  A multi-layer perceptron (MLP) is a type of neural networks which has a long
history of research and has been studied actively recently in computer vision
and graphics fields. One of the well-known problems of an MLP is the capability
of expressing high-frequency signals from low-dimensional inputs. There are
several studies for input encodings to improve the reconstruction quality of an
MLP by applying pre-processing against the input data. This paper proposes a
novel input encoding method, local positional encoding, which is an extension
of positional and grid encodings. Our proposed method combines these two
encoding techniques so that a small MLP learns high-frequency signals by using
positional encoding with fewer frequencies under the lower resolution of the
grid to consider the local position and scale in each grid cell. We demonstrate
the effectiveness of our proposed method by applying it to common 2D and 3D
regression tasks where it shows higher-quality results compared to positional
and grid encodings, and comparable results to hierarchical variants of grid
encoding such as multi-resolution grid encoding with equivalent memory
footprint.
