A Level Set Theory for Neural Implicit Evolution Under Explicit Flows

AbstractCoordinate-based neural networks parameterizing implicit surfaces have emerged as efficient representations of geometry. They effectively act parametric level sets with the zero-level set defining surface interest. We present a framework that allows applying deformation operations defined for triangle meshes onto such surfaces. Several these can be viewed energy-minimization problems induce an instantaneous flow field on explicit surface. Our method uses to deform by extending classical theory sets. also derive consolidated view existing methods differentiable extraction and rendering, formalizing connections level-set theory. show drift from our approach exhibits improvements applications like smoothing, mean-curvature flow, inverse rendering user-defined editing KeywordsImplicit surfacesLevel setsEuler-lagrangian