Multi-focus image fusion aims to generate an image with all objects in focus by integrating multiple partially focused images. It is challenging to find an effective focus measure to evaluate the clarity of source images. In this paper, a novel multi-focus image fusion algorithm based on Geometrical Sparse Representation (GSR) over single images is proposed. The main novelty of this work is that it shows the potential of GSR coefficients used for image fusion. Unlike the traditional sparse representation-based (SR) methods, the proposed algorithm does not need to train an overcomplete dictionary and vectorize the signal. In our algorithm, using a single dictionary image, the source images are first represented by geometrical sparse coefficients. Specifically, we employ a weighted GSR model in the sparse coding phase, ensuring the importance of the center pixel. Then, the weighted GSR coefficient is used to measure the activity level of the source image and an average pooling strategy is applied to obtain an initial decision map. Third, the decision map is refined with a simple post-processing. Finally, the fused all-in-focus image is constructed with the refined decision map. Experimental results demonstrate that the proposed method can be competitive with or even superior to the state-of-the-art fusion methods in both subjective and objective comparisons.

多焦点图像融合旨在通过整合多个部分聚焦的图像来生成所有对象均聚焦的图像。寻找一种有效的聚焦措施来评估源图像的清晰度是一项挑战。提出了一种基于几何稀疏表示（GSR）的单焦点多焦点图像融合算法。这项工作的主要新颖之处在于它显示了用于图像融合的GSR系数的潜力。与传统的基于稀疏表示的方法不同，该算法不需要训练过完备的字典并对信号进行矢量化处理。在我们的算法中，使用单个词典图像，首先用几何稀疏系数表示源图像。具体来说，我们在稀疏编码阶段采用了加权GSR模型，确保中心像素的重要性。然后，将加权的GSR系数用于测量源图像的活动水平，并应用平均合并策略以获得初始决策图。第三，通过简单的后处理完善决策图。最终，融合后的全聚焦图像由精制决策图构建。实验结果表明，在主观和客观比较中，所提出的方法都可以与先进的融合方法相竞争甚至更好。融合后的全焦点图像由精制的决策图构成。实验结果表明，在主观和客观比较中，所提出的方法都可以与先进的融合方法相竞争甚至更好。融合后的全焦点图像由精制的决策图构成。实验结果表明，在主观和客观比较中，所提出的方法都可以与先进的融合方法相竞争甚至更好。