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.