Recently, 3D face reconstruction and face alignment tasks are gradually combined into one task: 3D dense face alignment. Its goal is to reconstruct the 3D geometric structure of face with pose information. In this paper, we propose a graph convolution network to regress 3D face coordinates. Our method directly performs feature learning on the 3D face mesh, where the geometric structure and details are well preserved. Extensive experiments show that our approach gains superior performance over state-of-the-art methods on several challenging datasets.
CNNs are suitable to process grid-like data such as images. By contrast, graph convolution networks (GCNs) are suitable to process graph data such as 3D mesh. A comprehensive overview of GCNs is provided by @cite_25 . @cite_7 define the first graph convolution operator on meshes by parameterizing the surface around each point using geodesic polar coordinates and performing graph convolution on the angular bins. Then, different parameterization methods are proposed by @cite_13 @cite_5 , but the manners of graph convolution are similar. These methods only present generalization of convolutions to meshes. They do not design sampling operation on meshes. Therefore, coarse-to-fine features cannot be captured.
@cite_5 @cite_13 @cite_25 @cite_7
2798598284 2791092480 2809418595 2783032472
Two architectures that generalize convolutional neural networks (CNNs) for the processing of signals supported on graphs are introduced. We start with the selection graph neural network (GNN), which replaces linear time invariant filters with linear shift invariant graph filters to generate convolutional features and reinterprets pooling as a possibly nonlinear subsampling stage where nearby nodes pool their information in a set of preselected sample nodes. A key component of the architecture is to remember the position of sampled nodes to permit computation of convolutional features at deeper layers. The second architecture, dubbed aggregation GNN, diffuses the signal through the graph and stores the sequence of diffused components observed by a designated node. This procedure effectively aggregates all components into a stream of information having temporal structure to which the convolution and pooling stages of regular CNNs can be applied. A multinode version of aggregation GNNs is further introduced for operation in large-scale graphs. An important property of selection and aggregation GNNs is that they reduce to conventional CNNs when particularized to time signals reinterpreted as graph signals in a circulant graph. Comparative numerical analyses are performed in a source localization application over synthetic and real-world networks. Performance is also evaluated for an authorship attribution problem and text category classification. Multinode aggregation GNNs are consistently the best-performing GNN architecture. Convolutional neural networks (CNNs) have massively impacted visual recognition in 2D images, and are now ubiquitous in state-of-the-art approaches. CNNs do not easily extend, however, to data that are not represented by regular grids, such as 3D shape meshes or other graph-structured data, to which traditional local convolution operators do not directly apply. To address this problem, we propose a novel graph-convolution operator to establish correspondences between filter weights and graph neighborhoods with arbitrary connectivity. The key novelty of our approach is that these correspondences are dynamically computed from features learned by the network, rather than relying on predefined static coordinates over the graph as in previous work. We obtain excellent experimental results that significantly improve over previous state-of-the-art shape correspondence results. This shows that our approach can learn effective shape representations from raw input coordinates, without relying on shape descriptors. Convolutional neural networks (CNNs) have achieved great success on grid-like data such as images, but face tremendous challenges in learning from more generic data such as graphs. In CNNs, the trainable local filters enable the automatic extraction of high-level features. The computation with filters requires a fixed number of ordered units in the receptive fields. However, the number of neighboring units is neither fixed nor are they ordered in generic graphs, thereby hindering the applications of convolutional operations. Here, we address these challenges by proposing the learnable graph convolutional layer (LGCL). LGCL automatically selects a fixed number of neighboring nodes for each feature based on value ranking in order to transform graph data into grid-like structures in 1-D format, thereby enabling the use of regular convolutional operations on generic graphs. To enable model training on large-scale graphs, we propose a sub-graph training method to reduce the excessive memory and computational resource requirements suffered by prior methods on graph convolutions. Our experimental results on node classification tasks in both transductive and inductive learning settings demonstrate that our methods can achieve consistently better performance on the Cora, Citeseer, Pubmed citation network, and protein-protein interaction network datasets. Our results also indicate that the proposed methods using sub-graph training strategy are more efficient as compared to prior approaches. Conventional deep convolutional neural networks (CNNs) apply convolution operators uniformly in space across all feature maps for hundreds of layers - this incurs a high computational cost for real time applications. For many problems such as object detection and semantic segmentation, we are able to obtain a low-cost computation mask, either from a priori problem knowledge, or from a low resolution segmentation network. We show that such computation masks can be used to reduce computation in the high resolution main network. Variants of sparse activation CNNs have previously been explored on small scale tasks, and showed no degradation in terms of object classification accuracy, but often measured gains in terms of theoretical FLOPs without realizing a practical speed-up when compared to highly optimized dense convolution implementations. In this work, we leverage the sparsity structure of computation masks and propose a novel tiling-based sparse convolution algorithm. We verified the effectiveness of our sparse CNN on LiDAR based 3D object detection, and we report significant wall-clock speed-ups compared to dense convolution, as well as improved detection accuracy.