Marching Neurons: Accurate Surface Extraction for Neural Implicit Shapes
This provides a more accurate method for converting neural implicit representations to explicit meshes in 3D visual computing, though it appears incremental as it builds on existing implicit representation frameworks.
The paper tackles the problem of inaccurate surface extraction from neural implicit shapes caused by fixed-resolution sampling in conventional methods like Marching Cubes, introducing an analytical approach that leverages neuron partitioning to achieve unprecedented accuracy while maintaining competitive speed.
Accurate surface geometry representation is crucial in 3D visual computing. Explicit representations, such as polygonal meshes, and implicit representations, like signed distance functions, each have distinct advantages, making efficient conversions between them increasingly important. Conventional surface extraction methods for implicit representations, such as the widely used Marching Cubes algorithm, rely on spatial decomposition and sampling, leading to inaccuracies due to fixed and limited resolution. We introduce a novel approach for analytically extracting surfaces from neural implicit functions. Our method operates natively in parallel and can navigate large neural architectures. By leveraging the fact that each neuron partitions the domain, we develop a depth-first traversal strategy to efficiently track the encoded surface. The resulting meshes faithfully capture the full geometric information from the network without ad-hoc spatial discretization, achieving unprecedented accuracy across diverse shapes and network architectures while maintaining competitive speed.