Guan Wang

Tahmina Khanam, Hamid Laga, Mohammed Bennamoun et al.

We propose the first comprehensive approach for modeling and analyzing the spatiotemporal shape variability in tree-like 4D objects, i.e., 3D objects whose shapes bend, stretch, and change in their branching structure over time as they deform, grow, and interact with their environment. Our key contribution is the representation of tree-like 3D shapes using Square Root Velocity Function Trees (SRVFT). By solving the spatial registration in the SRVFT space, which is equipped with an L2 metric, 4D tree-shaped structures become time-parameterized trajectories in this space. This reduces the problem of modeling and analyzing 4D tree-like shapes to that of modeling and analyzing elastic trajectories in the SRVFT space, where elasticity refers to time warping. In this paper, we propose a novel mathematical representation of the shape space of such trajectories, a Riemannian metric on that space, and computational tools for fast and accurate spatiotemporal registration and geodesics computation between 4D tree-shaped structures. Leveraging these building blocks, we develop a full framework for modelling the spatiotemporal variability using statistical models and generating novel 4D tree-like structures from a set of exemplars. We demonstrate and validate the proposed framework using real 4D plant data.

Shuyin Xia, Guan Wang, Gaojie Xu et al.

The objective of graph coarsening is to generate smaller, more manageable graphs while preserving key information of the original graph. Previous work were mainly based on the perspective of spectrum-preserving, using some predefined coarsening rules to make the eigenvalues of the Laplacian matrix of the original graph and the coarsened graph match as much as possible. However, they largely overlooked the fact that the original graph is composed of subregions at different levels of granularity, where highly connected and similar nodes should be more inclined to be aggregated together as nodes in the coarsened graph. By combining the multi-granularity characteristics of the graph structure, we can generate coarsened graph at the optimal granularity. To this end, inspired by the application of granular-ball computing in multi-granularity, we propose a new multi-granularity, efficient, and adaptive coarsening method via granular-ball (GBGC), which significantly improves the coarsening results and efficiency. Specifically, GBGC introduces an adaptive granular-ball graph refinement mechanism, which adaptively splits the original graph from coarse to fine into granular-balls of different sizes and optimal granularity, and constructs the coarsened graph using these granular-balls as supernodes. In addition, compared with other state-of-the-art graph coarsening methods, the processing speed of this method can be increased by tens to hundreds of times and has lower time complexity. The accuracy of GBGC is almost always higher than that of the original graph due to the good robustness and generalization of the granular-ball computing, so it has the potential to become a standard graph data preprocessing method.