An adaptive approach for texture enhancement based on a fractional differential operator with non-integer step and order

• Design of a novel non-regular self-similar support region to exclude pixels with low correlation.
• Adoption of non-integral pixel steps to maximally exploit the inherently high degree of self-similarity in texture patterns.
• Introduction of a new adaptive fractional order selection mechanism to deal with complex texture patterns.
• Design of a non-regular fractional differential operator mask to perform image texture enhancement.

Image texture enhancement is an important topic in computer graphics, computer vision and pattern recognition. By applying the fractional derivative to analyze texture characteristics, a new fractional differential operator mask with adaptive non-integral step and order is proposed in this paper to enhance texture images. A non-regular self-similar support region is constructed based on a local texture similarity measure, which can effectively exclude pixels with low correlation and noise. Then, through applying sub-pixel division and introducing a local linear piecewise model to estimate the gray value in between the pixels, the resulting non-integral steps can improve the characterization of self-similarity that is inherent in many image types. Moreover, with in-depth understanding of the local texture pattern distribution in the support region, adaptive selection of the fractional derivative order is also performed to deal with complex texture details. Finally, the non-regular fractional differential operator mask which incorporates adaptive non-integral step and order is constructed. Experimental results show that, for images with rich texture contents, the effective characterization of the degree of self-similarity in the texture patterns based on our proposed approach leads to improved image enhancement results when compared with conventional approaches.