  Recently, neural fields, also known as coordinate-based MLPs, have achieved
impressive results in representing low-dimensional data. Unlike CNN, MLPs are
globally connected and lack local control; adjusting a local region leads to
global changes. Therefore, improving local neural fields usually leads to a
dilemma: filtering out local artifacts can simultaneously smooth away desired
details. Our solution is a new filtering technique that consists of two
counteractive operators: a smoothing operator that provides global smoothing
for better generalization, and conversely a recovering operator that provides
better controllability for local adjustments. We have found that using either
operator alone can lead to an increase in noisy artifacts or oversmoothed
regions. By combining the two operators, smoothing and sharpening can be
adjusted to first smooth the entire region and then recover fine-grained
details in regions overly smoothed. In this way, our filter helps neural fields
remove much noise while enhancing details. We demonstrate the benefits of our
filter on various tasks and show significant improvements over state-of-the-art
methods. Moreover, our filter also provides better performance in terms of
convergence speed and network stability.
