Neural 3D Morphable Models: Spiral Convolutional Networks for 3D Shape Representation Learning and Generation

Generative models for 3D geometric data arise in many important applications in 3D computer vision and graphics. In this paper, we focus on 3D deformable shapes that share a common topological structure, such as human faces and bodies. Morphable Models and their variants, despite their linear formulation, have been widely used for shape representation, while most of the recently proposed nonlinear approaches resort to intermediate representations, such as 3D voxel grids or 2D views. In this work, we introduce a novel graph convolutional operator, acting directly on the 3D mesh, that explicitly models the inductive bias of the fixed underlying graph. This is achieved by enforcing consistent local orderings of the vertices of the graph, through the spiral operator, thus breaking the permutation invariance property that is adopted by all the prior work on Graph Neural Networks. Our operator comes by construction with desirable properties (anisotropic, topology-aware, lightweight, easy-to-optimise), and by using it as a building block for traditional deep generative architectures, we demonstrate state-of-the-art results on a variety of 3D shape datasets compared to the linear Morphable Model and other graph convolutional operators.Comment: to appear at ICCV 201

An Implementation of Fully Convolutional Network for Surface Mesh Segmentation

This thesis presents an implementation of a 3-Dimensional triangular surface mesh segmentation architecture named Shape Fully Convolutional Network, which is proposed by Pengyu Wang and Yuan Gan in 2018. They designed a deep neural network that has a similar architecture as the Fully Convolutional Network, which provides a good segmentation result for 2D images, on 3D triangular surface meshes. In their implementation, 3D surface meshes are represented as graph structures to feed the network. There are three main barriers when applying the Fully Convolutional Network to graph-based data structures. • First, the pooling operation is much harder to apply to general graphs. • Second, the convolution order on a graph structure is unstable. • Third, the raw data of surface meshes cannot be directly applied to the network. To solve these problems, first, all the nodes inside the graph are re-ordered into a 1-dimensional list based on a multi-level graph coarsening algorithm, which allows the pooling operation to be applied as easily as a 1D pooling. Second, a self-defined generating layer is added before each convolution layer in the network to generate the neighbors of each node on the graph, and at the same time, sort all neighbors based on the L2 similarity to keep the convolution operation in a stable manner. Finally, three translation and rotation free low-level geometric features are pre-processed and used as input to train the network. This Shape Fully Convolution Network can effectively learn and predict triangular face-wise labels. In the end, to achieve a better result, the final labeling is optimized by the multi-label graph cut algorithm, which gives punishment to the predicted result based on the smoothness of the surface. The experiments show that the model can effectively learn and predict triangle-wise labels on surface meshes and yields good segmentation results

Geometric deep learning: going beyond Euclidean data

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them. Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field