  We present Perm, a learned parametric model of human 3D hair designed to
facilitate various hair-related applications. Unlike previous work that jointly
models the global hair shape and local strand details, 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. These decomposed textures
are later parameterized with different generative models, emulating common
stages in the hair modeling process. We conduct extensive experiments to
validate the architecture design of \textsc{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 3D hair
parameterization, hairstyle interpolation, single-view hair reconstruction, and
hair-conditioned image generation. Our code, data, and supplemental can be
found at our project page: https://cs.yale.edu/homes/che/projects/perm/
