Polynomial for real-time rendering of neural radiance fields

In neural radiance fields (NeRF), generating highly realistic rendering results requires extensive sampling of rays and online query of multilayer perceptrons. However, this results in slow rendering speeds. Previous research has addressed this issue by designing faster evaluation of neural scene representations or precomputing scene properties to reduce rendering time. In this paper, we propose a real-time rendering method called PNeRF. PNeRF utilizes continuous polynomial functions to approximate spatial volume density and color information. Additionally, we separate the view direction information from the rendering equation, leading to a new expression for the volume rendering equation. By taking the starting coordinates of the observation viewpoint and the observation direction vector as inputs to the neural network, we obtain the rendering result for the corresponding observation ray. Thus, the rendering for each ray only requires a single forward inference of the neural network. To further improve rendering speed, we design a six-axis spherical method to store the rendering results corresponding to the starting coordinates of the observation viewpoint and the observation direction vector. This allows us to significantly improve the rendering speed and maintain the rendering quality, with minimal storage space requirements. Experimental validation on LLFF datasets demonstrates that our method improves rendering speed while preserving rendering quality and requiring minimal storage space. These results indicate the potential of our method in the real-time rendering field, providing an effective solution for more efficient rendering.