Radiance Field Rendering Overview

• Radiance field rendering is a method that models the plenoptic function to generate novel views by integrating radiance and density along camera rays.
• Techniques range from implicit neural models like NeRF to explicit, point-based methods such as 3D Gaussian splatting, balancing fidelity and efficiency.
• Hybrid and adaptive approaches, including Fourier PlenOctree and adaptive shells, enable efficient rendering of dynamic scenes and high-frequency details.

Radiance field rendering is a class of computational methods for synthesizing photorealistic novel views of 3D scenes by directly modeling the light-radiation distribution in space, optionally as it evolves over time. The core principle is to represent the plenoptic function—which describes radiance as a function of spatial location and view direction—using learnable or structured data-driven models, then reconstruct images by querying and integrating these models along camera rays. Radiance field renderers have evolved rapidly, moving from slow implicit neural representations to explicit, real-time methods capable of handling static and dynamic scenes with high fidelity, scalability, and efficiency.

1. Underlying Principles and Representations

At the foundation, a radiance field maps a 3D position $\mathbf{x} \in \mathbb{R}^3$ and view direction $\mathbf{d} \in S^2$ to emitted color $\mathbf{c}$ and volumetric density $\sigma$: $$f_{\text{radiance}}(\mathbf{x}, \mathbf{d}) = (\mathbf{c}, \sigma)$$. Rendering synthesizes novel views by sampling points along camera rays and compositing their radiance and densities using volume integration:

$$C = \int_{n}^{f} \exp\left(-\int_{n}^{z} \sigma(r(z')) dz'\right) \sigma(r(z)) c(r(z), \mathbf{d}) dz$$

where $r(z)$ parameterizes each ray.

Representations broadly fall into two categories:

• Implicit neural fields (e.g., NeRF): A multilayer perceptron (MLP) infers $(\mathbf{c}, \sigma)$ per query, offering interpretability and storage efficiency but being computationally expensive for high-resolution rendering.
• Explicit, point-/voxel-based (e.g., 3D Gaussian Splatting, Plenoctree, surfel/convex primitives): Store per-element radiometric and geometric attributes, supporting massively parallel rasterization and order-of-magnitude acceleration at the cost of higher memory use.

Hybrid strategies—adaptive shells, bi-scale GES, frequency-adaptive splatting, etc.—further mix neural and explicit computations, targeting specific performance, quality, or manipulability trade-offs.

2. Acceleration via Structured and Point-Based Techniques

Rendering acceleration centers on reducing redundant computation and enabling parallelization:

• Voxel/Octree Structures (PlenOctree, Fourier PlenOctree): Static radiance field queries are accelerated by spatial subdivision, where leaf voxels store either view-independent densities and spherical harmonics (SH) coefficients or time-varying functions as Fourier spectra (Wang et al., 2022). The Fourier PlenOctree generalizes this to dynamic, free-viewpoint video rendering by storing Fourier coefficients in each leaf, reconstructing time-varying color and density via inverse discrete Fourier transforms.
• Point-Based Splatting (3DGS, TRIPS, GES): Instead of evaluating neural models per sample, scenes are encoded as collections of primitives—each with a position, covariance (for spatial extent), color, and often SH for view dependency. These primitives are projected (“splatted”) to image space and composited with alpha blending. TRIPS (Franke et al., 11 Jan 2024) introduces trilinear point splatting on multi-level image pyramids to address both large-scale coverage and fine detail, outperforming prior state-of-the-art in quality and speed.
• Advanced Primitives (Gabor Splatting, Convex Splatting): 3DGabSplat (Zhou et al., 7 Aug 2025) augments each primitive with directional 3D Gabor kernels, forming a filter bank that allows adaptive frequency response—capturing high-frequency details with fewer elements, and supporting frequency-adaptive optimization to avoid redundancy.

The table summarizes key explicit representations and their notable improvements:

Method	Primitive Type	Notable Advantages
3DGS	Gaussian	Anisotropy, real-time splatting, high detail
Isotropic GS	Spherical Gaussian	4 parameters, 100× faster, easy merging/splitting
GES	Surfels + 3D Gaussians	Sorting-free, view consistency, two-pass efficiency
3DCS	Smooth convexes	Hard-edge fidelity, low primitive count, sharpness
3DGabSplat	Gaussian + Gabor kernels	Frequency adaptation, PSNR/LPIPS gains, plug-and-play

3. Temporal and Dynamic Scene Extensions

Extending radiance fields to dynamic or time-varying scenes necessitates augmenting the core representation to encode the temporal dimension efficiently:

• Fourier PlenOctree (FPO): Time-varying density and SH coefficients are compressed into Fourier series per spatial leaf. For any $(x, y, z, t)$ sample, attributes are reconstructed via the inverse DFT:

$$\sigma(t; \mathbf{k}^\sigma) = \sum_{i = 0}^{n_1 - 1} k^\sigma_i \cdot \mathrm{IDFT}_i(t)$$

where the IDFT basis alternates cosine and sine, and $\mathbf{k}^\sigma$ are learned coefficients. Similar expansions are used for SH parameters (Wang et al., 2022). Efficient tree construction leverages NeRF predictions and volumetric fusion across multiple dense viewpoints, unified across frames for dynamic sequence encoding.

• VideoRF: Serializes a 4D radiance field as a 2D feature image stream; uses hardware-accelerated video codecs, spatial/temporal regularization, and a deferred shading pipeline for real-time streaming/decoding on mobile devices. Scene lookup is via a 3D-to-2D Morton-sorted mapping table, facilitating $O(1)$ feature queries (Wang et al., 2023).

Such approaches enable real-time rendering for dynamic, long-duration free-viewpoint videos and immersive telepresence.

4. Hybrid and Adaptive Rendering Formulations

Recent innovations shift between pure volume rendering and compact surface-based rendering to match local scene structure:

• Adaptive Shells: Each spatial location estimates a signed distance field $f(x)$ and a local kernel width $s(x)$, generalizing the SDF-to-density mapping:

$$\sigma(x) = \max\left(-\frac{d\Phi_s(f)}{df} / \Phi_s(f), 0\right), \quad \Phi_s(f) = \frac{1}{1 + \exp(-f/s(x))}$$

Solid-surface regions (small $s$) use single-sample ray queries; fuzzy regions (large $s$) retain volumetric integration. The method extracts explicit shell meshes via banded level set evolution for fast intersection, yielding order-of-magnitude speedup and improved PSNR, LPIPS, and frame rates, while enabling downstream animation and simulation (Wang et al., 2023).

• GES (Gaussian-enhanced Surfels): Combines a surfel (2D disc) representation—opaque, z-buffered for coarse-scale geometry—with a second-pass accumulation of (fewer) transparent 3D Gaussians for fine-scale detail. Depth testing and alpha accumulation are sorting-free due to the surfel pseudo-depth map, yielding stable, high-speed, popping-free synthesis. Variants (Mip-GES, Speedy-GES, Compact-GES) extend anti-aliasing, memory, and speed tradeoffs (Ye et al., 24 Apr 2025).

These strategies can be further complemented by foveated rendering (VR-Splatting (Franke et al., 23 Oct 2024)), which adaptively selects between computationally intensive, high-resolution renderers in the fovea and fast, perceptually lower-detail renderers in the periphery, enabling real-time high-fidelity VR experiences via human visual system models.

5. Frequency-Adaptive and Specialized Primitives

Classic 3D Gaussian splatting is low-pass by nature, thus representing high-frequency details inefficiently with redundant, overlapping primitives. 3DGabSplat (Zhou et al., 7 Aug 2025) explicitly parameterizes each primitive with multiple 3D Gabor kernels (Gaussian envelope modulated by cosine at learnable spatial frequencies and orientations):

$$g(\mathbf{x}) = \text{Gaussian}(\mathbf{x}) \cdot \left(1 - \sum_i \omega_{k,i}\right) + \sum_i \omega_{k,i} \cdot \cos(2\pi \mathbf{f}_{k,i}^T (\mathbf{x} - \mathbf{\mu}_k))$$

where $\omega_{k,i}$ are learned weights. Frequency-adaptive training resets and prunes/merges frequency parameters of new or redundant children during densification, preventing excess high-frequency artifact accumulation and ensuring efficient representation of textures and fine geometry. CUDA-based rasterization pipelines are extended to project frequency vectors through affine transforms and z-axis integration, composing view-dependent detail efficiently. Reported gains include up to 1.35 dB PSNR improvement over 3DGS, with simultaneous reduction in primitive count and memory.

6. Practical Applications, Integration, and Future Research

Radiance field rendering methodologies have been widely adopted in:

• Real-time and immersive view synthesis for VR/AR, where latency, fidelity, and stability (e.g., popping artifacts) drive the design of hybrid, adaptive, and foveated pipelines (Franke et al., 23 Oct 2024);
• 3D scene or object reconstruction, texture transfer, mesh generation, and animation, leveraging projections of radiance field representations onto mesh surfaces via Gaussian splats and cached per-pixel geometry (Lim et al., 17 Jun 2024);
• Federated and hierarchical optimization and rendering across devices and edge/cloud (e.g., for 6G networks) (Wu et al., 20 May 2024), with research addressing compression, joint communication–computation, semantic transmission, and over-the-air federated learning.

Emerging directions include convex primitive splatting for edge fidelity and memory savings (Held et al., 22 Nov 2024), plug-and-play frequency filtering (Zhou et al., 7 Aug 2025), and adaptive shells for surface–volume blending (Wang et al., 2023). Renderers are increasingly unified and modular to operate across NeRF, 3DGS, and sparse voxel formats—supporting single-pass plane sweeping and caching for multi-view display devices (e.g., Looking Glass light field displays (Kim et al., 25 Aug 2025)), with recorded 22× speedups compared to per-view approaches.

Potential research frontiers include optimizing the degree of spatial/frequency/adaptivity as a function of scene complexity and motion; fully differentiable renderers enabling integration with animation, simulation, and editing; and real-time deployment on consumer hardware and in bandwidth-constrained or edge-cloud environments.

7. Open Challenges and Outlook

While radiance field rendering has become highly efficient and generalizable, several open problems remain:

• Trade-offs between explicit and implicit representations balance computational cost, memory, and editing flexibility. Convex primitives and frequency-adaptive splats address limitations but may introduce complexity in implementation and training.
• Dynamic scenes and non-rigid motions push the limits of memory, temporal representation, and high-frequency signal capture. Methods such as FPO (Wang et al., 2022) and VideoRF (Wang et al., 2023) demonstrate progress but rely on dense/redundant inputs and may scale sublinearly with scene complexity.
• High-fidelity relighting and reflectance decomposition are beginning to be addressed using staged progressive radiance/physics blending, with spatially-adaptive progress maps to handle unmodeled phenomena (Ye et al., 14 Aug 2024).
• Specialized use cases (e.g., light field displays or edge-based rendering) motivate unified, multi-representation pipelines and hardware-aware acceleration, but mainstream accessibility and standardization are ongoing efforts.

Overall, radiance field rendering is at the core of a new generation of 3D content creation, visualization, and immersive interaction, with its rapid development driven by the interplay of representation, acceleration, and application demands across graphics, vision, and communications.