In this paper we investigate the problem of inducing a distribution over three-dimensional structures given twodimensional views of multiple objects taken from unknown viewpoints. Our approach called "projective generative adversarial networks" (PrGANs) trains a deep generative model of 3D shapes whose projections match the distributions of the input 2D views. The addition of a projection module allows us to infer the underlying 3D shape distribution without using any 3D, viewpoint information, or annotation during the learning phase. We show that our approach produces 3D shapes of comparable quality to GANs trained on 3D data for a number of shape categories including chairs, airplanes, and cars. Experiments also show that the disentangled representation of 2D shapes into geometry and viewpoint leads to a good generative model of 2D shapes. The key advantage is that our model allows us to predict 3D, viewpoint, and generate novel views from an input image in a completely unsupervised manner.

The reversible addition-fragmentation chain transfer radical polymerization (RAFT) with branching/ cross-linking is theoretically investigated on the basis of the method of moments. The system considered consists of the copolymerization of vinyl monomer in the presence of a small amount of divinyl comonomer. It is found that the gel point is significantly postponed by increasing the RAFT agent concentration. Flory's criterion, Fr w,0 ) 1, is found to be satisfied at the gel point in the RAFT cross-linking process regardless of the unequal reactivities of vinyl/divinyl monomers in the absence of cyclization. The gel conversion can be analytically expressed and is determined by the polymerization recipe and the relative reactivities of various double bonds. The gel point is postponed by the presence of intramolecular cyclization, and its effect becomes significant in a dilute polymerization system. Branching distribution is found to be very broad with a large fraction of linear primary and slightly branched chains. By the introduction of the dependence of the reactivity of the pendant double bond on the local heterogeneity, the branching distribution becomes narrower and can be fine-tuned.

We investigate the role of representations and architectures for classifying 3D shapes in terms of their computational efficiency, generalization, and robustness to adversarial transformations. By varying the number of training examples and employing cross-modal transfer learning we study the role of initialization of existing deep architectures for 3D shape classification. Our analysis shows that multiview methods continue to offer the best generalization even without pretraining on large labeled image datasets, and even when trained on simplified inputs such as binary silhouettes. Furthermore, the performance of voxel-based 3D convolutional networks and point-based architectures can be improved via cross-modal transfer from image representations. Finally, we analyze the robustness of 3D shape classifiers to adversarial transformations and present a novel approach for generating adversarial perturbations of a 3D shape for multiview classifiers using a differentiable renderer. We find that point-based networks are more robust to point position perturbations while voxel-based and multiview networks are easily fooled with the addition of imperceptible noise to the input.