# Perm: A Parametric Representation for Multi-Style 3D Hair Modeling

arXiv: https://arxiv.org/abs/2407.19451 · HTML: https://mlsanity.com/paper/2407.19451/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 89 references that are in the map.
- First posted on arXiv 28 Jul 2024.

## Builds on (most cited first, 30 of 34)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Expressive Body Capture: 3D Hands, Face, and Body from a Single Image](https://mlsanity.com/paper/1904.05866/) (2019)
- [AMASS: Archive of Motion Capture as Surface Shapes](https://mlsanity.com/paper/1904.03278/) (2019)
- [Efficient Geometry-aware 3D Generative Adversarial Networks](https://mlsanity.com/paper/2112.07945/) (2021)
- [Encoding in Style: a StyleGAN Encoder for Image-to-Image Translation](https://mlsanity.com/paper/2008.00951/) (2020)
- [Which Training Methods for GANs do actually Converge?](https://mlsanity.com/paper/1801.04406/) (2018)
- [Image2StyleGAN: How to Embed Images Into the StyleGAN Latent Space?](https://mlsanity.com/paper/1904.03189/) (2019)
- [Modular Primitives for High-Performance Differentiable Rendering](https://mlsanity.com/paper/2011.03277/) (2020)
- [3D Menagerie: Modeling the 3D shape and pose of animals](https://mlsanity.com/paper/1611.07700/) (2016)
- [State of the Art on Neural Rendering](https://mlsanity.com/paper/2004.03805/) (2020)
- [Modulated Periodic Activations for Generalizable Local Functional Representations](https://mlsanity.com/paper/2104.03960/) (2021)
- [GaussianHair: Hair Modeling and Rendering with Light-aware Gaussians](https://mlsanity.com/paper/2402.10483/) (2024)
- [Neural Haircut: Prior-Guided Strand-Based Hair Reconstruction](https://mlsanity.com/paper/2306.05872/) (2023)
- [Neural Strands: Learning Hair Geometry and Appearance from Multi-View Images](https://mlsanity.com/paper/2207.14067/) (2022)
- [HairStep: Transfer Synthetic to Real Using Strand and Depth Maps for Single-View 3D Hair Modeling](https://mlsanity.com/paper/2303.02700/) (2023)
- [NeuralHDHair: Automatic High-fidelity Hair Modeling from a Single Image Using Implicit Neural Representations](https://mlsanity.com/paper/2205.04175/) (2022)
- [NeuWigs: A Neural Dynamic Model for Volumetric Hair Capture and Animation](https://mlsanity.com/paper/2212.00613/) (2022)
- [HAAR: Text-Conditioned Generative Model of 3D Strand-based Human Hairstyles](https://mlsanity.com/paper/2312.11666/) (2023)
- [HVH: Learning a Hybrid Neural Volumetric Representation for Dynamic Hair Performance Capture](https://mlsanity.com/paper/2112.06904/) (2021)
- [GroomGen: A High-Quality Generative Hair Model Using Hierarchical Latent Representations](https://mlsanity.com/paper/2311.02062/) (2023)
- [DeepSketchHair: Deep Sketch-based 3D Hair Modeling](https://mlsanity.com/paper/1908.07198/) (2019)
- [MonoHair: High-Fidelity Hair Modeling from a Monocular Video](https://mlsanity.com/paper/2403.18356/) (2024)

## Built on by (most cited first, 22 of 22)

- [DiffLocks: Generating 3D Hair from a Single Image using Diffusion Models](https://mlsanity.com/paper/2505.06166/) (2025)
- [Quaffure: Real-Time Quasi-Static Neural Hair Simulation](https://mlsanity.com/paper/2412.10061/) (2024)
- [Im2Haircut: Single-view Strand-based Hair Reconstruction for Human Avatars](https://mlsanity.com/paper/2509.01469/) (2025)
- [3DGH: 3D Head Generation with Composable Hair and Face](https://mlsanity.com/paper/2506.20875/) (2025)
- [StrandHead: Text to Hair-Disentangled 3D Head Avatars Using Human-Centric Priors](https://mlsanity.com/paper/2412.11586/) (2024)
- [CHARM: Control-point-based 3D Anime Hairstyle Auto-Regressive Modeling](https://mlsanity.com/paper/2509.21114/) (2025)
- [Neuralocks: Real-Time Dynamic Neural Hair Simulation](https://mlsanity.com/paper/2507.05191/) (2025)
- [StrandDesigner: Towards Practical Strand Generation with Sketch Guidance](https://mlsanity.com/paper/2508.01650/) (2025)
- [DGH: Dynamic Gaussian Hair](https://mlsanity.com/paper/2512.17094/) (2025)
- [PhysHead: Simulation-Ready Gaussian Head Avatars](https://mlsanity.com/paper/2604.06467/) (2026)
- [OmniFit: Multi-modal 3D Body Fitting via Scale-agnostic Dense Landmark Prediction](https://mlsanity.com/paper/2604.21575/) (2026)
- [GeomHair: Reconstruction of Hair Strands from Colorless 3D Scans](https://mlsanity.com/paper/2505.05376/) (2025)
- [HairFormer: Transformer-Based Dynamic Neural Hair Simulation](https://mlsanity.com/paper/2507.12600/) (2025)
- [DiffProxy: Multi-View Human Mesh Recovery via Diffusion-Generated Dense Proxies](https://mlsanity.com/paper/2601.02267/) (2026)
- [CGHair: Compact Gaussian Hair Reconstruction with Card Clustering](https://mlsanity.com/paper/2604.03716/) (2026)
- [HairGPT: Strand-as-Language Autoregressive Modeling for Realistic 3D Hairstyle Synthesis](https://mlsanity.com/paper/2605.08824/) (2026)
- [HairLRM: Strand-based Hair Modeling via Large Reconstruction Models](https://mlsanity.com/paper/2606.15238/) (2026)
- [HairCS: Reconstructing Strand-Based Hair from Hair Cards](https://mlsanity.com/paper/2609.16465/) (2026)
- [FHAvatar: Fast and High-Fidelity Reconstruction of Face-and-Hair Composable 3D Head Avatar from Few Casual Captures](https://mlsanity.com/paper/2603.23345/) (2026)
- [Head Avatars with Dynamic Explicit Hair](https://mlsanity.com/paper/2607.23861/) (2026)
- [FurE: Efficient Instance-Specific 3D Fur Reconstruction without Animal-Fur Datasets](https://mlsanity.com/paper/2609.35770/) (2026)
- [HairFlow: Modeling 3D Hair Strands with Multi-Modal Conditioned Diffusion](https://mlsanity.com/paper/2610.17348/) (2026)

## Abstract (arXiv)

We present Perm, a learned parametric representation of human 3D hair designed to facilitate various hair-related applications. Unlike previous work that jointly models the global hair structure and local curl patterns, we propose to disentangle them using a PCA-based strand representation in the frequency domain, thereby allowing more precise editing and output control. Specifically, we leverage our strand representation to fit and decompose hair geometry textures into low- to high-frequency hair structures, termed guide textures and residual textures, respectively. These decomposed textures are later parameterized with different generative models, emulating common stages in the hair grooming process. We conduct extensive experiments to validate the architecture design of Perm, and finally deploy the trained model as a generic prior to solve task-agnostic problems, further showcasing its flexibility and superiority in tasks such as single-view hair reconstruction, hairstyle editing, and hair-conditioned image generation. More details can be found on our project page: https://cs.yale.edu/homes/che/projects/perm/.