低秩稀疏分解下多尺度积的运动目标检测方法

针对基于矩阵分解的运动目标检测方法易受自然场景中背景的小幅抖动和摄像头抖动等因素影响的问题,提出了一种利用多尺度积的低秩稀疏矩阵分解算法。算法假设,静态背景视频序列中，每帧图像背景可近似视为处于同一低秩子空间中，图像前景则可视为偏离低秩空间的残差部分。首先对图像序列进行滤波、仿射变换等预处理得到视频序列观测数据矩阵；然后对数据矩阵进行低秩稀疏分解得到序列图像的低秩背景部分和每帧图像的稀疏前景部分；最后对稀疏前景部分采用小波变换模极大值与多尺度积方法检测目标边缘，并进行形态学处理，得到准确的运动目标。实验结果表明，算法检测到的运动目标清晰、完整，能有效地处理光照变化、摄像头小幅度抖动、图像背景局部小幅度变化等情况下的运动目标检测。 

A method of low-rank decomposition with multi-scale product for moving object detection

Considering the small amplitude changes of the natural scene and camera shake problems that affect moving object detection based on rank decomposition, an effective algorithm of low-rank decomposition with multi-scale product is proposed. The basic theoretical proposition is that in the static background video sequences, every frame background images can be regarded approximately under the same low-rank subspace and the foreground change can be seen as sparse residuals. Firstly, the observation data matrix can be obtained through the preprocessing including filtering and affine transformation for every frame images; then, two components of the low-rank matrix and a sparse matrix can be obtained by low-rank decomposition on the image sequence; finally, with the multi-scale product the moving object edge is extracted via wavelet transform modulus maxima on the sparse foreground images, and a postprocessing by morphological is carried out to obtain the accurate moving object. Experimental results show that, by the proposed method, clear and complete objects can be obtained and this method can effectively handle the moving object detection problems under some complex situations such as light changes, the small amplitude changes of the image background and camera shake.