PEPS: Positional Encoding Projected Sampling -- Extended
For researchers in implicit neural representations, this work offers a more efficient encoding method that reduces parameter count while maintaining or improving performance.
The paper proposes Positional Encoding Projected Sampling (PEPS), which treats positional encoding as a series of meaningful points and uses their motion for learned positional encoding. The method outperforms state-of-the-art in image representation, texture compression, and signed distance functions, requiring 25% fewer parameters for equivalent reconstruction error.
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.