非凸加权核范数及其在运动目标检测中的应用

目的 近年来,低秩矩阵分解被越来越多的应用到运动目标检测中。但该类方法一般将矩阵秩函数松弛为矩阵核函数优化,导致背景恢复精度不高;并且没有考虑到前景目标的先验知识,即区域连续性。为此提出一种结合非凸加权核范数和前景目标区域连续性的目标检测算法。方法 本文提出的运动目标检测模型以鲁棒主成分分析(RPCA)作为基础,在该基础上采用矩阵非凸核范数取代传统的核范数逼近矩阵低秩约束,并结合了前景目标区域连续性的先验知识。该方法恢复出的低秩矩阵即为背景图像矩阵,而稀疏大噪声矩阵则是前景目标位置矩阵。结果 无论是在仿真数据集还是在真实数据集上,本文方法都能够取得比其他低秩类方法更好的效果。在不同数据集上,该方法相对于RPCA方法,前景目标检测性能提升25%左右,背景恢复误差降低0.5左右;而相对于DECOLOR方法,前景目标检测性能提升约2%左右,背景恢复误差降低0.2左右。结论 矩阵秩函数的非凸松弛能够比凸松弛更准确的表征出低秩特征,从而在运动目标检测应用中更准确的恢复出背景。前景目标的区域连续性先验知识能够有效地过滤掉非目标大噪声产生的影响,使得较运动目标检测的精度得到大幅提高。因此,本文方法在动态纹理背景、光照渐变等较复杂场景中均能够较精确地检测出运动目标区域。但由于区域连续性的要求,本文方法对于小区域多目标的检测效果不甚理想。

Weighted nonconvex nuclear norm and its application in the moving target detection

Objective Several low-rank matrix decomposition-based approaches have been proposed for moving object detection in recent years. However, most of these methods use the nuclear norm to substitute rank functions for optimization. As a result, the precision of background recovery is relatively low. Another problem is the failure of these methods to use prior knowledge of the regional continuity of foreground objects, which is important information for object detection. To solve these issues, we propose a novel object detection method that combines the weighted non-convex nuclear norm and the regional continuity of the foreground object. Method The new object detection model is designed on the basis of the robust principal component analysis. The proposed model uses the weighted non-convex nuclear norm to replace the traditional nuclear norm for low-rank constraints. Furthermore, the prior knowledge of the regional continuity of the foreground object is added to restrain the clustered objects. By using this model, the recovered low-rank matrix becomes the background image matrix, and the large sparse noise matrix becomes the foreground object matrix. Result Experiments demonstrate that the proposed method outperforms other low-rank decomposition-based approaches in both the simulated data and real sequences. Specifically, the proposed methodology shows an increased projected target detection performance that is 25% and 2% greater than that of RPCA and DECOLOR. With respect to the two approaches, the proposed method reduces background recovery errors by about 0.5 and 0.2. Conclusion The non-convex relaxation of rank functions possesses better properties than the convex one in approximating matrix ranks, which is useful in restoring background images in motion object detection. The regional continuity of foreground objects allows the efficient exclusion of scattered outliers to enhance the effect of the objects detected. Therefore, this method can detect moving targets accurately in complex scenes, such as those with dynamic backgrounds and illumination-changing scenarios. However, the proposed method is not ideal for multi-object detection in small areas because of regional continuity requirements.