中文摘要：

为了解决分数阶微分应用于图像处理中难以确定分数阶微分阶次的问题,首先分析了图像的分数阶微分增强效果在一定范围内随着分数阶微分阶次的增大而增大以及图像的平均亮度越大,恰可感知的亮度差异就越大的特点;然后,根据图像的整体灰度分布和局部灰度值构造了自适应分段函数来确定分数阶微分阶次。实验结果表明,该方法能自动寻找最佳微分阶次,增强后的图像视觉效果明显,图像增强视觉效果接近或超过最佳微分阶次下的视觉效果,增强图像的对比度明显高于最佳微分阶次下的对比度。

英文摘要：

In order to determine the appropriate differential order when fractional differential being applied to image enhancement,this paper proposed an adaptive method. First of all,it analyzed the facts that enhancement effect increased with fractional differential order when order was in a certain range,and the just noticeable difference（ JND） increased with average brightness of the image. Then,together with results mentioned above,it established a piecewise function to determine adaptive order according to the overall gray distribution and local pixel value. Experiments show that the proposed method can automatically determine the appropriate differential order,and can significantly improve visual effect. Experiments also show that the image enhancement effect is close to or better than that of the optimal differential order,and the contrast of enhanced image is higher than that of the best order.