Deep Geometric Prior for Surface Reconstruction
This addresses the fundamental geometry processing problem of surface reconstruction for applications in computer graphics and vision, offering a novel approach that is incremental in its use of deep learning for prior-based reconstruction.
The authors tackled the problem of reconstructing surfaces from point clouds by using a deep neural network as a geometric prior, overfitting local chart parameterizations to parts of the point cloud with Wasserstein distance and enforcing consistency to produce a manifold atlas. They showed that this method performs well without training data or explicit regularization, approximating sharp features and handling noisy inputs, and compared favorably with existing methods on a standard benchmark.
The reconstruction of a discrete surface from a point cloud is a fundamental geometry processing problem that has been studied for decades, with many methods developed. We propose the use of a deep neural network as a geometric prior for surface reconstruction. Specifically, we overfit a neural network representing a local chart parameterization to part of an input point cloud using the Wasserstein distance as a measure of approximation. By jointly fitting many such networks to overlapping parts of the point cloud, while enforcing a consistency condition, we compute a manifold atlas. By sampling this atlas, we can produce a dense reconstruction of the surface approximating the input cloud. The entire procedure does not require any training data or explicit regularization, yet, we show that it is able to perform remarkably well: not introducing typical overfitting artifacts, and approximating sharp features closely at the same time. We experimentally show that this geometric prior produces good results for both man-made objects containing sharp features and smoother organic objects, as well as noisy inputs. We compare our method with a number of well-known reconstruction methods on a standard surface reconstruction benchmark.