Learning and Meshing from Deep Implicit Surface Networks Using an Efficient Implementation of Analytic Marching.

Area of Science:

• Computer Vision
• Computer Graphics
• Robotics
• Computational Geometry

Background:

• Surface reconstruction is crucial for 3D applications.
• Implicit field functions define surfaces via their zero-level sets.
• Multi-layer Perceptrons (MLPs) with ReLU activations partition input space into linear regions.

Purpose of the Study:

• To develop a method for recovering surface meshes from MLP-based implicit functions.
• To leverage the local linearity of MLPs for accurate mesh generation.
• To establish theoretical guarantees for mesh connectivity and planarity.

Main Methods:

• Identifying analytic cells and faces within MLP-defined linear regions.
• Proving that these analytic faces form a closed, piecewise planar surface.
• Developing the analytic marching algorithm to traverse analytic cells and extract the mesh.

Main Results:

• The analytic marching algorithm precisely recovers the surface mesh.
• The method is applicable to advanced MLPs, including those with shortcut connections and max pooling.
• Demonstrated advantages in meshing accuracy and efficiency over existing techniques.

Conclusions:

• The proposed analytic marching algorithm provides an exact and efficient method for surface mesh reconstruction from implicit neural representations.
• The theoretical framework guarantees the formation of closed, piecewise planar meshes.
• This work advances the state-of-the-art in 3D surface reconstruction from neural fields.