Fractional computation has been recently designed as a major mathematical tool in image and signal processing fields. This study presents a novel operator established for two-dimensional fractional differentiation. It is developed based on the one-dimensional Charef fractional differentiation extension. A new multi-directional mask is proposed and a new adaptive fractional-order computation is introduced. The proposed method uses the gradient computation properties. It has been applied in edge detection and de-noising problems using real and synthetic images. Obtained results have been compared to those given by integer and fractional useful operators. Results demonstrate that the fractional edge images obtained using the proposed operator has more complete and clear contour information and more abundant texture detail information. The performances have been improved by the proposed method.

中文翻译：

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用于图像处理应用的双向分数阶导数掩模

最近，分数计算已被设计为图像和信号处理领域中的主要数学工具。这项研究提出了一种为二维分数微分建立的新型算子。它是基于一维Charef分数微分扩展而开发的。提出了一种新的多方向掩模，并引入了一种新的自适应分数阶计算。所提出的方法利用了梯度计算特性。它已应用在使用真实和合成图像的边缘检测和降噪问题中。将获得的结果与整数和小数有用运算符给出的结果进行了比较。结果表明，使用提出的算子获得的分数边缘图像具有更完整和清晰的轮廓信息以及更丰富的纹理细节信息。