A quaternion-based switching filter for colour image denoising
Introduction
Images are often contaminated by noise during acquisition, transmission, and storage, and which will significantly degrade the quality and accuracy of image processing. Therefore, it is of vital importance to restore the corruptions in the image before performing any subsequent procedures.
The method based on order statistics filters is used widely, which exploit the rank order information of the pixels in a filtering window. Such as vector median filter (VFM) [1], basic vector directional filter (BVDF) [2] and directional distance filter (DDF) [3]. Meanwhile, various modified vector median filters, such as the weighted median (WM) filter [4] and the fuzzy-rule-based median (FM) filter [5], have also been developed. The disadvantage of above vector median filters is that all pixels in colour image are treated equally. When pixels are noise-free, it will blur image details. And which results in undesirable distortions and also causes loss of valuable information from the image data.
To avoid the damage of noise-free pixels, some published papers suggested switching strategies. Adaptive vector median filter (AVMF) [6], fast peer group filter (FPGF) [7] and vector lower–upper–middle smoother (VLUM) [8], [9] are widely used for impulse noise removal by certain switching scheme. Based on these switching vector filters, many researchers have done a great number of studies, and which are classified as: (1) improving noise detection: noise detection by combining edge detection [9], noise detection based on cellular automata (CA) [10], [11] and noise detection based on histogram [12], [13] etc. (2) improving filtering algorithm: adapted switching vector filters [14], [15], [16], iterated switching filters [17] and switching filters based on fuzzy or optimization theory [18], [19], [20]etc. for example, a system using particle swarm optimization, and support vector regression is presented to design a median-type filter with a 2-level impulse detector for image enhancement [21]. It proposes an adaptive fuzzy inference system based impulse detection method for the restoration of images [22], [23]. An efficient approach to detect the impulse noise from the corrupted image using feed forward neural network (FFNN) is presented [24]. (3) Improving algorithm based on colour transform: vector filter by CIELAB colour transform [25]and improving filter by using Quaternion theory to transform [26], [27] etc.
To improve the filtering results, this paper has proposes a RGB colour image as a pure quaternion form. We use the quaternion-based distance to measures differences between two colour pixels. It can discriminate pixels exactly. And then, an efficient two-stage impulse detector is presented. The noisy pixels are replaced by using VMF and the noise-free ones are unchanged. Finally, to remove Gaussian noise, we combine quaternion-based switching filter (QSF) and non-local means (NLM) filter. It is demonstrated that the proposed filter performs impressively in noise suppression and edge preservation.
The remaining work is arranged as follows. In Section 2, we briefly review related works. Section 3 states basic principles for the proposed method. In Section 4, the experimental results and performance comparisons between the proposed method and other filtering techniques are reported. Finally, conclusions are drawn in Section 5.
Section snippets
Related works
Quaternion was discovered by Hamilton in 1843 [28]. A quaternion q is a four-dimensional number, which consists of one real part and three imaginary parts. And it is usually represented in the following algebraic form (Eq. (1)).where a, b, c, and d are real coefficients. And i, j, and k are complex operators that satisfy the following rules (Eq. (2)).
The modulus and conjugate of quaternion q are defined respectively as follows (Eq. (3)).
Quaternion-based distance of colour image
From the relate work, the pure quaternion form of colour pixel is , Given the colour pixels and , we can obtain the difference of colour pixels (Eq. (11)). Quaternion represents the colour pixel difference between and .
When the intensity values of and are similar, approaches zero. When the intensity values of and are large, is large. The proposed method employs quaternion-based
Experiments and results
We choose some colour images obtained in actual experiments to assess the performance of our algorithm. The execute time (in seconds) is measured on a desktop personal computer with 2.0 GHz CPU and 1.0 G RAM by using Matlab7.0. In order to evaluate both the noise suppression and detail preservation capabilities of the proposed filter, the peak signal-to-noise ratio (PSNR), the normalized mean square error (NMSE) and the mean square error (MSE) are used to measure the distortion between two colour
Conclusions
This paper presents a novel quaternion switching filter for suppression of noise in colour images. The proposed method identifies the difference between two colour pixels based on the quaternion unit transform. In noise-detection, we design a two-stage noise detection method to determine the noise pixels with higher accuracy and efficiency. To remove mixture noise effectively, we combine QSF and NLM. The extensive experimental results have shown that the proposed method can overcome some of
Acknowledgements
This research work is supported by the Science Foundation of Hubei University of Technology in China under Grant no. BSQD13028 and BSQD12118. The authors gratefully acknowledge Dr. L.J. Spreeuwers, Chair for Biometric Pattern Recognition Services at Cyber Security and Safety Group of University of Twente, and Dr. Lixin Fan, Principal Scientist at Nokia Research Center, for their constructive comments and suggestions.
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