# PREF: Phasorial Embedding Fields for Compact Neural Representations

arXiv: https://arxiv.org/abs/2205.13524 · HTML: https://mlsanity.com/paper/2205.13524/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 72 references that are in the map.
- First posted on arXiv 26 May 2022.

## Builds on (most cited first, 30 of 47)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (2020)
- [Efficient Geometry-aware 3D Generative Adversarial Networks](https://mlsanity.com/paper/2112.07945/) (2021)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [Alias-Free Generative Adversarial Networks](https://mlsanity.com/paper/2106.12423/) (2021)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [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)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [NeRF++: Analyzing and Improving Neural Radiance Fields](https://mlsanity.com/paper/2010.07492/) (2020)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [MVSNeRF: Fast Generalizable Radiance Field Reconstruction from Multi-View Stereo](https://mlsanity.com/paper/2103.15595/) (2021)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Differentiable Volumetric Rendering: Learning Implicit 3D Representations without 3D Supervision](https://mlsanity.com/paper/1912.07372/) (2019)
- [KiloNeRF: Speeding up Neural Radiance Fields with Thousands of Tiny MLPs](https://mlsanity.com/paper/2103.13744/) (2021)
- [Local Light Field Fusion: Practical View Synthesis with Prescriptive Sampling Guidelines](https://mlsanity.com/paper/1905.00889/) (2019)
- [UNISURF: Unifying Neural Implicit Surfaces and Radiance Fields for Multi-View Reconstruction](https://mlsanity.com/paper/2104.10078/) (2021)
- [BARF: Bundle-Adjusting Neural Radiance Fields](https://mlsanity.com/paper/2104.06405/) (2021)

## Built on by (most cited first, 10 of 10)

- [CompGS: Smaller and Faster Gaussian Splatting with Vector Quantization](https://mlsanity.com/paper/2311.18159/) (2023)
- [Factor Fields: A Unified Framework for Neural Fields and Beyond](https://mlsanity.com/paper/2302.01226/) (2023)
- [Masked Wavelet Representation for Compact Neural Radiance Fields](https://mlsanity.com/paper/2212.09069/) (2022)
- [TeTriRF: Temporal Tri-Plane Radiance Fields for Efficient Free-Viewpoint Video](https://mlsanity.com/paper/2312.06713/) (2023)
- [Implicit Gaussian Splatting with Efficient Multi-Level Tri-Plane Representation](https://mlsanity.com/paper/2408.10041/) (2024)
- [OPE-SR: Orthogonal Position Encoding for Designing a Parameter-free Upsampling Module in Arbitrary-scale Image Super-Resolution](https://mlsanity.com/paper/2303.01091/) (2023)
- [DaReNeRF: Direction-aware Representation for Dynamic Scenes](https://mlsanity.com/paper/2403.02265/) (2024)
- [PREF: Predictability Regularized Neural Motion Fields](https://mlsanity.com/paper/2209.10691/) (2022)
- [General Neural Gauge Fields](https://mlsanity.com/paper/2305.03462/) (2023)
- [DaRePlane: Direction-aware Representations for Dynamic Scene Reconstruction](https://mlsanity.com/paper/2410.14169/) (2024)

## Abstract (arXiv)

We present an efficient frequency-based neural representation termed PREF: a shallow MLP augmented with a phasor volume that covers significant border spectra than previous Fourier feature mapping or Positional Encoding. At the core is our compact 3D phasor volume where frequencies distribute uniformly along a 2D plane and dilate along a 1D axis. To this end, we develop a tailored and efficient Fourier transform that combines both Fast Fourier transform and local interpolation to accelerate na"ive Fourier mapping. We also introduce a Parsvel regularizer that stables frequency-based learning. In these ways, Our PREF reduces the costly MLP in the frequency-based representation, thereby significantly closing the efficiency gap between it and other hybrid representations, and improving its interpretability. Comprehensive experiments demonstrate that our PREF is able to capture high-frequency details while remaining compact and robust, including 2D image generalization, 3D signed distance function regression and 5D neural radiance field reconstruction.