Implicit Neural Representation of Tileable Material Textures
Hallison Paz Tiago Novello Luiz Velho
We explore sinusoidal neural networks to represent periodic tileable
textures. Our approach leverages the Fourier series by initializing the first
layer of a sinusoidal neural network with integer frequencies with a period
$P$. We prove that the compositions of sinusoidal layers generate only integer
frequencies with period $P$. As a result, our network learns a continuous
representation of a periodic pattern, enabling direct evaluation at any spatial
coordinate without the need for interpolation. To enforce the resulting pattern
to be tileable, we add a regularization term, based on the Poisson equation, to
the loss function. Our proposed neural implicit representation is compact and
enables efficient reconstruction of high-resolution textures with high visual
fidelity and sharpness across multiple levels of detail. We present
applications of our approach in the domain of anti-aliased surface.