DeepCurrents: Learning Implicit Representations of Shapes with Boundaries
This work addresses a limitation in shape reconstruction for computer graphics and geometry processing, offering a novel approach for handling open surfaces.
The paper tackles the problem of reconstructing shapes with boundary curves, which existing implicit methods cannot handle, by proposing a hybrid representation that combines explicit boundary curves with implicit learned interiors, achieving the ability to represent arbitrary surfaces.
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.