Learning SO(3) Equivariant Representations with Spherical CNNs

We address the problem of 3D rotation equivariance in convolutional neural networks. 3D rotations have been a challenging nuisance in 3D classification tasks requiring higher capacity and extended data augmentation in order to tackle it. We model 3D data with multi-valued spherical functions and we propose a novel spherical convolutional network that implements exact convolutions on the sphere by realizing them in the spherical harmonic domain. Resulting filters have local symmetry and are localized by enforcing smooth spectra. We apply a novel pooling on the spectral domain and our operations are independent of the underlying spherical resolution throughout the network. We show that networks with much lower capacity and without requiring data augmentation can exhibit performance comparable to the state of the art in standard retrieval and classification benchmarks.Comment: Camera-ready. Accepted to ECCV'18 as oral presentatio

Sketch-based 3D Shape Retrieval using Convolutional Neural Networks

Retrieving 3D models from 2D human sketches has received considerable attention in the areas of graphics, image retrieval, and computer vision. Almost always in state of the art approaches a large amount of "best views" are computed for 3D models, with the hope that the query sketch matches one of these 2D projections of 3D models using predefined features. We argue that this two stage approach (view selection -- matching) is pragmatic but also problematic because the "best views" are subjective and ambiguous, which makes the matching inputs obscure. This imprecise nature of matching further makes it challenging to choose features manually. Instead of relying on the elusive concept of "best views" and the hand-crafted features, we propose to define our views using a minimalism approach and learn features for both sketches and views. Specifically, we drastically reduce the number of views to only two predefined directions for the whole dataset. Then, we learn two Siamese Convolutional Neural Networks (CNNs), one for the views and one for the sketches. The loss function is defined on the within-domain as well as the cross-domain similarities. Our experiments on three benchmark datasets demonstrate that our method is significantly better than state of the art approaches, and outperforms them in all conventional metrics.Comment: CVPR 201

DeformNet: Free-Form Deformation Network for 3D Shape Reconstruction from a Single Image

3D reconstruction from a single image is a key problem in multiple applications ranging from robotic manipulation to augmented reality. Prior methods have tackled this problem through generative models which predict 3D reconstructions as voxels or point clouds. However, these methods can be computationally expensive and miss fine details. We introduce a new differentiable layer for 3D data deformation and use it in DeformNet to learn a model for 3D reconstruction-through-deformation. DeformNet takes an image input, searches the nearest shape template from a database, and deforms the template to match the query image. We evaluate our approach on the ShapeNet dataset and show that - (a) the Free-Form Deformation layer is a powerful new building block for Deep Learning models that manipulate 3D data (b) DeformNet uses this FFD layer combined with shape retrieval for smooth and detail-preserving 3D reconstruction of qualitatively plausible point clouds with respect to a single query image (c) compared to other state-of-the-art 3D reconstruction methods, DeformNet quantitatively matches or outperforms their benchmarks by significant margins. For more information, visit: https://deformnet-site.github.io/DeformNet-website/ .Comment: 11 pages, 9 figures, NIP