Image Enhancement Using Adaptive Fractional Order Filter

Image enhancement is an important preprocessing task as the contrast is low in most of the medical images,Therefore,enhancement becomes the mandatory process before actual image processing should start.This research article proposes an enhancement of the model-based differential operator for the images in general and Echocardiographic images,the proposed operators are based on Grunwald-Letnikov(G-L),Riemann-Liouville(R-L)and Caputo(Li&Xie),which are the definitions of fractional order calculus.In this fractional-order,differentiation is well focused on the enhancement of echocardiographic images.This provoked for developing a non-linear filter mask for image enhancement.The designed filter is simple and effective in terms of improving the contrast of the input low contrast images and preserving the textural features,particularly in smooth areas.The novelty of the proposed method involves a procedure of partitioning the image into homogenous regions,details,and edges.Thereafter,a fractional differential mask is appropriately chosen adaptively for enhancing the partitioned pixels present in the image.It is also incorporated into the Hessian matrix with is a second-order derivative for every pixel and the parameters such as average gradient and entropy are used for qualitative analysis.The wide range of existing state-of-the-art techniques such as fixed order fractional differential filter for enhancement,histogram equalization,integer-order differential methods have been used.The proposed algorithm resulted in the enhancement of the input images with an increased value of average gradient as well as entropy in comparison to the previous methods.The values obtained are very close(almost equal to 99.9%)to the original values of the average gradient and entropy of the images.The results of the simulation validate the effectiveness of the proposed algorithm.

Fractional differential approach to detecting textural features of digital image and its fractional differential filter implementation

This paper mainly discusses fractional differential approach to detecting textural features of digital image and its fractional differential filter. Firstly, both the geo- metric meaning and the kinetic physical meaning of fractional differential are clearly explained in view of information theory and kinetics, respectively. Secondly, it puts forward and discusses the definitions and theories of fractional stationary point, fractional equilibrium coefficient, fractional stable coefficient, and fractional grayscale co-occurrence matrix. At the same time, it particularly discusses frac- tional grayscale co-occurrence matrix approach to detecting textural features of digital image. Thirdly, it discusses in detail the structures and parameters of nxn any order fractional differential mask on negative x-coordinate, positive x-coordi- nate, negative y-coordinate, positive y-coordinate, left downward diagonal, left upward diagonal, right downward diagonal, and right upward diagonal, respectively. Furthermore, it discusses the numerical implementation algorithms of fractional differential mask for digital image. Lastly, based on the above-mentioned discus- sion, it puts forward and discusses the theory and implementation of fractional differential filter for digital image. Experiments show that the fractional differential-based image operator has excellent feedback for enhancing the textural details of rich-grained digital images.