Abstract We define a novel type of ensemble graph convolutional network (GCN) model. Using optimized linear projection operators to map between spatial scales of graph, this ensemble model learns to aggregate information from each scale for its final prediction. We calculate these linear projection operators as the infima of an objective function relating the structure matrices used for each GCN. Equipped with these projections, our model (a Graph Prolongation-Convolutional Network) outperforms other GCN ensemble models at predicting the potential energy of monomer subunits in a coarse-grained mechanochemical simulation of microtubule bending. We demonstrate these performance gains by measuring an estimate of the Floating Point OPerations spent to train each model, as well as wall-clock time. Because our model learns at multiple scales, it is possible to train at each scale according to a predetermined schedule of coarse vs. fine training. We examine several such schedules adapted from the algebraic multigrid literature, and quantify the computational benefit of each. We also compare this model to another model which features an optimized coarsening of the input graph. Finally, we derive backpropagation rules for the input of our network model with respect to its output, and discuss how our method may be extended to very large graphs.
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Joint 3D Human Shape Recovery and Pose Estimation from a Single Image with Bilayer Graph
The ability to estimate the 3D human shape and pose from images can be useful in many contexts. Recent approaches have explored using graph convolutional networks and achieved promising results. The fact that the 3D shape is represented by a mesh, an undirected graph, makes graph convolutional networks a natural fit for this problem. However, graph convolutional networks have limited representation power Information from nodes in the graph is passed to connected neighbors, and propagation of information requires successive graph convolutions. To overcome this limitation, we propose a dual-scale graph approach. We use a coarse graph, derived from a dense graph, to estimate the human’s 3D pose, and the dense graph to estimate the 3D shape. Information in coarse graphs can be propagated over longer distances compared to dense graphs. In addition, information about pose can guide to recover local shape detail and vice versa. We recognize that the connection between coarse and dense is itself a graph, and introduce graph fusion blocks to exchange information between graphs with different scales. We train our model end-to-end and show that we can achieve state-of-the-art results for several evaluation datasets. The code is available at the following link, https://github.com/yuxwind/BiGraphBody.
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- Award ID(s):
- 1764071
- NSF-PAR ID:
- 10382087
- Date Published:
- Journal Name:
- 2021 International Conference on 3D Vision (3DV)
- Page Range / eLocation ID:
- 505 to 514
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/3DV53792.2021.00060
