  Recently introduced implicit field representations offer an effective way of
generating 3D object shapes. They leverage implicit decoder trained to take a
3D point coordinate concatenated with a shape encoding and to output a value
which indicates whether the point is outside the shape or not. Although this
approach enables efficient rendering of visually plausible objects, it has two
significant limitations. First, it is based on a single neural network
dedicated for all objects from a training set which results in a cumbersome
training procedure and its application in real life. More importantly, the
implicit decoder takes only points sampled within voxels (and not the entire
voxels) which yields problems at the classification boundaries and results in
empty spaces within the rendered mesh.
  To solve the above limitations, we introduce a new HyperCube architecture
based on interval arithmetic network, that enables direct processing of 3D
voxels, trained using a hypernetwork paradigm to enforce model convergence.
Instead of processing individual 3D samples from within a voxel, our approach
allows to input the entire voxel (3D cube) represented with its convex hull
coordinates, while the target network constructed by a hypernet assigns it to
an inside or outside category. As a result our HyperCube model outperforms the
competing approaches both in terms of training and inference efficiency, as
well as the final mesh quality.
