由于分数阶微积分在细节加强处理方面具有良好的性能,其在边缘检测中的应用正在逐渐增多。目前用分数阶微积分进行边缘检测的研究中大多在RGB空间中进行,但由于RGB颜色空间中亮度信息和色度信息不能相互分离,在其中进行边缘提取不能综合得到亮度边缘和色度边缘,所以分数阶微积分在其他亮度信息和色度信息分开的颜色空间中的应用研究具有一定的理论意义和实际价值。为了综合利用图像的颜色信息,在CIE L^*a^*b^*颜色空间中利用分数阶微分进行边缘检测。相比于直接在RGB颜色空间中得到的边缘,本文方法提取到的图像边缘更符合人眼的视觉感知,边缘的连续性以及抗干扰性也更好。通过与其他经典算法的对比分析表明,本文方法存在明显的优势。

The fractional calculus is used in edge detection much more frequently due to its good performance in strengthening details, Among those studies, most are made in RGB color space. However, the brightness information and the chrominance information are related to each other in RGB color space. This defect prevents us from obtaining both the brightness edge and the chrominance edge simultaneously. Therefore, using fractional calculus in other color spaces whose brightness information and chrominance information are separated, is significant in theory and practice. In this paper, to make the most use of both brightness and color information, we propose a novel edge detection method by using fractional differentiation in CIE L^*a^*b^* color space for edge detection. Compared with detecting edges directly in the RGB color space, the edge extracted by the proposed method is much more consistent with human visual preception. Furthermore, the continuity and the anti-disturbance are better too. By contrast to other classical algorithms, the proposed method also has significant advantage.