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.
Single-image 3D reconstruction can be realized without 3D supervision. Perspective transformer nets (PTN) @cite_38 learn 3D structures using silhouette images from multiple viewpoints. Our 3D reconstruction method is also based on silhouette images. However, we use polygon meshes whereas they used voxels.
@cite_38
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Understanding the 3D world is a fundamental problem in computer vision. However, learning a good representation of 3D objects is still an open problem due to the high dimensionality of the data and many factors of variation involved. In this work, we investigate the task of single-view 3D object reconstruction from a learning agent's perspective. We formulate the learning process as an interaction between 3D and 2D representations and propose an encoder-decoder network with a novel projection loss defined by the perspective transformation. More importantly, the projection loss enables the unsupervised learning using 2D observation without explicit 3D supervision. We demonstrate the ability of the model in generating 3D volume from a single 2D image with three sets of experiments: (1) learning from single-class objects; (2) learning from multi-class objects and (3) testing on novel object classes. Results show superior performance and better generalization ability for 3D object reconstruction when the projection loss is involved.