Quaternion switching filter for impulse noise reduction in color image

Abstract

A novel approach to impulse noise reduction in color image is introduced in this paper. By applying the quaternion unit transform theory, the difference between two color pixels can be represented in the quaternion form. Based on the difference mentioned above, an efficient filter that can switch between the vector median filter (VMF) and the identity filter (no filtering operation) is proposed. Extensive simulation result indicates that the proposed filter achieves a trade-off between noise suppression and detail preservation in both correlated and uncorrelated impulse noise scenarios when compared with other widely used filters. Furthermore, the computational complexity analysis shows that the proposed filter is quite efficient.

Introduction

Color images are often corrupted by impulse noise due to malfunctioning sensors, faulty memory locations in the hardware, aging of the storage material or transmission errors [1], [2]. Although the traditional impulse noise reduction method in gray scale images can be applied to filtering the color channels separately, satisfactory results cannot be obtained due to the correlation of different channels. Many researches have shown that the nonlinear vector filtering technique, which treats the color sample pixels as three-dimensional vectors in RGB color domain, is more appropriate to suppress the color impulse noise [3]. One of the most important classes of nonlinear vector filters is based on the order-statistic theory, such as the vector median filter (VMF) and its extensions [4], [5], [6], [7], [8], [9]. By means of a suitable distance to measure the similarity between two color vectors, these filters replace the center pixel of a filtering window with a vector median and produce a robust performance. Besides the widely used Euclidean distance, many other distances or similarity measures can be employed in this class of filters, such as the Cosine distance, various fuzzy metrics and so on [10], [11], [12]. The main weakness of the traditional vector median filters is the loss of image details because the filters modify every pixel in the image regardless whether it is corrupted or not. One solution to this problem is to appropriately modify the distances by weighting coefficients to perform a weighted vector median operation. The filters based on this strategy produce much better results because it takes into account the importance of the specific samples in the filtering window [13], [14], [15], [16], [17]; however, these filters also process every pixel including the ones that are not corrupted by noise.

To avoid damage of noise-free pixels, a switching strategy, which detects the corrupted pixels is carried out before noise removal. If the pixel is detected as noise, it is replaced by the output of VMF or other filters; otherwise, it remains unchanged. Based on this strategy, many switching filters have been proposed, such as the adaptive vector median filter (AVMF) [18], the robust switching vector median filter (RSVMF) [19], the adaptive center-weighted vector median filter (ACWVMF) [20], [21], the class of vector sigma filters [20], [22], and so on. To decrease the number of misclassified pixels, several improved noise detection techniques have been presented recently. In [1], [23], [24], [25], [26], the switching filters based on the peer group technique are introduced. In [27], a fast similarity-based vector filter (FSVF) is proposed based on the concept of similarity between pixels and non-parametric estimation. In [28], [29], the fuzzy rank-ordered differences filter (FRF) and the improved FSVF are presented, which take advantage of the fuzzy metrics to detect noisy pixels. As an extension of two-dimensional complex numbers to four dimensions, the quaternion theory has been applied in color image processing [30], [31], [32]. In [33], [34], [35], three quaternion-based switching filters are introduced for impulse noise reduction. In conclusion, various switching filters have been proposed; however, the new distance measure and noise detection techniques are still being studied for higher detection accuracy.

To improve the filtering results, this paper introduces a switching filter based on the quaternion theory. We represent a RGB color image as a pure quaternion form and measure both the intensity and chromaticity differences between two color pixels with the quaternion unit transform. Then we define a novel color pixel distance as the summation of the intensity and chromaticity differences. Consider a 3×3 filtering window, we calculate the color pixel differences in four directions and determine the center pixel to be noisy if the minimum of the four differences exceeds a threshold. This detection step is employed to determine the real noisy pixels and preserve the noise-free ones on the edges. Finally, the noisy pixels are replaced by the VMF output and the noise-free ones are unchanged.

This paper is organized as follows. In the next section the basic knowledge and applications of quaternions are introduced. In Section 3 the new switching filter based on the quaternion theory is presented. Experiments are carried out in Section 4 to assess the proposed filter and compare it with other widely used filters. Finally conclusions are drawn in Section 5.