液晶与显示, 2012, 27 (1): 121, 网络出版: 2012-02-13
分数阶微分在图像纹理增强中的应用
Fractional Differential and Its Application in Image Texture Enhancement
摘要
为了实现对模糊图像边缘及纹理的增强,使图像的细节信息更加清晰,需要对图像进行锐化增强。现有的增强方法一般是整数阶微分锐化及高通滤波,由于这些方法的处理效果仍不理想,文中引入了分数阶微分算子。分数阶微分不仅可以很好地增强图像的边缘和纹理信息,还可以保留平滑区域信息,抑制较大噪声。研究并分析了Tiansi分数阶微分算子的原理及特点,并对其进行了改进,提出了一种新的分数阶微分算子,可以更好地增强图像的边缘和纹理信息,同时保证图像的亮度不产生大幅度变化,而且可以抑制较小噪声的影响。从定量的角度分析,改进的分数阶微分算子的平均梯度最大可比原图像提高3.8倍。从而验证了改进的分数阶微分算子比整数阶微分算子如Laplace算子及Tiansi分数阶微分算子具有优越性,且算法简单易于实现,可应用于工程中的实时图像处理系统中。
Abstract
In order to enhance the edge and texture of the blurred image, making the details clearer, it is need to sharpen the image edge. The existing enhancement methods are integer-order differential sharpening and high-pass filter. As the enhanced effect of these methods is still not ideal, this paper introduces fractional differential operator. Fractional differential operator can greatly enhance the image edges and the texture details, can retain the smooth region information non-linearly and avoid large noise. The principle and the advantages and disadvantages of Tiansi fractional differential operator is studied and analyzed. This paper propose a new fractional differential operator, which can enhance the image edge and texture details better, while ensuring the image brightness balanced, and inhibiting the small noise. From the quantitative point of view, the average gradient of this improved fractional diffe-rential operator increases 3.8 times than original image. It verifies that the improved fractional differential operator has an advantage over the integer-order differential operator such as the Laplace operator and Tiansi fractional differential operator. And the algorithm is simple and easy to implement. It can be used for engineering applications in real-time image processing system.
赵建. 分数阶微分在图像纹理增强中的应用[J]. 液晶与显示, 2012, 27(1): 121. ZHAO Jian. Fractional Differential and Its Application in Image Texture Enhancement[J]. Chinese Journal of Liquid Crystals and Displays, 2012, 27(1): 121.