Sensor-Physics NeRF Framework

• Sensor-physics grounded NeRF is a framework that directly integrates sensor measurement models into neural radiance fields for enhanced 3D mapping.
• It employs physics-guided loss functions and Bayesian data fusion to regularize neural predictions, achieving up to 46% faster training and improved reconstruction accuracy.
• The framework supports diverse modalities including TOF, photometric, and event sensors to deliver robust novel view synthesis, HDR deblurring, and quantitative depth recovery.

A sensor-physics grounded NeRF framework refers to a class of neural radiance field (NeRF) architectures and optimization protocols in which the neural 3D representation is explicitly coupled to the physical measurement process and propagation models of the underlying sensors. Such frameworks align neural volume representations, rendering equations, and learning losses with the mathematical laws governing sensor modalities—most prominently time-of-flight (TOF) ranging, photometric capture with nonlinear response, event-driven vision, and radiative transfer in media. Across recent literature, sensor-physics grounded NeRFs have demonstrated robust 3D reconstruction, mapping, and novel view synthesis in environments with sparse views, degraded media, or low-cost sensors, by leveraging physical priors to constrain, regularize, and accelerate neural learning.

1. Foundational Sensor Physics and Imaging Models

Sensor-physics grounded NeRF designs begin with an explicit mathematical characterization of how each involved sensor captures the physical scene.

Time-of-Flight Ranging: Both infrared (IRS) and ultrasonic (USS) rangefinders measure the time delay \$t\$ between emission and echo, yielding depth as

$$D_{\rm IRS} = \tfrac{c}{2}\,t_{\rm IRS}, \quad D_{\rm USS} = \tfrac{v_{\rm s}}{2}\,t_{\rm USS}$$

where \$c\$ is the speed of light and \$v_s\$ the speed of sound. Practical measurements include zero-mean Gaussian noise and different beam apertures (wide for USS, narrow for IRS) (Schmid et al., 2024).

Photometric Sensors and Events: Conventional cameras integrate radiance over an exposure window and perform nonlinear mapping via a camera response function (CRF), blurring moving objects and compressing dynamic range. Event cameras asynchronously detect sign-thresholded changes in log-radiance: $$\partial_t\log L(x, y, t), \quad \nabla_{xy}\log L(x, y, t)$$ This yields complementary spatial and temporal data for reconstruction (Qi et al., 21 Jan 2026).

Radiative Transfer in Participating Media: Media interactions such as absorption and scattering are modeled via Beer-Lambert law, generalized to unify direct, in-scatter, and attenuation: $$I = J\,e^{-\sigma^{\rm attn}z} + B\,\bigl(1 - e^{-\sigma^{\rm scat}z}\bigr)$$ Direct object radiance and ambient backscatter are decomposed into particle densities in volumetric rendering (Liu et al., 25 Oct 2025).

2. Physics-Guided Constraints and Bayesian Data Fusion

Sensor-aware NeRF frameworks fuse raw sensor measurements and neural predictions into scene occupancy or volumetric representations using physics-guided constraints and Bayesian inference.

Bayesian Occupancy Grid Updates: In VIRUS-NeRF, measurements from IRS and USS are combined with neural density predictions in a Bayes-filtered occupancy grid. For each cell,

$$P(c_i^{\rm occ}|M_{1:n}) = \frac{P(M_n|c_i^{\rm occ})\,P(c_i^{\rm occ}|M_{1:n-1})}{P(M_n|c_i^{\rm occ})\,P(c_i^{\rm occ}|M_{1:n-1}) + P(M_n|c_i^{\rm emp})\,P(c_i^{\rm emp}|M_{1:n-1})}$$

NeRF densities are projected to probabilities using a smooth sigmoid-like function parameterized by the adaptive threshold \$\sigma_T\$ and slope \$\zeta\$ (Schmid et al., 2024).

Physics-Guided Losses: PhysicsNeRF incorporates four constraints:

• Depth ranking: Using monocular depth estimates to enforce correct ordinal relations.
• Cross-view consistency: Penalizing mismatches in radiance/color predictions for corresponding 3D points across views.
• Sparsity priors: Regularizing volumetric density to suppress spurious occupancy away from measured surfaces.
• Gradient regularization: Promoting smooth radiance field predictions (Barhdadi et al., 29 May 2025).

Media Propagation Losses: I²-NeRF introduces mutual-exclusion, monotonicity, and compensated patch-wise SSIM losses to enforce physically plausible attenuation, depth recovery, and separation of object/medium densities (Liu et al., 25 Oct 2025).

3. Rendering Protocols: Physics-Aligned Ray Marching and Mapping Fields

The rendering process is adapted to focus neural computation and loss functions on regions or modalities validated by physical models.

Probabilistic Ray Marching: Instead of thresholding neural density heuristically, VIRUS-NeRF samples only in voxels where occupancy probability \$P(c_i^{\rm occ})\$ exceeds a cutoff. This skips empty regions and accelerates convergence, achieving a notable 46% speed-up in training (Schmid et al., 2024).

Event-Integrated Volume Rendering: See-NeRF uses a dual mapping field architecture:

• The RGB mapping field simulates temporal integration and non-linear CRF, generating synthetic LDR images from integrated HDR radiance.
• The Event mapping field models contrast thresholding, latency, and photometric quantization, yielding synthetic event streams directly comparable to observed data. This joint supervision drives the underlying NeRF to learn sharp HDR geometry capable of robust deblurring (Qi et al., 21 Jan 2026).

Uniform Media Sampling: I²-NeRF’s reverse-stratified upsampling ensures near-uniform coverage of both opaque surfaces and translucent media, preserving metric isometry for accurate physical measurements (Liu et al., 25 Oct 2025).

4. Network Architectures and Encoding Strategies

Sensor-physics grounded NeRF frameworks combine feature-efficient encodings and modular network designs accommodating physical priors.

Multi-Resolution Hash Encoding: VIRUS-NeRF inherits a 16-level hash table scheme from Instant-NGP, concatenating spatial features for MLP-based prediction of color and density (Schmid et al., 2024).

Dual-Scale Encoding: PhysicsNeRF uses a compact 0.67M-parameter architecture, encoding each spatial coordinate at two different frequencies and deploying independent MLP branches per scale. Auxiliary physics losses are activated progressively according to a curriculum schedule \$\alpha(t)\$ (Barhdadi et al., 29 May 2025).

Dedicated Media and Object Encoders: I²-NeRF employs ZipNeRF-style hash-grid encoders for object and medium, feeding separate MLPs to predict respective densities, attenuation, and vertical coordinates for media transmittance (Liu et al., 25 Oct 2025).

Mapping Fields in See-NeRF: Separate MLPs specialize in simulating sensor-specific transformations—CRF for RGB pixels, event quantization for asynchronous spikes—using positional encodings identical to the main NeRF. This modularity enables robust alignment with physical imaging pipelines (Qi et al., 21 Jan 2026).

5. Quantitative Performance and Practical Implications

Sensor-physics grounded NeRF frameworks exhibit robust reconstruction, mapping accuracy, and operational efficiency.

Mapping Coverage and Accuracy: In 2D office environments, VIRUS-NeRF achieves

• ≥95% of LiDAR coverage up to 2 m, ≈90% up to 100 m
• Mean nearest-neighbour distance (NND) ≈0.32 m, slightly outperforming 16-beam LiDAR in small scenes
• In larger spaces, accuracy is bounded by USS sensor range (Schmid et al., 2024)

Training Speed: Bayesian occupancy culling cuts per-step MLP calls by 30%, yielding 46% faster training iterations; stable NND achieved in ~20 s versus ~36 s for bare Instant-NGP (Schmid et al., 2024).

Sparse-View Generalization: PhysicsNeRF, using only 8 views, achieves average training PSNR of 21.4 dB and test PSNR of 15.2 dB (gap 6.2 dB). Ablations confirm the necessity of all physics-guided losses to minimize the generalization gap (Barhdadi et al., 29 May 2025).

HDR Deblurring and Event Data: See-NeRF attains state-of-the-art PSNR (24.13 dB synthetic, 26.49 dB real) and significantly outperforms baselines in novel-view synthesis under extreme lighting and blur (Qi et al., 21 Jan 2026).

Physical Quantity Estimation: I²-NeRF enables accurate depth recovery (e.g., 7.2 m vs. actual 7.5 m in ocean scenes), PSNR gains in low-light scenarios, and patch-wise SSIM fidelity in underwater environments (Liu et al., 25 Oct 2025).

6. Limitations and Prospects for Sensor-Physics Grounded NeRFs

Despite performance gains, several limitations and research directions remain.

• Persistent generalization gaps (5.7–6.2 dB in PhysicsNeRF) highlight that fixed-form physics priors are insufficient for under-determined inverse problems at extreme view sparsity.
• Optimization landscapes can be rugged due to enforcement of hard constraints, requiring careful curriculum schedules and regularization parameter selection.
• Current frameworks use static physical priors; learnable or adaptive regularization (scene- or region-specific) is an open area.
• Integration of further modalities (radar, semantic, temporal) and hierarchical models may supply stronger constraints and extend physical fidelity.
• Theoretical analysis of minimum sensor/view density for reliable generalization is unresolved.

A plausible implication is that sensor-physics grounding provides substantial efficiency and accuracy benefits—but for full scene understanding or dynamic environments, adaptive, multi-modal and context-sensitive extensions will be required (Schmid et al., 2024, Barhdadi et al., 29 May 2025, Qi et al., 21 Jan 2026, Liu et al., 25 Oct 2025).

7. Applications, Extensibility, and Broader Impact

Sensor-physics grounded NeRF frameworks have demonstrated utility in mobile robotics, industrial mapping, HDR imaging, event-based systems, and media-degraded 3D capture.

• Mobile Robotics: VIRUS-NeRF enables cost-effective obstacle detection and path planning by replacing expensive LiDAR with off-the-shelf IRS/USS sensors costing under €50 per module, preserving critical coverage and accuracy for safety tasks (Schmid et al., 2024).
• HDR and Deblurring: Event-integrated See-NeRF reconstructs high-quality, sharp 3D scenes from single blurred LDR images, making robust imaging feasible in uncontrolled lighting without expensive multi-exposure datasets (Qi et al., 21 Jan 2026).
• Media-Environments: I²-NeRF accurately reconstructs scenes submerged or obscured by scattering media (e.g., underwater, low-light, haze), and can estimate physical properties such as water depth directly via network predictions (Liu et al., 25 Oct 2025).
• Modular Design: Many frameworks accept plug-in modalities (radar, additional depth sensors), and their physics-grounded occupancy and loss formulations are broadly reusable, confirming the principle’s generality.

This suggests the continued adoption of sensor-physics grounded NeRFs for real-time, resource-constrained, and physically interpreted 3D tasks across robotics, autonomous vehicles, and scientific imaging.