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About this paper
Romy Williamson, Niloy J. Mitra
A new method, Spherical Neural Surfaces (SNS), allows for the direct computation of classical geometry processing operators, such as curvature and the Laplace-Beltrami Operator, on continuous neural representations of genus-0 surfaces, bypassing the need for discrete meshing. This framework demonstrates improved accuracy and robustness for tasks like heat flow and mean curvature flow compared to traditional discrete approaches.
Key insights
- Representing genus-0 surfaces as an MLP restricted to a spherical domain provides a seamless, continuous, and differentiable surface parametrization.
- Automatic differentiation enables the precise, analytical computation of classical differential geometry quantities and operators directly from a neural surface.
- Continuous spectral analysis (finding LBO eigenfunctions) is achievable on neural surfaces by framing it as a Monte Carlo sampled optimization problem of the Rayleigh Quotient.
Summary by alphaXiv.
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