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Abstract: In this paper we propose a concavely regularized convex relaxation based graph matching algorithm. The graph matching problem is firstly formulated as a constrained convex quadratic program by relaxing the feasible set from the permutation matrices to doubly stochastic matrices. To gradually push the doubly stochastic matrix back to be a permutation one, an objective function is constructed by adding a simple weighted concave regularization to the convex relaxation. By gradually increasing the weight of the concave term, minimization of the objective function will gradually push the doubly stochastic matrix back to be a permutation one. A concave–convex procedure (CCCP) together with the Frank–Wolfe algorithm is adopted to minimize the objective function. The algorithm can be used on any types of graphs and exhibits a comparable performance as the PATH following algorithm, a state-of-the-art graph matching algorithm but applicable only on undirected graphs. [Copyright &y& Elsevier]

Facial landmark tracking often adopts static models to generically fit per frame of video. This is considered inappropriate since such models ignore the informative correlation between previous and current frames. Moreover, most of these methods fail to balance the speed and accuracy for video-based facial landmark tracking simultaneously. In this paper, we propose an efficient online framework for video-based face alignment, named Incrementally Cascaded Broad Learning framework (ICBL). ICBL aims to continuously enhance the prediction capability of tracking model for sequential data. It is capable of learning the spatial appearance on specific-person statistics from continuous facial frames and using such knowledge to incrementally tune a cascade of regressors in parallel. To achieve this goal, we approximate the facial shape space by sampling from a dynamic distribution which is continuously updated by person-specific statistics from the tracked facial frames. This dramatically facilitates cascade regression to incrementally update all cascade-regressors in parallel, thus allowing a fast update of the whole model. Furthermore, we successfully incorporate both the linear and non-linear mappings into our parallel cascade framework and introduce Broad Learning (BL) algorithm as a solution for them simultaneously. Experimental results on the most popular and large-scale benchmark for facial landmark tracking show highly competitive performance of proposed ICBL in comparisons with the state-of-the-arts. The code of our ICBL framework has been available from https://github.com/CaifengLiu/Facial-landmark-tracking-by-ICBL. [ABSTRACT FROM AUTHOR]

Graph matching is a fundamental problem in artificial intelligence and structural data processing. Hypergraph matching has recently become popular in the graph matching community. Existing hypergraph matching algorithms usually resort to the continuous methods, while the combinatorial nature of hypergraph matching is not well considered. Therefore in this paper, we propose a novel hypergraph matching algorithm by introducing the affinity tensor updating based graduated projection. Specifically, the hypergraph matching problem is first formulated as a combinatorial optimization problem in a high order polynomial form. Then this NP-hard problem is relaxed and interpreted in a probabilistic manner, which is approximately solved by iterative techniques. The updating of the affinity tensor is performed in each iteration, besides the updating of probabilistic assignment vector. Experimental results on both synthetic and real-world datasets witness the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]