  Nowadays, many visual scene understanding problems are addressed by dense
prediction networks. But pixel-wise dense annotations are very expensive (e.g.,
for scene parsing) or impossible (e.g., for intrinsic image decomposition),
motivating us to leverage cheap point-level weak supervision. However, existing
pointly-supervised methods still use the same architecture designed for full
supervision. In stark contrast to them, we propose a new paradigm that makes
predictions for point coordinate queries, as inspired by the recent success of
implicit representations, like distance or radiance fields. As such, the method
is named as dense prediction fields (DPFs). DPFs generate expressive
intermediate features for continuous sub-pixel locations, thus allowing outputs
of an arbitrary resolution. DPFs are naturally compatible with point-level
supervision. We showcase the effectiveness of DPFs using two substantially
different tasks: high-level semantic parsing and low-level intrinsic image
decomposition. In these two cases, supervision comes in the form of
single-point semantic category and two-point relative reflectance,
respectively. As benchmarked by three large-scale public datasets
PASCALContext, ADE20K and IIW, DPFs set new state-of-the-art performance on all
of them with significant margins.
  Code can be accessed at https://github.com/cxx226/DPF.
