基于分数阶微分的图像增强算法

相比传统的基于整数阶微分的图像增强算子,分数阶微分增强算子能提升图像的高频边缘信息,且非线性保留图像纹理细节和平滑区域的中低频信息。文中根据Riemann-Liouville分数阶微分定义,构造了5×5大小的分数阶微分增强算子模板,同时采用传统的整数阶图像增强算子Sobel算子、Prewitt算子和Laplacian算子,分别对灰度图像和彩色图像进行图像增强处理实验。最后,引入图像熵的计算,对图像增强的结果进行熵值大小的计算与分析。随着分数阶微分阶次的增加,分数阶微分增强算子处理后的图像熵值呈上升趋势,说明图像的纹理细节信息得到了加强。

Image Enhancement Algorithm Based on Fractional Differential

Different from the traditional image enhancement algorithms, the fractional differential image en- hancement algorithm can enhance the high frequency of the image, and keep the middle and the low frequency of the image corresponding to the image texture detail and smoothing region. The paper designs a 5 × 5 image enhancement template based on the Riemann-Liouville fractional differential definition, and uses the fractional differential image enhancement algorithms （Sobel, Prewitt, and Laplacian） to experiment the image enhaneement effect. Finally the entropy of the results by these image enhancement algorithms are analyzed, which shows that the image entropy after the processing increases with the fractional differential order, a proof of enhancement of image texture details.