Image Processing, IEEE Transactions on - CiteSeerX

IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 12, NO. 1, JANUARY 2003

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Selective Removal of Impulse Noise Based on Homogeneity Level Information Gouchol Pok, Jyh-Charn Liu, and Attoor Sanju Nair

Abstract—In this paper, we propose a decision-based, signaladaptive median filtering algorithm for removal of impulse noise. Our algorithm achieves accurate noise detection and high SNR measures without smearing the fine details and edges in the image. The notion of homogeneity level is defined for pixel values based on their global and local statistical properties. The cooccurrence matrix technique is used to represent the correlations between a pixel and its neighbors, and to derive the upper and lower bound of the homogeneity level. Noise detection is performed at two stages: noise candidates are first selected using the homogeneity level, and then a refining process follows to eliminate false detections. The noise detection scheme does not use a quantitative decision measure, but uses qualitative structural information, and it is not subject to burdensome computations for optimization of the threshold values. Empirical results indicate that our scheme performs significantly better than other median filters, in terms of noise suppression and detail preservation.

Fig. 1.

System flowchart of CSAM filtering.

TABLE I IDENTIFICATION OF NOISE FOR THE LENA IMAGE

Index Terms—Adaptive median filter, cooccurrence matrix, homogeneity level, impulse noise.

I. INTRODUCTION

M

EDIAN filter is a nonlinear filtering technique widely used for removal of impulse noise [2], [6], [10]. Despite its effectiveness in smoothing noise, the median filter tends to remove fine details when it is applied to an image uniformly. To address this drawback, a number of modified median filters have been proposed, e.g., minimum–maximum exclusive mean (MMEM) filter [7], prescanned minmax center-weighted (PMCW) filter [14], and decision-based median filters [4], [5], [8], [13]. In these methods, the filtering operation adapts to the local properties and structures in the image. In the decision-based filtering, for example, image pixels are first classified as corrupted and uncorrupted, and then passed through the median and identity filters, respectively. The main issue of the decision-based filter lies in building a decision rule, or a noise measure, that can discriminate the uncorrupted pixels from the corrupted ones as precisely as possible. In the method proposed by Han et al. [7], pixels that have values close to the maximum and minimum in a filter window of remaining pixels in the are discarded, and the average Manuscript received February 13, 2001; revised May 1, 2002. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Uday B. Desai. G. Pok is with the Department of Computer Science, Yanbian University, Yanji, China (e-mail: [email protected]). J.-C. Liu is with the Department of Computer Science, Texas A&M University, College Station, TX 77843 USA (e-mail: [email protected]). A. S. Nair is with the Department of Electrical Engineering, Texas A&M University, College Station, TX 77843 USA (e-mail: [email protected]). Digital Object Identifier 10.1109/TIP.2002.804278

TABLE II IDENTIFICATION OF NOISE FOR THE BRIDGE IMAGE

window are computed. If the difference between the center pixel exceeds a threshold, the center pixel is replaced by ; and otherwise, unchanged. Florencio et al. [5] proposed a decision measure, based on a second order statistic called normalized deviation DEV

(1)

where is the gray level of the center pixel , and and respectively are the mean and the standard deviation of gray levels in the horizontal ( ) and vertical ( ) nine-point window around . Without explicit classification of pixels, Wang [14] presented an iterative, center-weighted filtering method [9], in which the center weights and the window size adaptively increase with filtering iterations.

1057-7149/03$17.00 © 2003 IEEE

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(a) Fig. 2.

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Graphical representation of (a) cooccurrence matrix and (b) histogram P (I = 100; 1).

Fig. 3. Upper and lower bound of the PWD matrix shown in Fig. 2(a).

Kasparis et al. [8] presented an adaptive threshold selection method in which the threshold varies with the local average intensities. Two thresholds, corresponding to the “salt” and “pepper” components, are experimentally determined to optimize the trade-off between noise removal and detail preservation. In the adaptive scheme proposed by Sawant et al. [13], the difference of the noisy and the median-filtered image, and the difference of the noisy and the Gaussian-smoothed image were computed. The ratio of the two differences was used as a decision measure. Signal-dependent rank-order mean (SDROM) filter [1] uses a framework in which the filtering operation is conditioned on a state variable. The output is defined as a weighted sum of the signal value and the ROM value; the weighting coefficients being a function of the state variable are optimized on image training data. In the two-state approach, SDROM merely switches between the signal and the ROM values: 1 or 0. The rank-ordered mean is computed

by rank ordering pixels in a 3 3 window and computing where is the set of rank-ordered pixels. Two issues are involved in developing a decision process. Firstly, a decision measure should be defined, as a statistical parameter, to capture and represent the local property of the region. Secondly, a mechanism to compute a threshold value should be determined. If a decision measure does not reflect the local SNR measure, the performance of the decision-based filter depends on the values of a threshold, and thus one needs to optimize the thresholding. As observed in existing decision-based filters, however, threshold values optimized for high PSNR measures can lead to poor noise detection. In this paper, we propose a decision-based, signal-adaptive median filter that achieves nearly perfect detection of impulse noise, and superb visual quality for the restoration results. For identification of the noise, we propose the notion of homogeneity level, which is defined on the basis of the pairwise correlations between neighboring image pixels. The pairwise correlations are obtained by the cooccurrence matrix. Given a and pixel value , we compute the upper and lower bounds, for acceptable signal deviations from . In a filter window, the number of pixels that have the same and different homogeneity level classifications as the center pixel are denoted as and , respectively. The center pixel is considered a noise and , and . candidate if it is not in the range of Further steps will be applied to noise candidates to differentiate noise and signal using the local image structure. Finally, the median filter is applied only to the noisy pixels. Our scheme is highly accurate and robust in noise detection. Experimental results show that our scheme significantly outperforms other techniques for both objective (SNR) and subjective (visual perception) performance measures. The proposed scheme does not amplify the noise through iterations, making it a highly

POK et al.: SELECTIVE REMOVAL OF IMPULSE NOISE BASED ON HOMOGENEITY LEVEL INFORMATION

Fig. 4.

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Noise identification. (a) Lena image corrupted by 10% impulse noise; false detections at (b) first iteration; (c) second iteration; and (d) third iteration.

stable solution approach for noise filtering, and other similar applications. In the rest of this paper, we present the proposed algorithm in Section II, the experimental results in Section III, and summarize the paper in Section IV. II. CONDITIONAL SIGNAL-ADAPTIVE MEDIAN (CSAM) FILTER A decision-based median filter consists of two major functions: decision making and noise filtering. The first function is to determine presence of noise in a filter window, and the second to smooth the noise pixels. When necessary, as in our scheme, detection and filtering can be iteratively applied to the input image. The operation of median filters is straight-forward, that is, noise is replaced with the median of the pixels in the filter window. On the other hand, design of the decision-making process is much more complicated, since two pertinent issues,

defining a decision measure and searching for an optimal threshold value, must be adequately addressed to achieve robust noise detection. If a decision measure is defined so that the computation of a threshold does not involve the center pixel value, we have experimentally observed that a lot of noise were not detected with a high rate of false detection (see Tables I and II). The conditional signal-adaptive median (CSAM) filter, shown in Fig. 1, addresses these problems with a simple and robust decision-making scheme that can iteratively detect corrupted image pixels, with little visual quality loss, and at very high SNRs. A. Filter Design A signal-adaptive filter adapts its operation in accordance with local image characteristics. To represent local image char-

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Fig. 5. False detection of noise for the Lena image with Florencio’s method [5]. (a) 20% and (b) 30% impulse noise.

acteristics, we introduce the notion of homogeneity level that defines the acceptable range of deviations from a pixel value. Noise candidates are first determined using the homogeneity level, and then the candidates are further classified into signal and noise based on the structural information. We present details of the CSAM filtering algorithm next as shown in Fig. 1. Step 1) Calculation of the bounds of homogeneity level: for small For a pixel value , some deviations from (i.e., ) can be considered as homogeneous with . Homogeneity level associated with is represented by an interval with the and lower bound , so that any in upper bound is considered homogeneous with . More details on calculating the bounds are described in the next subsection. Step 2) Detection of impulse noise candidates: In a 3 3 window, we denote the center pixel as , and its eight neighbors . Let the value of be . For , let be the number of s that are homogeneous with , that is, , and be the number of the ones that are not. The is simple: if impulse noise detection decision rule for , is counted as signal, and otherwise as noise candidate. Let denote the set of noise candidate pixels, and be the set of , remaining pixels, which are mostly signals, we have where is the corrupted input image. Step 3) Refined selection of impulse noise: usually contains some falsely detected signals. To minimize the false detections, we use the following step to remove noise-free pixels from the noise candidate set , using a different filtering rule. These falsely detected image pixels mostly locate around the edges and fine details, e.g., see Figs. 4(b) and 6(b), and they can be characterized as high-frequency signals with low SNR measure. Based on this observation, we augment the analysis window to 5 5, so that edge information can be better presented in the analysis window. Then, pixels are divided into two groups; those homogeneous with , denoted by , and the remaining pixels. Now, , let be the number of s that belong to , and for all be the number of those that belong to . If , is

counted as signal and its membership is changed from to . does not This step is repeated until the number of pixels in decrease further. We note that this step is highly computational efficient, because it only applies to pixels in , which constitute of a small portion of the total image pixels. Step 4) Median filtering: We define the notion of an -neighborhood isolated pixel, which is essentially a noisy pixel with noisy pixels in its 3 3 kernel. To remove noise effectively, , 1, 2, are identified all -neighborhood isolated pixels, for and a median filter of window size 3 is applied to these pixels. A median filter of window size 5 is applied to the remaining noisy pixels. The choice of a window of size 5 for the later stage of median filtering is based on the fact that a median filter of size 3 will not be effective when there are more noisy pixels in the 3-neighborhood of the pixel in question. CSAM has highly robust, accurate performance in impulse noise detection. In our experiments, whose results are illustrated in Tables I and II, noise detection is nearly perfect for images corrupted by up to 20% to 30% of impulse noise. We further note that perfect identification of noise is essentially to an iterative filtering process. Otherwise, iterative filtering tends to amplify the noise effect and result in smeared image details [14]. Some intuitive observations may help understanding the behavior of CSAM. The first step is to calculate the acceptable “natural/normal” dynamic ranges of image pixels of natural images, i.e., the upper and lower bounds of the homogeneity levels for each pixel value of the image. We note that this is the global distribution of acceptable pixel values for any pixel location. Step 2) not only picks up isolated impulse noise, but also likely some edge points. Then, in the Step 3), by using a larger window we have a much better chance to identify the pixels located near or on the edges. Obviously, we will need to use a new decision rule to differentiate noise from normal signal. The iterative algorithm helps to correct false detections in each run. Such an observation, although not a formal proof, could be supported by the simulation results shown in Fig. 4(b) and (c).


Fig. 6.

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Noise identification. (a) Lena image corrupted by 30% impulse noise; false detections at (b) first iteration; (c) second iteration; and (d) third iteration.

B. Computing the Homogeneity Levels The homogeneity level of a pixel value is defined as the acceptable upper and lower bounds of deviations in a noise-free region. This is based on the simple observation on the fact that natural images can be well characterized by the Gaussian distribution. Impulse noise can be characterized as extremely large or small pixel values at isolated random locations, and thus they likely would locate beyond the homogeneity levels, except for certain sharp image features like edges. The two bounds are estimated from the global statistics of pairwise correlations between every pixel and its neighbors, by using the cooccurrence image under consideration has matrix. We assume that . In a 3 8-bit gray scale pixel resolution, that is, 3 window at , the center pixel is denoted as ,

and its neighbors as is defined as with respect to

where

if otherwise.

. The cooccurrence matrix

and

,

(2)

Note that and take integer values ranging from 0 to 255, represents a histogram. The histogram and for each , contains the global statistics about the pairwise correlations between a pixel and its neighbors, and from these statistics we can and for estimate the homogeneity levels. To determine

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Fig. 7. False detection of noise for the Lena image with Kasparis’s method (CMF) [8]. (a) 20% and (b) 30% impulse noise.

each , we first replace histogram entries for and , to avoid biased estimation of the global statistics. Then, we employ a simple technique that thresholds the moving averaged values in the tail regions as follows:

TABLE III COMPARATIVE RESTORATION RESULTS IN PSNR

(3)

(4)

where is a threshold. These equations simply search for the histogram slot where the 3-point moving average is less than , which indicates that most slots around it have small values. For most cases, a moving average window size of 3 and a threshold gave good results. The cooccurrence matrix obsize of tained from the 10% noisy Lena image is graphically shown in Fig. 2(a), in which the grayscale intensity of the each pixel location ( , ) represents the normalized occurrence count for , and its neighbors being . By normalization the value we mean that we divided each count value by the maximum of all, and multiple the result by 255. The calculated value is , we then printed as a pixel point on this graph. For to 255 in further plotted the cooccurrence counts for Fig. 2(b). One can see from these graphs that natural images have high locality, making it possible to differentiate them from and for the sharply isolated impulse noise. The bounds corresponding to the cooccurrence matrix in all Fig. 2(a) is shown in Fig. 3.

performance measures: false noise detection rate, quantitative measure such as PSNR and MAE, and perceptual gains. For the experiments, 8-bit 512 512 images, that are corrupted by 10%, 20%, and 30% of impulse noise, are used. The impulse noise is randomly generated as 0 or 255 with equal probability for all the pixels. A number of simulations were performed by varying the values of the parameters of each method, and only the best result of each compared method is described below. As performance measures, we used the peak signal-tonoise ratio (PSNR) and the mean absolute error (MAE) defined as

PSNR

MAE

III. EXPERIMENTAL RESULTS In this section, the proposed algorithm is evaluated and compared with other filtering techniques in terms of a number of

where

is the total number of pixels in an image.


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Fig. 8. Restoration results for (a) 10% and (b) 30% impulse noise Lena image, and (c) 10% and (d) 30% impulse noise bridge image.

One important characteristic of the CSAM filter is that it can detect almost all noise while false noise detection is very low, as illustrated in Figs. 4–7. In Tables I and II, “miss” refers to number of noisy pixels that were not detected, and “false-hit” refers to the number of signal pixels misclassified as noise. Compared with other techniques, the CSAM filter performs better in identifying the noisy pixels. It makes an iterative filtering scheme operate properly without the noise amplification effect. The CSAM filter also outperforms other techniques for the performance measured in PSNR and the perceptual quality. Referring to Table III, the proposed CSAM filter achieved signif-

icant improvement over other techniques, ranging from 2.3 dB to 8.3 dB in PSNR. IV. CONCLUSION In this paper, we presented a new framework for the removal of impulse noise in which filtering operation is selectively applied to the pixels that are classified as corrupted. The novel feature of the algorithm lies in introducing the notion of homogeneity level that is used for computing the signal-adaptive and flexible thresholds. In addition to that, structural information is also applied to maximize the true detection rate. We have shown experimentally that the proposed algorithm significantly outper-

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Fig. 9. Restoration results for (a) 10% and (b) 30% impulse noise Lena image for SDROM filter.

form a number of existing techniques. The gains are obtained in terms of the perceptual quality and the PSNR of the restoration results (see Figs. 8 and 9).

Gouchol Pok received the B.Sc. degree in mathematics from Yonsei University, Korea, in 1981, and the Ph.D. degree in computer science from Texas A&M University, College Station, in 1999. During 1984-1995, he was with Korea Development Institute (KDI), and during 1999-2000 he was a Postdoctoral Research Associate at Texas A&M University. Since 2001, he has been with Yanbian University of Science and Technology, Yanji, China, where he is now an Associate Professor. His research interests include image processing, pattern recognition,

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and neural networks.

Jyh-Charn Liu received thes Ph.D. degree from the Electrical Engineering and Computer Science Department, University of Michigan, Ann Arbor, in 1989. He is Associate Professor with the Computer Science Department, Texas A&M University, College Station. He joined Texas A&M University as Assistant Professor in 1989, and became tenured Associate Professor 1995. He specializes in the area of image processing, real-time computing, and network security. He is also involved with development of large scale information systems, telemedicine technologies, and imagery database. He is actively involved in different professional activities, conference organizations, and he has extensive outreach to professional communities.

Attoor Sanju Nair received the undergraduate degree in electronics and communication engineering from PSG College of Technology, India, and is currently pursuing the M.S. degree in electrical engineering at Texas A&M University, College Station. His research interests include pattern recognition and image processing.