基于Riemann-Liouville改进的1~2阶分数阶边缘提取新模型

针对数字图像的处理中采用整数步长与0~1阶分数阶微分的掩模算子未能精确定位边缘信息、缺少图像的纹理细节的问题,在Laplacian算子的基础上提出了一种新的边缘检测掩模算子。该算法从Riemann-Liouville(R-L)定义出发,推出1~2阶分数阶微分在中频信号的增强效果优于0~1阶分数阶微分并显著提升了高频信号,最终得到精确的检测效果。仿真结果表明:提出的算子能更好地提取边缘信息,尤其对灰度变化不大的平滑区域中纹理细节丰富的图像,该算子检测到的信息优于现有0~1阶微分算子,针对主观识别有更高的准确率;客观上采用扫描法的定位误差统计,该算子的综合定位误差率为7.41%,低于整数阶微分算子(最低为10.36%)与0~1阶微分算子(最低为9.97%),有效提高了边缘定位精度。该算子尤其适用于具有较高频信息的图像边缘检测中。

New improved 1-2-order fractional differential edge detection model based on Riemann-Liouville integral

Focusing on the issues of failing to pinpoint the edge information accurately and lacking texture detail of image by using integer order differential or 0-1-order fractional differential mask operators in digital image processing, a new 1-2-order edge detection operator based on Laplacian operator was proposed. Deduced from the definition of Riemann-Liouville (R-L),the 1-2-order fractional differential had the advantage in enhancing high-frequency signal and reinforcing medium frequency signal. The simulation results demonstrate that the proposed operator can take an higher recognition rate on the subjective recognition, and it's better at extracting the edge information, especially for the image with rich texture detail in the smooth region with little change of gray scale. Objectively, the integrated location error rate is 7.41% which is less than that of integer order differential operators (a minimum of 10.36%) and 0-1-order differential operator (a minimum of 9.97%). Quantitative indicators show the new fractional operator can effectively improve the positioning accuracy of the edge, and the proposed operator is particularly suitable for edge detection with high frequency information.