Differentiable Subdivision Surface Fitting

TL;DR

This paper introduces a differentiable surface fitting method using Loop subdivision surfaces and IMLS, enabling integration with deep learning for robust surface reconstruction from point clouds and meshes.

Contribution

It presents a novel differentiable fitting technique for Loop subdivision surfaces to point clouds, facilitating deep learning integration and improved surface topology handling.

Findings

Effective surface fitting via differentiable optimization

Integration with deep learning for surface reconstruction

Robust reconstruction of dense mesh sequences

Abstract

In this paper, we present a powerful differentiable surface fitting technique to derive a compact surface representation for a given dense point cloud or mesh, with application in the domains of graphics and CAD/CAM. We have chosen the Loop subdivision surface, which in the limit yields the smooth surface underlying the point cloud, and can handle complex surface topology better than other popular compact representations, such as NURBS. The principal idea is to fit the Loop subdivision surface not directly to the point cloud, but to the IMLS (implicit moving least squares) surface defined over the point cloud. As both Loop subdivision and IMLS have analytical expressions, we are able to formulate the problem as an unconstrained minimization problem of a completely differentiable function that can be solved with standard numerical solvers. Differentiability enables us to integrate the subdivision surface into any deep learning method for point clouds or meshes. We demonstrate the versatility and potential of this approach by using it in conjunction with a differentiable renderer to robustly reconstruct compact surface representations of spatial-temporal sequences of dense meshes.