# Multiscale Tensor Decomposition and Rendering Equation Encoding for View Synthesis

arXiv: https://arxiv.org/abs/2303.03808 · HTML: https://mlsanity.com/paper/2303.03808/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 41 references that are in the map.
- First posted on arXiv 7 Mar 2023.

## Builds on (most cited first, 27 of 27)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Feature Pyramid Networks for Object Detection](https://mlsanity.com/paper/1612.03144/) (2016)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [Deep High-Resolution Representation Learning for Human Pose Estimation](https://mlsanity.com/paper/1902.09212/) (2019)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [Direct Voxel Grid Optimization: Super-fast Convergence for Radiance Fields Reconstruction](https://mlsanity.com/paper/2111.11215/) (2021)
- [Neural Sparse Voxel Fields](https://mlsanity.com/paper/2007.11571/) (2020)
- [PlenOctrees for Real-time Rendering of Neural Radiance Fields](https://mlsanity.com/paper/2103.14024/) (2021)
- [Ref-NeRF: Structured View-Dependent Appearance for Neural Radiance Fields](https://mlsanity.com/paper/2112.03907/) (2021)
- [NeRV: Neural Reflectance and Visibility Fields for Relighting and View Synthesis](https://mlsanity.com/paper/2012.03927/) (2020)
- [NeRD: Neural Reflectance Decomposition from Image Collections](https://mlsanity.com/paper/2012.03918/) (2020)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [Advances in Neural Rendering](https://mlsanity.com/paper/2111.05849/) (2021)
- [Neural Point-Based Graphics](https://mlsanity.com/paper/1906.08240/) (2019)
- [Neural-PIL: Neural Pre-Integrated Lighting for Reflectance Decomposition](https://mlsanity.com/paper/2110.14373/) (2021)
- [Shape, Light, and Material Decomposition from Images using Monte Carlo Rendering and Denoising](https://mlsanity.com/paper/2206.03380/) (2022)
- [NeRFactor: Neural Factorization of Shape and Reflectance Under an Unknown Illumination](https://mlsanity.com/paper/2106.01970/) (2021)
- [Light Field Neural Rendering](https://mlsanity.com/paper/2112.09687/) (2021)
- [Neural Radiance Transfer Fields for Relightable Novel-view Synthesis with Global Illumination](https://mlsanity.com/paper/2207.13607/) (2022)
- [Deep Surface Light Fields](https://mlsanity.com/paper/1810.06514/) (2018)
- [Learning Implicit Surface Light Fields](https://mlsanity.com/paper/2003.12406/) (2020)

## Built on by (most cited first, 18 of 18)

- [Compact 3D Gaussian Representation for Radiance Field](https://mlsanity.com/paper/2311.13681/) (2023)
- [ContextGS: Compact 3D Gaussian Splatting with Anchor Level Context Model](https://mlsanity.com/paper/2405.20721/) (2024)
- [Spec-Gaussian: Anisotropic View-Dependent Appearance for 3D Gaussian Splatting](https://mlsanity.com/paper/2402.15870/) (2024)
- [NeuRBF: A Neural Fields Representation with Adaptive Radial Basis Functions](https://mlsanity.com/paper/2309.15426/) (2023)
- [Compact 3D Gaussian Splatting for Static and Dynamic Radiance Fields](https://mlsanity.com/paper/2408.03822/) (2024)
- [Optimized Minimal 3D Gaussian Splatting](https://mlsanity.com/paper/2503.16924/) (2025)
- [SlimmeRF: Slimmable Radiance Fields](https://mlsanity.com/paper/2312.10034/) (2023)
- [Improving Robustness for Joint Optimization of Camera Poses and Decomposed Low-Rank Tensorial Radiance Fields](https://mlsanity.com/paper/2402.13252/) (2024)
- [SurFhead: Affine Rig Blending for Geometrically Accurate 2D Gaussian Surfel Head Avatars](https://mlsanity.com/paper/2410.11682/) (2024)
- [SVDinsTN: A Tensor Network Paradigm for Efficient Structure Search from Regularized Modeling Perspective](https://mlsanity.com/paper/2305.14912/) (2023)
- [Volume Feature Rendering for Fast Neural Radiance Field Reconstruction](https://mlsanity.com/paper/2305.17916/) (2023)
- [AniSDF: Fused-Granularity Neural Surfaces with Anisotropic Encoding for High-Fidelity 3D Reconstruction](https://mlsanity.com/paper/2410.01202/) (2024)
- [Spatially-Adaptive Hash Encodings For Neural Surface Reconstruction](https://mlsanity.com/paper/2412.05179/) (2024)
- [Fast Satellite Tensorial Radiance Field for Multi-date Satellite Imagery of Large Size](https://mlsanity.com/paper/2309.11767/) (2023)
- [Anisotropic Neural Representation Learning for High-Quality Neural Rendering](https://mlsanity.com/paper/2311.18311/) (2023)
- [Factorized Multi-Resolution HashGrid for Efficient Neural Radiance Fields: Execution on Edge-Devices](https://mlsanity.com/paper/2604.02836/) (2026)
- [TT-SEAL: TTD-Aware Selective Encryption for Adversarially-Robust and Low-Latency Edge AI](https://mlsanity.com/paper/2602.22238/) (2026)
- [Tensor Decomposition Structure Search Framework from an Interaction Perspective](https://mlsanity.com/paper/2603.02720/) (2026)

## Abstract (arXiv)

Rendering novel views from captured multi-view images has made considerable progress since the emergence of the neural radiance field. This paper aims to further advance the quality of view synthesis by proposing a novel approach dubbed the neural radiance feature field (NRFF). We first propose a multiscale tensor decomposition scheme to organize learnable features so as to represent scenes from coarse to fine scales. We demonstrate many benefits of the proposed multiscale representation, including more accurate scene shape and appearance reconstruction, and faster convergence compared with the single-scale representation. Instead of encoding view directions to model view-dependent effects, we further propose to encode the rendering equation in the feature space by employing the anisotropic spherical Gaussian mixture predicted from the proposed multiscale representation. The proposed NRFF improves state-of-the-art rendering results by over 1 dB in PSNR on both the NeRF and NSVF synthetic datasets. A significant improvement has also been observed on the real-world Tanks & Temples dataset. Code can be found at https://github.com/imkanghan/nrff.