  Neural fields have gained significant attention in the computer vision
community due to their excellent performance in novel view synthesis, geometry
reconstruction, and generative modeling. Some of their advantages are a sound
theoretic foundation and an easy implementation in current deep learning
frameworks. While neural fields have been applied to signals on manifolds,
e.g., for texture reconstruction, their representation has been limited to
extrinsically embedding the shape into Euclidean space. The extrinsic embedding
ignores known intrinsic manifold properties and is inflexible wrt. transfer of
the learned function. To overcome these limitations, this work introduces
intrinsic neural fields, a novel and versatile representation for neural fields
on manifolds. Intrinsic neural fields combine the advantages of neural fields
with the spectral properties of the Laplace-Beltrami operator. We show
theoretically that intrinsic neural fields inherit many desirable properties of
the extrinsic neural field framework but exhibit additional intrinsic
qualities, like isometry invariance. In experiments, we show intrinsic neural
fields can reconstruct high-fidelity textures from images with state-of-the-art
quality and are robust to the discretization of the underlying manifold. We
demonstrate the versatility of intrinsic neural fields by tackling various
applications: texture transfer between deformed shapes & different shapes,
texture reconstruction from real-world images with view dependence, and
discretization-agnostic learning on meshes and point clouds.

Computer Vision and Pattern Recognition;Machine Learning