  We propose to recover 3D shape structures from single RGB images, where
structure refers to shape parts represented by cuboids and part relations
encompassing connectivity and symmetry. Given a single 2D image with an object
depicted, our goal is automatically recover a cuboid structure of the object
parts as well as their mutual relations. We develop a convolutional-recursive
auto-encoder comprised of structure parsing of a 2D image followed by structure
recovering of a cuboid hierarchy. The encoder is achieved by a multi-scale
convolutional network trained with the task of shape contour estimation,
thereby learning to discern object structures in various forms and scales. The
decoder fuses the features of the structure parsing network and the original
image, and recursively decodes a hierarchy of cuboids. Since the decoder
network is learned to recover part relations including connectivity and
symmetry explicitly, the plausibility and generality of part structure recovery
can be ensured. The two networks are jointly trained using the training data of
contour-mask and cuboid structure pairs. Such pairs are generated by rendering
stock 3D CAD models coming with part segmentation. Our method achieves
unprecedentedly faithful and detailed recovery of diverse 3D part structures
from single-view 2D images. We demonstrate two applications of our method
including structure-guided completion of 3D volumes reconstructed from
single-view images and structure-aware interactive editing of 2D images.
