High-fidelity Multi-view Hair Reconstruction via Spherical Orientation Distribution Functions

High-fidelity multi-view 3D hair reconstruction from casual handheld captures remains a formidable challenge due to severe self-occlusions and the intricate topology of individual strands. A critical bottleneck in existing 3D hair representations—both volumetric grids and continuous implicit fields—is the reliance on deterministic spatial queries that assign a single local orientation. This unimodal assumption inevitably collapses and averages crossing or layered strands into erroneous directions, leading to a loss of internal structural details. To overcome this, we introduce SODF-Hair, a novel framework that represents local hair structures using Spherical Orientation Distribution Functions (SODFs). By encoding a multi-modal distribution within each voxel, our SODF representation effectively resolves the structural ambiguities of tangled and overlapping fibers, preserving complex local variations even under limited grid resolutions. Our pipeline explicitly decomposes the reconstruction into exterior observation and interior completion. To bridge 2D image evidence into 3D, we first reconstruct a visible hair-segment shell using fixed-scale oriented 3D Gaussian proxies. Their elongated covariances yield projections that match the streak-like texture of visible hair in the input images, enabling the recovery of fine visible segment geometry while preventing the proxies from degenerating into free-form blobs. We then formulate the recovery of invisible internal structures as an inpainting task. A geometry-conditioned probabilistic model, leveraging a compact latent SODF codec and rectified flow matching, predicts the missing multi-modal distributions within the closed volume. Finally, rather than prematurely committing to a single streamline, we assemble explicit scalp-connected strands via a field-guided beam search and constrained graph optimization. Extensive evaluations suggest that our approach faithfully preserves subject-specific visible details while generating structurally coherent internal strand geometry, demonstrating robust performance across diverse hairstyles.