Implicit Neural Representation of Tileable Material Textures
This work addresses the problem of generating anti-aliased surface textures for computer graphics applications, but it is incremental as it builds on existing sinusoidal neural network methods with specific adaptations for tileability.
The authors tackled the problem of representing periodic tileable textures by using sinusoidal neural networks initialized with integer frequencies, which ensures the network learns a continuous representation that can be evaluated at any spatial coordinate without interpolation. They achieved compact neural implicit representations that enable efficient reconstruction of high-resolution textures with high visual fidelity and sharpness across multiple levels of detail.
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.