Phase Transitions, Distance Functions, and Implicit Neural Representations
This work addresses a key bottleneck in geometric deep learning and 3D vision by providing a unified training approach for INRs, though it is incremental as it builds on existing INR paradigms.
The paper tackles the problem of training Implicit Neural Representations (INRs) for surface reconstruction by proposing a loss function inspired by phase transitions, which learns a density converging to occupancy and its log transform to distance, leading to state-of-the-art reconstructions on a standard benchmark.
Representing surfaces as zero level sets of neural networks recently emerged as a powerful modeling paradigm, named Implicit Neural Representations (INRs), serving numerous downstream applications in geometric deep learning and 3D vision. Training INRs previously required choosing between occupancy and distance function representation and different losses with unknown limit behavior and/or bias. In this paper we draw inspiration from the theory of phase transitions of fluids and suggest a loss for training INRs that learns a density function that converges to a proper occupancy function, while its log transform converges to a distance function. Furthermore, we analyze the limit minimizer of this loss showing it satisfies the reconstruction constraints and has minimal surface perimeter, a desirable inductive bias for surface reconstruction. Training INRs with this new loss leads to state-of-the-art reconstructions on a standard benchmark.