Multi-focus image fusion is a technique that merges partially focused images to create a totally focused image. However, most existing focus measures suffer from inaccurate detection of low-frequency regions. This study introduces a novel focus measure called the sum of Gaussian-based fractional order differentiation (SGFD). Unlike traditional integer order differential operators, fractional order differential operators can retain more low-frequency information. As a result, SGFD outperforms conventional focus measures. The process begins with the initial fusion using the nonsubsampled shearlet transform (NSST) and SGFD, which produces the initial fused image and its corresponding difference images. Additionally, the feature map of SGFD is extracted from the source image, and the initial decision map is obtained through quadtree decomposition. Further refinement of the initial decision map yields the final decision map. Furthermore, residual regions are derived from the initial difference images and the final decision map. With residual removal, the final fused image is generated from the initial fused image. Extensive experiments are carried out to compare the proposed approach to 11 state-of-the-art approaches. The results demonstrate that the proposed SGFD-based approach surpasses the others regarding subjective visual quality and objective metrics.

多焦点图像融合是一种合并部分聚焦图像以创建完全聚焦图像的技术。然而，大多数现有的焦点测量都存在低频区域检测不准确的问题。本研究引入了一种新颖的焦点度量，称为基于高斯的分数阶微分之和（SGFD）。与传统的整数阶微分算子不同，分数阶微分算子可以保留更多的低频信息。因此，SGFD 优于传统的焦点测量方法。该过程首先使用非下采样剪切波变换 (NSST) 和 SGFD 进行初始融合，生成初始融合图像及其相应的差异图像。另外，从源图像中提取SGFD的特征图，并通过四叉树分解得到初始决策图。初始决策图的进一步细化产生最终决策图。此外，残差区域是从初始差异图像和最终决策图导出的。通过残差去除，最终的融合图像是从初始融合图像生成的。进行了大量的实验来将所提出的方法与 11 种最先进的方法进行比较。结果表明，所提出的基于 SGFD 的方法在主观视觉质量和客观指标方面优于其他方法。