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Recently, much attention has been drawn to the problem of matrix completion, which arises in a number of fields, including computer vision, pattern recognition, sensor network, and recommendation systems. This paper proposes a novel algorithm, named robust alternative minimization (RAM), which is based on the constraint of low rank to complete an unknown matrix. The proposed RAM algorithm can effectively reduce the relative reconstruction error of the recovered matrix. It is numerically easier to minimize the objective function and more stable for large-scale matrix completion compared with other existing methods. It is robust and efficient for low-rank matrix completion, and the convergence of the RAM algorithm is also established. Numerical results showed that both the recovery accuracy and running time of the RAM algorithm are competitive with other reported methods. Moreover, the applications of the RAM algorithm to low-rank image recovery demonstrated that it achieves satisfactory performance. [ABSTRACT FROM AUTHOR]

Eye detection plays an important role in many practical applications. This paper presents a novel two-step scheme for eye detection. The first step models an eye by a newly defined visual-context pattern (VCP), and the second step applies semisupervised boosting for precise detection. VCP describes both the space and appearance relations between an eye region (region of eye) and a reference region (region of reference). The context feature of a VCP is extracted by using the integral image. Aiming to reduce the human labeling efforts, we apply semisupervised boosting, which integrates the context feature and the Haar-like features for precise eye detection. Experimental results on several standard face data sets demonstrate that the proposed approach is effective, robust, and efficient. We finally show that this approach is ready for practical applications. [ABSTRACT FROM AUTHOR]