Geometric foundations for geometry processing of neural implicit representations of signed distance functions

Abstract

This work explores using neural networks to approximate Signed Distance Functions for representing 3D shapes. The work explains fundamental geometry concepts and their application to these functions, as well as the workings of neural networks as function approximators. By connecting these concepts, it explains how neural networks can represent 3D shapes and how to perform shape smoothing and sharpening on them. The objective of this work was to provide a solid foundation for further exploration of this topic, with a focus on providing a mathematical explanation of these techniques. Future research can explore other types of operations and efficient ways of creating and manipulating these representations.