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

On a conjecture about tricyclic graphs with maximal energy

For a given simple graph $G$, the energy of $G$, denoted by $\mathcal {E}(G)$, is defined as the sum of the absolute values of all eigenvalues of its adjacency matrix, which was defined by I. Gutman. The problem on determining the maximal energy tends to be complicated for a given class of graphs. There are many approaches on the maximal energy of trees, unicyclic graphs and bicyclic graphs, respectively. Let $P^{6,6,6}_n$ denote the graph with $n\geq 20$ vertices obtained from three copies of $C_6$ and a path $P_{n-18}$ by adding a single edge between each of two copies of $C_6$ to one endpoint of the path and a single edge from the third $C_6$ to the other endpoint of the $P_{n-18}$. Very recently, Aouchiche et al. [M. Aouchiche, G. Caporossi, P. Hansen, Open problems on graph eigenvalues studied with AutoGraphiX, {\it Europ. J. Comput. Optim.} {\bf 1}(2013), 181--199] put forward the following conjecture: Let $G$ be a tricyclic graphs on $n$ vertices with $n=20$ or $n\geq22$, then $\mathcal{E}(G)\leq \mathcal{E}(P_{n}^{6,6,6})$ with equality if and only if $G\cong P_{n}^{6,6,6}$. Let $G(n;a,b,k)$ denote the set of all connected bipartite tricyclic graphs on $n$ vertices with three vertex-disjoint cycles $C_{a}$, $C_{b}$ and $C_{k}$, where $n\geq 20$. In this paper, we try to prove that the conjecture is true for graphs in the class $G\in G(n;a,b,k)$, but as a consequence we can only show that this is true for most of the graphs in the class except for 9 families of such graphs.Comment: 32 pages, 12 figure