  Existing 3D surface representation approaches are unable to accurately
classify pixels and their orientation lying on the boundary of an object. Thus
resulting in coarse representations which usually require post-processing steps
to extract 3D surface meshes. To overcome this limitation, we propose an
end-to-end trainable model that directly predicts implicit surface
representations of arbitrary topology by optimising a novel geometric loss
function. Specifically, we propose to represent the output as an oriented level
set of a continuous embedding function, and incorporate this in a deep
end-to-end learning framework by introducing a variational shape inference
formulation. We investigate the benefits of our approach on the task of 3D
surface prediction and demonstrate its ability to produce a more accurate
reconstruction compared to voxel-based representations. We further show that
our model is flexible and can be applied to a variety of shape inference
problems.
