DeepCurrents: Learning Implicit Representations of Shapes with Boundaries

TL;DR

DeepCurrents introduces a hybrid shape representation combining explicit boundary curves with implicit interior learning, enabling reconstruction of arbitrary surfaces with boundaries using deep neural networks and geometric measure theory.

Contribution

It proposes a novel hybrid shape representation that integrates explicit boundary curves with implicit interior functions, extending surface reconstruction capabilities.

Findings

Successfully reconstructs shapes with boundary curves.

Learns shape families jointly with boundary curves and latent codes.

Uses geometric measure theory for parameterization and minimal surface optimization.

Abstract

Recent techniques have been successful in reconstructing surfaces as level sets of learned functions (such as signed distance fields) parameterized by deep neural networks. Many of these methods, however, learn only closed surfaces and are unable to reconstruct shapes with boundary curves. We propose a hybrid shape representation that combines explicit boundary curves with implicit learned interiors. Using machinery from geometric measure theory, we parameterize currents using deep networks and use stochastic gradient descent to solve a minimal surface problem. By modifying the metric according to target geometry coming, e.g., from a mesh or point cloud, we can use this approach to represent arbitrary surfaces, learning implicitly defined shapes with explicitly defined boundary curves. We further demonstrate learning families of shapes jointly parameterized by boundary curves and latent codes.