Implicit neural representations (INRs) are increasingly being used as tools to map coordinates to signals, encompassing applications from neural fields to texture compression, shape representations, and beyond. Most INR methods are based on using high-dimensional projections of the initial coordinates through encoders such as grid or positional encoding. Nevertheless, positional encoding is often insufficient and grids, as we show in this paper, require high resolution for being able to learn. In this paper, we demonstrate that positional encoding can be used not only as a high-dimensional embedding but also decomposed as a series of meaningful points. We propose the Positional Encoding Projected Sampling, where we treat the projection of the original coordinate at each frequency as a point of interest. We describe the motion of each point with respect to the frequencies and show that it follows a unique pattern. Finally, we use the unique motion of each point as a basis decomposition for doing learned positional encoding using grids. We prove, using three competitive applications; image representation, texture compression, and signed distance function; that the proposed approach outperforms the current state of the art methods, and often requires 25\% less parameters for equivalent reconstruction error or rendering.

翻译：摘要：隐式神经表示（INR）正越来越多地被用作将坐标映射到信号的工具，其应用涵盖从神经场到纹理压缩、形状表示等领域。大多数INR方法基于通过编码器（如网格或位置编码）对初始坐标进行高维投影。然而，位置编码往往不足，而如本文所示，网格需要高分辨率才能有效学习。在本文中，我们论证了位置编码不仅可用作高维嵌入，还可分解为一系列有意义的点。我们提出位置编码投影采样（PEPS），将原始坐标在每个频率下的投影视为兴趣点。我们描述每个点相对于频率的运动规律，并展示其遵循独特模式。最后，我们利用每个点的独特运动作为基分解，通过网格实现基于学习的位置编码。通过三个竞争性应用（图像表示、纹理压缩和有符号距离函数）的验证，我们证明所提方法优于当前最先进方法，且在等效重建误差或渲染效果下，通常可减少25%的参数需求。