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.
A key goal of computer vision is to recover the underlying 3D structure from 2D observations of the world. In this paper we learn strong deep generative models of 3D structures, and recover these structures from 3D and 2D images via probabilistic inference. We demonstrate high-quality samples and report log-likelihoods on several datasets, including ShapeNet [2], and establish the first benchmarks in the literature. We also show how these models and their inference networks can be trained end-to-end from 2D images. This demonstrates for the first time the feasibility of learning to infer 3D representations of the world in a purely unsupervised manner. This article presents a general class of associative reinforcement learning algorithms for connectionist networks containing stochastic units. These algorithms, called REINFORCE algorithms, are shown to make weight adjustments in a direction that lies along the gradient of expected reinforcement in both immediate-reinforcement tasks and certain limited forms of delayed-reinforcement tasks, and they do this without explicitly computing gradient estimates or even storing information from which such estimates could be computed. Specific examples of such algorithms are presented, some of which bear a close relationship to certain existing algorithms while others are novel but potentially interesting in their own right. Also given are results that show how such algorithms can be naturally integrated with backpropagation. We close with a brief discussion of a number of additional issues surrounding the use of such algorithms, including what is known about their limiting behaviors as well as further considerations that might be used to help develop similar but potentially more powerful reinforcement learning algorithms. Inverse graphics attempts to take sensor data and infer 3D geometry, illumination, materials, and motions such that a graphics renderer could realistically reproduce the observed scene. Renderers, however, are designed to solve the forward process of image synthesis. To go in the other direction, we propose an approximate differentiable renderer (DR) that explicitly models the relationship between changes in model parameters and image observations. We describe a publicly available OpenDR framework that makes it easy to express a forward graphics model and then automatically obtain derivatives with respect to the model parameters and to optimize over them. Built on a new auto-differentiation package and OpenGL, OpenDR provides a local optimization method that can be incorporated into probabilistic programming frameworks. We demonstrate the power and simplicity of programming with OpenDR by using it to solve the problem of estimating human body shape from Kinect depth and RGB data. In this paper, we study the problem of semantic annotation on 3D models that are represented as shape graphs. A functional view is taken to represent localized information on graphs, so that annotations such as part segment or keypoint are nothing but 0-1 indicator vertex functions. Compared with images that are 2D grids, shape graphs are irregular and non-isomorphic data structures. To enable the prediction of vertex functions on them by convolutional neural networks, we resort to spectral CNN method that enables weight sharing by parameterizing kernels in the spectral domain spanned by graph laplacian eigenbases. Under this setting, our network, named SyncSpecCNN, strive to overcome two key challenges: how to share coefficients and conduct multi-scale analysis in different parts of the graph for a single shape, and how to share information across related but different shapes that may be represented by very different graphs. Towards these goals, we introduce a spectral parameterization of dilated convolutional kernels and a spectral transformer network. Experimentally we tested our SyncSpecCNN on various tasks, including 3D shape part segmentation and 3D keypoint prediction. State-of-the-art performance has been achieved on all benchmark datasets. This paper introduces a deep architecture for segmenting 3D objects into their labeled semantic parts. Our architecture combines image-based Fully Convolutional Networks (FCNs) and surface-based Conditional Random Fields (CRFs) to yield coherent segmentations of 3D shapes. The image-based FCNs are used for efficient view-based reasoning about 3D object parts. Through a special projection layer, FCN outputs are effectively aggregated across multiple views and scales, then are projected onto the 3D object surfaces. Finally, a surface-based CRF combines the projected outputs with geometric consistency cues to yield coherent segmentations. The whole architecture (multi-view FCNs and CRF) is trained end-to-end. Our approach significantly outperforms the existing state-of-the-art methods in the currently largest segmentation benchmark (ShapeNet). Finally, we demonstrate promising segmentation results on noisy 3D shapes acquired from consumer-grade depth cameras.