Abstract: To overcome the problem of no effective method to detect the focus point in multi-focus image fusion, an efficient algorithm based on RPCA （Robust Principal Component Analysis） and region detection is proposed. Firstly, the source images are decomposed into sparse images and low rank images by the theory of RPCA. Secondly, the focus decision diagram of the source image is obtained using the method of region detection in the sparse image. In addition, the consistency operation of three directions and region growing method process is used to get the final decision diagram in the focus decision diagram. Finally, the fusion image is obtained via the final decision diagram. Simulation results demonstrate that the proposed fusion algorithm substantially outperforms the best-known multi-focus image fusion algorithms in four objective evaluation metrics（i.e. standard deviation, average gradient, spatial frequency, mutual information）. The proposed fusion algorithm shows the effectiveness in three subjective evaluation metrics（i.e. contrast, texture clarity, brightness）.

Key words: multi-focus image fusion, Robust Principal Component Analysis（RPCA） decomposition, region detection, region growing method

摘要： 针对多聚焦图像融合中难以有效检测聚焦点的问题，提出了一种基于鲁棒主成分分析（RPCA）和区域检测的多聚焦图像融合方法。将RPCA理论运用到多聚焦图像融合中，把源图像分解为稀疏图像和低秩图像；对稀疏矩阵采用区域检测的方法得到源图像的聚焦判决图；对聚焦判决图进行三方向一致性和区域生长法处理得到最终决策图；根据最终决策图对源图像进行融合。实验结果表明，在主观评价方面，所提出的方法在对比度、纹理清晰度、亮度等几方面都有显著的提高；在客观评价方面，用标准差、平均梯度、空间频率和互信息四项评价指标说明了该方法的有效性。

关键词: 多聚焦图像融合, RPCA分解, 区域检测, 区域生长法