Abstract3D Morphable Face Models (3DMM) have been used in pattern recognition for some time now. They have been applied as a basis for 3D face recognition, as well as in an assistive role for 2D face recognition to perform geometric and photometric normalisation of the input image, or in 2D face recognition system training. The statistical distribution underlying 3DMM is Gaussian. However, the single-Gaussian model seems at odds with reality when we consider different cohorts of data, e.g. Black and Chinese faces. Their means are clearly different. This paper introduces the Gaussian Mixture 3DMM (GM-3DMM) which models the global population as a mixture of Gaussian subpopulations, each with its own mean. The proposed GM-3DMM extends the traditional 3DMM naturally, by adopting a shared covariance structure to mitigate small sample estimation problems associated with data in high dimensional spaces. We construct a GM-3DMM, the training of which involves a multiple cohort dataset, SURREY-JNU, comprising 942 3D face scans of people with mixed backgrounds. Experiments in fitting the GM-3DMM to 2D face images to facilitate their geometric and photometric normalisation for pose and illumination invariant face recognition demonstrate the merits of the proposed mixture of Gaussians 3D face model.
Discriminative dictionary learning (DDL) has recently gained significant attention due to its impressive performance in various pattern classification tasks. However, the locality of atoms is not fully explored in conventional DDL approaches which hampers their classification performance. In this paper, we propose a locality constraint dictionary learning with support vector discriminative term (LCDL-SV), in which the locality information is preserved by employing the graph Laplacian matrix of the learned dictionary. To jointly learn a classifier during the training phase, a support vector discriminative term is incorporated into the proposed objective function. Moreover, in the classification stage, the identity of test data is jointly determined by the regularized residual and the learned multi-class support vector machine. Finally, the resulting optimization problem is solved by utilizing the alternative strategy. Experimental results on benchmark databases demonstrate the superiority of our proposed method over previous dictionary learning approaches on both hand-crafted and deep features.
Attitude determination using the accelerometer-magnetometer combination is basically an applied mathematical problem. Commonly, such attitude determination tasks should be accomplished with reference information of sensors, e.g. the magnetometer's reference vector, from calibration processes. However, this piece of important information cannot be accurately acquired or would differ with the change of body's position. In this paper, to solve such problem, the conventional accelerometer-magnetometer combination fusion equations are transformed into a brand new set of equations, which are free of reference information. Quaternion solutions to the novel equations are obtained via analytic computation techniques. According to the unique design, the proposed attitude estimator owns very fast computation speed compared with representative methods including iterative ones and algebraic ones. Experiments and simulations are carried out to give demonstrations and comparisons, which verify the correctness and effectiveness of the proposed method. The results also show that using the proposed quaternion solution, fusion with gyroscope can be more efficiently obtained.
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