  In visual computing, 3D geometry is represented in many different forms
including meshes, point clouds, voxel grids, level sets, and depth images. Each
representation is suited for different tasks thus making the transformation of
one representation into another (forward map) an important and common problem.
We propose Omnidirectional Distance Fields (ODFs), a new 3D shape
representation that encodes geometry by storing the depth to the object's
surface from any 3D position in any viewing direction. Since rays are the
fundamental unit of an ODF, it can be used to easily transform to and from
common 3D representations like meshes or point clouds. Different from level set
methods that are limited to representing closed surfaces, ODFs are unsigned and
can thus model open surfaces (e.g., garments). We demonstrate that ODFs can be
effectively learned with a neural network (NeuralODF) despite the inherent
discontinuities at occlusion boundaries. We also introduce efficient forward
mapping algorithms for transforming ODFs to and from common 3D representations.
Specifically, we introduce an efficient Jumping Cubes algorithm for generating
meshes from ODFs. Experiments demonstrate that NeuralODF can learn to capture
high-quality shape by overfitting to a single object, and also learn to
generalize on common shape categories.
