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.

我们探索正弦神经网络来表示周期性平铺纹理。我们的方法利用傅里叶级数，通过将正弦神经网络的第一层初始化为具有周期 P 的整数频率。我们证明了正弦层的组合仅生成具有周期 P 的整数频率。因此，我们的网络学习了周期模式的连续表示，无需插值即可在任何空间坐标处直接评估。为了强制生成的模式具有可平铺性，我们向损失函数中添加了基于泊松方程的正则化项。我们提出的神经隐式表示方法紧凑且能够在多个细节级别上以高视觉保真度和锐度高效地重建高分辨率纹理。我们在抗锯齿表面领域展示了我们方法的应用。

可平铺材质纹理的隐式神经表示

Implicit Neural Representation of Tileable Material Textures

3D content creation from a single image is a long-standing yet highly
desirable task. Recent advances introduce 2D diffusion priors, yielding
reasonable results. However, existing methods are not hyper-realistic enough
for post-generation usage, as users cannot view, render and edit the resulting
3D content from a full range. To address these challenges, we introduce
HyperDreamer with several key designs and appealing properties: 1) Viewable:
360 degree mesh modeling with high-resolution textures enables the creation of
visually compelling 3D models from a full range of observation points. 2)
Renderable: Fine-grained semantic segmentation and data-driven priors are
incorporated as guidance to learn reasonable albedo, roughness, and specular
properties of the materials, enabling semantic-aware arbitrary material
estimation. 3) Editable: For a generated model or their own data, users can
interactively select any region via a few clicks and efficiently edit the
texture with text-based guidance. Extensive experiments demonstrate the
effectiveness of HyperDreamer in modeling region-aware materials with
high-resolution textures and enabling user-friendly editing. We believe that
HyperDreamer holds promise for advancing 3D content creation and finding
applications in various domains.

HyperDreamer 是一个可视化、可渲染和可编辑的 3D 内容创建工具，通过 360 度网格建模、高分辨率纹理和语义分割等技术，能够从单张图片中生成逼真的 3D 模型，并支持用户友好的编辑操作。