A Variable Order Fractional Differential-Based Texture Enhancement Algorithm with Application in Medical Imaging

Texture enhancement is one of the most important techniques in digital image processing and plays an essential role in medical imaging since textures discriminate information. Most image texture enhancement techniques use classical integral order differential mask operators or fractional differential mask operators using fixed fractional order. These masks can produce excessive enhancement of low spatial frequency content, insufficient enhancement of large spatial frequency content, and retention of high spatial frequency noise. To improve upon existing approaches of texture enhancement, we derive an improved Variable Order Fractional Centered Difference (VOFCD) scheme which dynamically adjusts the fractional differential order instead of fixing it. The new VOFCD technique is based on the second order Riesz fractional differential operator using a Lagrange 3-point interpolation formula, for both grey scale and colour image enhancement. We then use this method to enhance photographs and a set of medical images related to patients with stroke and Parkinson’s disease. The experiments show that our improved fractional differential mask has a higher signal to noise ratio value than the other fractional differential mask operators. Based on the corresponding quantitative analysis we conclude that the new method offers a superior texture enhancement over existing methods.

纹理增强是数字图像处理领域的核心技术之一，且在医学成像中发挥着不可或缺的作用——这是因为纹理携带着具有区分性的信息。现有多数图像纹理增强技术采用经典整数阶微分掩模算子（integral order differential mask operators），或是采用固定分数阶的分数阶微分掩模算子（fractional differential mask operators）。此类掩模往往存在三大问题：低频空间频率内容增强过度、大空间频率内容增强不足，且会保留高频噪声。为改进现有的纹理增强方法，本文提出一种改进的可变阶分数中心差分（Variable Order Fractional Centered Difference, VOFCD）方案，该方案可动态调整分数阶微分阶数，而非采用固定阶数。该新型VOFCD技术基于二阶里斯（Riesz）分数阶微分算子，并结合拉格朗日（Lagrange）三点插值公式，可同时适用于灰度图像与彩色图像的增强任务。随后，本文使用该方法对普通照片以及一组针对脑卒中与帕金森病患者的医学图像进行了增强处理。实验结果表明，相较于其他分数阶微分掩模算子，本文提出的改进型分数阶微分掩模拥有更高的信噪比（signal to noise ratio）。通过对应的定量分析，本文最终得出结论：该新型方法在纹理增强效果上优于现有各类方法。