Abstract

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.

1. Introduction

Image texture enhancement aims to improve the quality of an image by modifying its attributes. A number of cutting-edge techniques have been proposed which can be divided into two categories: transform-based [1] and spatial domain-based [2]. Transform-based methods regulate coefficients associated with the frequency domain, followed by an inverse transform to obtain the resulting image, based on which image enhancement can be achieved. However, these methods may introduce ringing effect and additional noise. On the other hand, spatial domain-based methods can avoid these problems without the need to perform frequency domain transform, resulting in less computation. Among the different enhancement approaches, the differential mask operator stands out as a particularly important example. Differential operator masks can be further categorized as integral differential and fractional differential operators. As for image improvement, most integral-differential operators (e.g., Sobel, Prewitt, and Laplacian of Gaussian operators) behave well when used for enhancing high-frequency features. Nevertheless, their performance deteriorates significantly when applied to smooth regions.

4. Conclusion

In this paper, we have proposed an adaptive fractional differential operator mask for image enhancement. Through the identification of the main limitations of the previous fractional derivativebased methods, we obtain better performance by introducing a non-regular support region, and adaptively determining the associated fractional order such that the high degree of self-similarity in most images could be judiciously taken into consideration. In view of the capability of our proposed approach in enhancing important details of a large variety of image types, we shall further apply the algorithm as a pre-processing step to different areas such as object recognition and biometric analysis.