. Given a single image, our framework employs a convolutional autoencoder to extract the image's latent space, z, that is used to classify it to an index, c, using a multi-label classifier and regress it to a compact shape parametrization using a feedforward network. We use a graph embedding, G, that compactly represents 3D mesh objects to reconstruct the 3D model. Firstly, the estimated index, c, selects the closest 3D model to the image from the graph. Secondly, the selected model is deformed through the estimated parameters -free-form deformation (FFD), ∆P, and sparse linear combination parameters (i.e. α's). In this example, model 1 is selected (arrows 1 and 2), FFD is then applied (arrows 3 and 4), and finally the linear combination with the nodes 3, 4, 5, 6, and 7 (blue arrows on the graph that indicates the models in dense correspondence with node 1) are performed (arrow 5) to reconstruct the final 3D mesh model (arrow 6). One challenge that remains open in 3D deep learning is how to efficiently represent 3D data to feed deep networks. Recent works have relied on volumetric or point cloud representations, but such approaches suffer from a number of issues such as computational complexity, unordered data, and lack of finer geometry. This paper demonstrates that a mesh representation (i.e. vertices and faces to form polygonal surfaces) is able to capture fine-grained geometry for 3D reconstruction tasks. A mesh however is also unstructured data similar to point clouds. We address this problem by proposing a learning framework to infer the parameters of a compact mesh representation rather than learning from the mesh itself. This compact representation encodes a mesh using free-form deformation and a sparse linear combination of models allowing us to reconstruct 3D meshes from single images. In contrast to prior work, we do not rely on silhouettes and landmarks to perform 3D reconstruction. We evaluate our method on synthetic and real-world datasets with very promising results. Our framework efficiently reconstructs 3D objects in a low-dimensional way while preserving its important geometrical aspects.
Recent methods REF use linear combinations of a dictionary of CAD models and learn the parameters of the combination to represent the models, which are limited to the capacity of the constructed dictionary.
Image 2 Mesh : A Learning Framework for Single Image 3 D Reconstruction