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Doubly Hierarchical Geometric Representations for Strand-based Human Hairstyle Generation
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Proposes a doubly hierarchical strand-hair representation (DCT low-pass guide curves sampled by k-medoids, then densification and high-frequency DCT refinement) and a VAE-based generator for strand hairstyles.
Problem
Generating realistic strand-based 3D hairstyles, where existing methods sample guide strands on a scalp UV grid and rely on pretrained strand codecs, losing hairstyle detail and suffering from Gibbs oscillations under Fourier decomposition.
Approach
Separate low-frequency guide structure from high-frequency curl/noise using DCT on strand derivatives, select guide strands as k-medoids centres of dense low-pass strands (proven to minimise bidirectional chamfer distance), and train a PVCNN-style dual-branch VAE plus graph-based implicit densification end-to-end.
Key results
- Guide curve reconstruction CD of 0.906e-4 to input sampled strands versus 1.521e-4 for grid-based sampling, and 8.079e-4 vs 9.090e-4 to GT dense hair.
- Densification CD to GT dense hair of 0.209e-4 vs 0.311e-4 for nearest-neighbour upsampling.
- User study (54 valid responses): average realism 6.933 vs 6.106 for HAAR; curly hair 6.656 vs 4.933.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use k-medoids guide sampling instead of grid sampling, FPS, or k-means + projection | Guide curve extraction · Guide curve extraction | bidirectional chamfer distance (CD ×10−4): 0.683; 0.139; 0.116 -> 0.101 | Helped |
| Use the proposed representation and off-the-grid architecture instead of grid-based representations | Guide curve VAE · Guide curve reconstruction | CD to input sampled strands (×10−4): 1.521; 1.597 -> 0.906 | Helped |
| Use learned densification instead of nearest-neighbour upsampling | Densification · VAE-reconstructed guide curves | CD to GT dense hair (×10−4): 0.311 -> 0.209 | Helped |
| Generate hairstyles with the proposed method instead of HAAR | Hairstyle generation · All hairstyles | subjective rating (1 to 10): 6.106 ± 0.254 -> 6.933 ± 0.237 | Helped |
| Use randomly sampled strands instead of k-medoids guide strands (ablation) | Guide curve VAE and densification · Low-frequency guide curves and densification | guide-to-GT guide CD (×10−4): 0.906 -> 0.997 | Hurt |
| Represent low-pass curves in frequency space instead of spatial space (ablation) | Guide curve VAE and densification · Low-frequency guide curves and densification | guide-to-GT guide CD (×10−4): 0.906 -> 1.152 | Hurt |
| Use a pretrained off-the-shelf strand codec (ablation) | Guide curve VAE and densification · Low-frequency guide curves and densification | guide-to-GT guide CD (×10−4): 0.906 -> 0.966 | Hurt |
| Remove graph aggregation from densification (ablation) | Densification · Low-frequency guide curves and densification | dense-to-GT dense CD (×10−4): 0.209 -> 0.214 | Hurt |
| Use an off-the-shelf strand codec for high-frequency reconstruction (ablation) | High-frequency VAE · High-frequency reconstruction | MAE: 0.137 -> 0.145 | Hurt |
| Set the low-pass frequency threshold to 4 instead of 8 (ablation) | Hierarchical hair representation · VAE reconstruction | CD (×10−4): 1.010 -> 1.494 | Hurt |
| Set the low-pass frequency threshold to 6 instead of 8 (ablation) | Hierarchical hair representation · VAE reconstruction | CD (×10−4): 1.010 -> 1.122 | Hurt |
| Set the low-pass frequency threshold to 10 instead of 8 (ablation) | Hierarchical hair representation · VAE reconstruction | CD (×10−4): 1.010 -> 1.014 | No clear effect |
Surprising findings
- Generating guide strands is about 0.7 s per batch of 32 versus 0.09 s for a pure 2D convolutional baseline, and full generation takes about 12 s, showing a runtime cost of the geometric deep learning design.
Limitations
- Limited training data scarcity of high-quality strand hairstyles restricts diversity of guide-curve geometry.
- No suitable quantitative metrics for strand hair generation quality; evaluation relies on chamfer distance and a small user study.
- Slower inference than purely convolutional architectures; occasional flying strands and head penetration failures.
Experimental setup
Datasets: 343 synthetic hairstyles from mesh hair cards 26 Blender particle hair projects augmented to 315
Benchmarks: 30 held-out test hairstyles (in-house)
Metrics: bidirectional chamfer distance mean absolute error on high-frequency DCT coefficients user-rated realism score (1-10)
Baselines: GroomGen HAAR Grid-based + strand codec Grid-based sampling Farthest point sampling k-means + projection Nearest-neighbour upsampling
Builds on: PVCNN PointNet SetVAE Strand codec VAE (Wang et al. 2022) Spectral bias / frequency principle
Closest papers by meaning
- Perm: A Parametric Representation for Multi-Style 3D Hair Modeling (ICLR 2025 · similarity 0.91)
- Text-Conditioned Generative Model of 3D Strand-based Human Hairstyles (CVPR 2024 · similarity 0.91)
- DiffLocks: Generating 3D Hair from a Single Image using Diffusion Models (CVPR 2025 · similarity 0.91)
- Dr.Hair: Reconstructing Scalp-Connected Hair Strands without Pre-Training via Differentiable Rendering of Line Segments (CVPR 2024 · similarity 0.89)
- DGH: Dynamic Gaussian Hair (NeurIPS 2025 · similarity 0.88)
- MonoHair: High-Fidelity Hair Modeling from a Monocular Video (CVPR 2024 · similarity 0.87)
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