MeshSDF: Differentiable IsoSurface Extraction
Abstract
Geometric Deep Learning has recently made striking progress with the advent of continuous Deep Implicit Fields. They allow for detailed modeling of watertight surfaces of arbitrary topology while not relying on a 3D Euclidean grid, resulting in a learnable parameterization that is not limited in resolution. Unfortunately, these methods are often not suitable for applications that require an explicit meshbased surface representation because converting an implicit field to such a representation relies on the Marching Cubes algorithm, which cannot be differentiated with respect to the underlying implicit field. In this work, we remove this limitation and introduce a differentiable way to produce explicit surface mesh representations from Deep Signed Distance Functions. Our key insight is that by reasoning on how implicit field perturbations impact local surface geometry, one can ultimately differentiate the 3D location of surface samples with respect to the underlying deep implicit field. We exploit this to define MeshSDF, an endtoend differentiable mesh representation which can vary its topology. We use two different applications to validate our theoretical insight: SingleView Reconstruction via Differentiable Rendering and PhysicallyDriven Shape Optimization. In both cases our differentiable parameterization gives us an edge over stateoftheart algorithms.
 Publication:

arXiv eprints
 Pub Date:
 June 2020
 arXiv:
 arXiv:2006.03997
 Bibcode:
 2020arXiv200603997R
 Keywords:

 Computer Science  Computer Vision and Pattern Recognition;
 30L05;
 I.2.10;
 I.4.8;
 J.6
 EPrint:
 11 pages, 5 figures, submitted to NeurIPS 2020