G-L fractional differential operator modified using auto-correlation function: Texture enhancement in images

Abstract

Texture plays an important role in the low-level image analysis and understanding in the field of computer vision. Texture based image enhancement is very important in many applications. In order to attain texture enhancement in images, a modified version of the Grunwald-Letnikov (G-L) definition based fractional differential operator is proposed in this paper. Considering the G-L based fractional differential operator’s basic definition and implementation, a filter is devised and its applicability for texture enhancement is analyzed. Subsequently, the filter is modified by considering the auto-correlation effect between pixels in a neighborhood. Experiments are carried out on a number of standard texture-rich images and it is proved that the modified filter enhances the image contrast by nonlinearly enhancing the image textural features. In addition, the texture enhancement is quantitatively proven by a few Gray Level Co-occurrence Matrix (GLCM) measures, such as contrast, correlation, energy and homogeneity. Their % of Improvement is discussed in detail and the substantial improvement attained by the modified G-L FD operator over the basic G-L FD operator is well proved.