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.

Publication

In *ArXiv 2017*

Date

November, 2017

Links

Given a single image, our framework employs a convolutional autoencoder to extract the image’s latent space, $\mathbf{z}$, 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, $\mathcal{G}$, 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), $\mathbf{\Delta P}$, and sparse linear combination parameters (i.e. $\alpha$’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).

Qualitative results for the synthetic dataset. Column (a) shows the input image. Column (b) shows the selected model from the graph. Column (c ) shows the selected model with the FFD parameters applied. The final 3D model reconstructed by applying the linear combination parameters is shown in column (d) and the ground truth in (e).

Qualitative results for the real-world dataset. Column (a) shows the input image. Column (b) shows the selected model. Column (c ) shows the selected model deformed by the FFD parameters. The final 3D model reconstructed by applying the linear combination parameters is shown in column (d). We compare with [18] in column (e) and the ground truth is shown in column (f).

A closer look at the 3D reconstruction.

Qualitative results for the synthetic dataset. Column (a) shows the input image. Column (b) shows the selected model from the graph. Column (c ) shows the selected model with the FFD parameters applied. The final 3D model reconstructed by applying the linear combination parameters is shown in column (d). The voxelized final model is shown in column (e) and the ground truth in column (f). In the success cases (blues), one can see that the final models are similar to the ground truth with slightly differences that can be hard to point it out. A failure case is shown on the last row in red where a “wrong” model was selected from the graph.

Qualitative results for the real-world dataset. Column (a) shows the input image. Column (b) shows the selected model. Column (c ) shows the selected model deformed by the FFD parameters. The final 3D model reconstructed by applying the linear combination parameters is shown in column (d). We compare with [18] in column (e) and the ground truth is shown in column (f).

**Please check the supplementary material out for more examples.**