel count by nearly half with only marginal degradation in RMSE (<5%).

6. Extensions, Limitations, and System Variants

Incremental surfel fusion with information filter has seen extensions toward:

• Photometric/Geometric Consistency Optimization: Integrating differentiable rendering and batch optimization enforces cross-view consistency.
• Sensor-Agnostic Modeling: Both LiDAR and RGB-D pipelines have adopted information-formulated incremental fusion, with sensor-adaptive noise modeling.
• Dynamic World Models: Prediction steps incorporate process noise and explicit motion models in highly dynamic scenarios, though static models are most common in practice.

Limitations include mis-estimation of redundancy in dynamic scenes (e.g., NID triggering unnecessary fusion due to motion), overhead of NID computation at high resolutions, and potential tracking drift in highly repetitive environments.

7. Impact and Benchmarking

The impact of information filter-based incremental surfel fusion is manifested in improved scalability, reconstruction accuracy, and reduced computational cost. Systems such as EGG-Fusion report over 20% accuracy gains versus state-of-the-art Gaussian Splatting-based methods, mean accuracy of $0.90$ cm on Replica, and real-time throughput of $24$ FPS (Pan et al., 1 Dec 2025). On both synthetic and real datasets, NID-based systems halve the number of fused frames and surfels, with only marginal increase in trajectory error (Gallagher et al., 2021). These approaches are thus central to current real-time SLAM and mapping solutions encompassing large-scale, redundancy-rich 3D environments.