  For modeling the 3D world behind 2D images, which 3D representation is most
appropriate? A polygon mesh is a promising candidate for its compactness and
geometric properties. However, it is not straightforward to model a polygon
mesh from 2D images using neural networks because the conversion from a mesh to
an image, or rendering, involves a discrete operation called rasterization,
which prevents back-propagation. Therefore, in this work, we propose an
approximate gradient for rasterization that enables the integration of
rendering into neural networks. Using this renderer, we perform single-image 3D
mesh reconstruction with silhouette image supervision and our system
outperforms the existing voxel-based approach. Additionally, we perform
gradient-based 3D mesh editing operations, such as 2D-to-3D style transfer and
3D DeepDream, with 2D supervision for the first time. These applications
demonstrate the potential of the integration of a mesh renderer into neural
networks and the effectiveness of our proposed renderer.
