MeshUDF: Fast and Differentiable Meshing of Unsigned Distance Field Networks

Recent work modelling 3D open surfaces train deep neural networks to approximate Unsigned Distance Fields (UDFs) and implicitly represent shapes. To convert this representation to an explicit mesh, they either use computationally expensive methods to mesh a dense point cloud sampling of the surface, or distort the surface by inflating it into a Signed Distance Field (SDF). By contrast, we propose to directly mesh deep UDFs as open surfaces with an extension of marching cubes, by locally detecting surface crossings. Our method is order of magnitude faster than meshing a dense point cloud, and more accurate than inflating open surfaces. Moreover, we make our surface extraction differentiable, and show it can help fit sparse supervision signals.

Learning to Orient Surfaces by Self-supervised Spherical CNNs

Defining and reliably finding a canonical orientation for 3D surfaces is key to many Computer Vision and Robotics applications. This task is commonly addressed by handcrafted algorithms exploiting geometric cues deemed as distinctive and robust by the designer. Yet, one might conjecture that humans learn the notion of the inherent orientation of 3D objects from experience and that machines may do so alike. In this work, we show the feasibility of learning a robust canonical orientation for surfaces represented as point clouds. Based on the observation that the quintessential property of a canonical orientation is equivariance to 3D rotations, we propose to employ Spherical CNNs, a recently introduced machinery that can learn equivariant representations defined on the Special Orthogonal group SO(3). Specifically, spherical correlations compute feature maps whose elements define 3D rotations. Our method learns such feature maps from raw data by a self-supervised training procedure and robustly selects a rotation to transform the input point cloud into a learned canonical orientation. Thereby, we realize the first end-to-end learning approach to define and extract the canonical orientation of 3D shapes, which we aptly dub Compass. Experiments on several public datasets prove its effectiveness at orienting local surface patches as well as whole objects.