Max-Cut and Max-Bisection are NP-hard on unit disk graphs

We prove that the Max-Cut and Max-Bisection problems are NP-hard on unit disk graphs. We also show that $\lambda$-precision graphs are planar for $\lambda$ > 1 / \sqrt{2}$

A graph-based mathematical morphology reader

This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active and diverse field of research

PersonRank: Detecting Important People in Images

Always, some individuals in images are more important/attractive than others in some events such as presentation, basketball game or speech. However, it is challenging to find important people among all individuals in images directly based on their spatial or appearance information due to the existence of diverse variations of pose, action, appearance of persons and various changes of occasions. We overcome this difficulty by constructing a multiple Hyper-Interaction Graph to treat each individual in an image as a node and inferring the most active node referring to interactions estimated by various types of clews. We model pairwise interactions between persons as the edge message communicated between nodes, resulting in a bidirectional pairwise-interaction graph. To enrich the personperson interaction estimation, we further introduce a unidirectional hyper-interaction graph that models the consensus of interaction between a focal person and any person in a local region around. Finally, we modify the PageRank algorithm to infer the activeness of persons on the multiple Hybrid-Interaction Graph (HIG), the union of the pairwise-interaction and hyperinteraction graphs, and we call our algorithm the PersonRank. In order to provide publicable datasets for evaluation, we have contributed a new dataset called Multi-scene Important People Image Dataset and gathered a NCAA Basketball Image Dataset from sports game sequences. We have demonstrated that the proposed PersonRank outperforms related methods clearly and substantially.Comment: 8 pages, conferenc

Mining Point Cloud Local Structures by Kernel Correlation and Graph Pooling

Unlike on images, semantic learning on 3D point clouds using a deep network is challenging due to the naturally unordered data structure. Among existing works, PointNet has achieved promising results by directly learning on point sets. However, it does not take full advantage of a point's local neighborhood that contains fine-grained structural information which turns out to be helpful towards better semantic learning. In this regard, we present two new operations to improve PointNet with a more efficient exploitation of local structures. The first one focuses on local 3D geometric structures. In analogy to a convolution kernel for images, we define a point-set kernel as a set of learnable 3D points that jointly respond to a set of neighboring data points according to their geometric affinities measured by kernel correlation, adapted from a similar technique for point cloud registration. The second one exploits local high-dimensional feature structures by recursive feature aggregation on a nearest-neighbor-graph computed from 3D positions. Experiments show that our network can efficiently capture local information and robustly achieve better performances on major datasets. Our code is available at http://www.merl.com/research/license#KCNetComment: Accepted in CVPR'18. *indicates equal contributio