Title: HyperCube: Implicit Field Representations of Voxelized 3D Models. Abstract: 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. 