A Switching Bilateral Filter for Images with Edge Preservation Properties

V.Jayaraj Digital Signal Processing Lab,

Department of ECE, Sri Krishna College of Engg. & Tech

Coimbatore, Tamilnadu, India jayarajmevlsi@gmail.com

D.Ebenezer Digital Signal Processing Lab,

Department of ECE, Sri Krishna College of Engg. & Tech

Coimbatore, Tamilnadu, India

N.Krishna Prakash Department of EEE,

Sri Krishna College of Engg. & Tech Coimbatore, Tamilnadu, India

nkrishnaprakash@rediffmail.com

Abstract— In this paper, we propose a Switching Bilateral Filter for universal noise removal. The algorithm contains two stages: detection followed by filtering. We propose a new scheme called as Quadrant Median Vector, which contains important features like edges and fine details. The Quadrant Median Vector is utilized to allocate a Reference Median which is in turn compared with a current pixel to classify it as impulse noise, Gaussian noise, or noise-free. The proposed switching bilateral filter removes both Gaussian and impulse noise without using additional weighting function. The range filter inside the bilateral filter switches between the Gaussian and impulse modes depending on the noise classification result. Simulation results show that our noise detector has a high noise detection rate as well as a high classification rate for salt-and-pepper, uniform impulse noise and mixed impulse noise. In addition, the computational complexity of SBF is significantly less than that of other mixed noise filters.

Keywords — Non-linear Filters, Switching Bilateral Filter, Quadrant Median Vector, Reference Median, Universal filter, Gaussian noise, Impulse noise.

I. INTRODUCTION Noise is introduced into images during acquisition, signal

amplification and transmission. An important problem of image processing is to effectively remove noise from an image while keeping its features. The solution depends on the type of noise added to the image. Fortunately, two noise models can be used to represent most noise in images: additive Gaussian noise and impulse noise. Additive Gaussian noise is characterized by adding to each image pixel a value with a zero-mean Gaussian distribution. Such noise is usually introduced during image acquisition. The zero-mean distribution property allows such noise to be removed by averaging pixel values locally. Gaussian noise removal involves smoothing pixels inside distinct regions of an image with the side effect of blurring edges and details significantly. To solve this problem, non-linear methods, that utilize local measures such as weighting to smooth the noise in the image, have been proposed, e.g., the bilateral filter by Tomasi and Manducci[1]. Alpha-Trimmed mean (ATMF) filter is useful for the multiple types of noise such as the combination of salt-and-pepper and Gaussian noise. But its efficiency is low. Alpha-Trimmed Midpoint (ATMP) [2] filter is recognized as a good compromise between the midpoint [3], Mean and median filters. Several existing algorithms remove impulse noise or gaussian noise separately But none of the

above-mentioned algorithms remove mixed noise without increasing the, computational complexity. Impulse noise is characterized by replacing a portion of an image’s pixel with noise values leaving the remainder unchanged. Such noise is introduced due to transmission errors. Tomasi and Manducci’s bilateral filter cannot adequately remove such noise because the difference between the noise pixel and surrounding pixels surrounding it is too large. Therefore, local weighting is too small to change the noise value. Thus, separate classes of non-linear filters have been developed specifically for removing impulse noise such as extensions of the median filter rank statistics and the learning algorithm[4] - [16]. The common idea among these filters is to detect impulse pixels and replace them with estimated values, while leaving the remaining pixels unchanged. Filters that can remove Gaussian or impulse noise, or any mixture thereof, have also been proposed [17].

In this paper, we propose a universal noise removal filter based on the detect and replace methodology. To detect noise, the absolute difference between a current pixel value and the reference median is computed. If the absolute difference is large, then the current pixel is considered as impulse or Gaussian noise. On the other hand, when the absolute difference is small, the current pixel may be considered as noise-free. It is very important to find a proper reference median in the window, because a non-proper one would lead to false detection. In order to find the proper reference median, we have to understand properties such as edge or texture in the current window. We define a Quadrant Median Vector (QMV) and present an approach to recognize edge and texture. Based on the edge content in the window, a proper reference median can be selected. To achieve good visual image quality, it is important that the estimator not only replaces noisy pixels but also preserves the edge. The bilateral filter can achieve this, but it cannot remove impulse noise. We, therefore, propose a Switching Bilateral Filter (SBF) for removing both Gaussian and impulse noise. From the noise classification result in the noise detector, SBF switches between the Gaussian and impulse modes. SBF shows very good results in removing salt-and-pepper, uniform impulse and Gaussian noise. It efficiently removes both types of mixed noise, salt-and-pepper with uniform impulse noise and salt and pepper with Gaussian noise.

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II. QUADRANT MEDIAN VECTOR NOISE DETECTION SCHEME Existing two-state noise detectors fail in several

conditions when a portion of the pixels in an image is contaminated with impulse noise. For example, when the number of pixels with impulse noise is equal to or larger than half of the size of a processing window, the median of the processing window falls to the value of the impulse noise. One of the reasons that previous approaches fail to detect these cases is because the processing window size is too small to process information to distinguish texture or noise. For images with fine details, a processing window of size 3 X 3 may fail to distinguish between noise and detail. For a larger window size, such as 5 X 5, the resulting median value drifts from the median value of a small-size window because new textures are added into the larger window. Using a median value from a larger window may cause false noise detection and blur the image during filtering.

To overcome the previous problems, we propose a Quadrant Median Vector scheme (QMV). We start from a larger window but observe medians from sub-windows in the larger one. The medians in the sub-windows are sorted and the result vector is called QMV, and it reveals edge and texture information in the larger window. With the median values in the sub-window and edge/texture information in the larger window, the median drifting problem in the larger window or lack of texture information problems can be avoided. For a window Q0 with size (2N + 1) X (2N + 1), we divide the window into four sub-windows of size (N +1) X (N +1), with the central pixel as the corner pixel in the four sub-windows (N = 2). Let xi,j be the luminance of the central pixel located at the position (i, j) in a window. Then, the set of elements in a window can be expressed as Z=xi+s, j+t; ; -N<S<N ,-N<t<N (3) The pixels in the four sub-window blocks of the size (N +1) X (N+1) are defined as Z1 = xi+s,j+t ; 0 < s < N, 0 < t < N Z2 = xi+s,j+t ; -N < s < 0, 0 < t < N (4) Z3 = xi+s,j+t ; -N < s < 0, -N < t < 0 Z4 = xi+s,j+t ; 0 < s < N, -N < t < 0

In the following discussion, we assume N = 2 and the window size is 5 X 5, with its four quadrant blocks of size

3 X 3. Each quadrant block has a median value expressed as Mp = median(Zp); p = 1 to 4

Let M1, M2, M3, and M4 denote the medians of the sub blocks 1,2,3 &4 sub block 1 is on top right, sub block 2 is on top left, sub block 3 is on bottom left, and sub block 4 is on bottom right. These four median values Mp are sorted in ascending order and the QMV is defined as QMV = [QM1; QM2; QMV3; QM4] (5) where, QM1, QM2, QM3, and QM4 are the medians M1, M2, M3, and M4 sorted in an ascending order such that

QM1 < QM2 < QM3 < QM4.

A. Reference Median After sorting the medians of the four sub-windows, some

of the median values are very similar while others are different, leading to the formation of clusters. The clusters of QM1 , QM2, QM3 and QM4 and the order of the four medians M1 ,M2,M3 and M4, which are mapped in to the clusters, include important features of the windows such as edge details. When the number of medians inside a cluster is more than that inside other clusters, the cluster with the most number of medians represents the majority feature in this window. This cluster is defined as a major cluster and the average of QM2 and QM3 is used as the reference median value for comparison. When the difference between the current pixel value and the reference median in the major cluster is large, then the current pixel is not similar to the majority of the block and is very likely to be a noise pixel. To determine the cluster distribution, we define QMDB as the difference between the two boundary values (the maximum and minimum) of the sorted medians.

QMDB = QM4 - QM1 (6) In addition, QMDC is defined as the difference between the two center values of the sorted quadrant medians.

QMDC = QM3 - QM2 (7) QMDB and QMDC provide a measure of the similarity between the four quadrant blocks. Based on the information of QMDB and QMDC, the edge details can be obtained. Let avg represents the average value of the four median values Mp. avg=(QM1+ QM2+ QM3+ QM4)/4 (8) The Reference Median (RM) is defined as RM= ( QM2+QM3)/2 QMDC ≤ ρ = QM3 QMDC > ρ and avg > QM3 = QM2 QMDC > ρ and avg > QM2 Where ρ is a threshold parameter whose value is set to 40.

B. Noise Detector Design A noise detector is used in the proposed filter to determine

whether or not the current pixel is corrupted. This decision is made using the features of QMV, which can show the property of the background and is more reliable than only one median value. We obtain the reference median for noise identification from QMV. If the reference median is wrong or not proper, it can lead to lost detection or over detection. The lost noisy pixels have a great negative effect on the results and the undesired filtering removes the details. When a current pixel is very different from the reference median, it is identified as an impulse noise. When the difference between the current pixel and reference median is not too much, it may be a Gaussian noise or a noise-free pixel. Because the image background can give four different QMV values, the reference median can be selected from QMV. The decision making mechanism is realized by employing a reference median and two thresholds Tk1 and Tk2. The noise detection algorithm is as follows If │x i, j - RM│ ≥ Tk1

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x i, j is corrupted by Impulse noise Else If │ x i, j - RM│ ≥ Tk2 x i, j is corrupted by Gaussian noise Else x i, j is noise free Tk1 and Tk2 are thresholds for identifying impulse noise or Gaussian noise. From simulations on a large variety of images, excellent results were obtained using thresholds selected from the following set of values. The selection of [Tk1, Tk2] = [15 to 30, 4 to 25] yields satisfactory results in filtering uniform impulse and Gaussian noise.

III. BILATERAL FILTER The bilateral filter proposed by Tomasi and Manduchi is a

nonlinear filter which removes Gaussian noise while preserving edges. Each pixel is replaced by a weighted average of the intensities in the window. The weighting function gives high weighting to those pixels that are both near the central pixel and similar to the central pixel. Let x i, j be the current pixel, and x i+s, j+t be the pixels in a (2N + 1) X (2N + 1) window that surrounds x i, j. The output of bilateral filter yi, j is defined as follows

s N t N

G R i s , j ts N t N

s N t N

G Rs N t N

W ( s ,t )W ( s ,t )xy( i , j )

W ( s ,t )W ( s ,t )

= =

+ += − = −

= =

= − = −

=∑ ∑

∑ ∑ (9)

2 2)

G 2s

( s ( j )W ( s , t ) e x p2

− + −= −σ

(10)

i , j i s , j tR

R

2( x x )W ( s,t ) exp22

+ +−= −σ

(11)

The bilateral filter shows great results in removing Gaussian noise while keeping the edge, but it is difficult to remove impulse noise. Because the noisy pixel is very different from its neighbors, the surrounding weights are too small to change the noisy pixel in the range filter. In order to remove impulse noise and Gaussian noise using a bilateral filter, we propose a switching bilateral filter.

IV. PROPOSED SWITCHING BILATERAL FILTER In this section, we propose a new universal noise removal

algorithm: the Switching Bilateral Filter (SBF). Let x i, j be the current pixel, and let x i+s, j+t be the pixels in a (2N+1)X(2N+1) window surrounding x i, j . Finally, the output of SBF is defined as follows:

s N t N

G S R i s , j ts N t N

s N t N

G S Rs N t N

W ( s , t )W ( s , t ) xy ( i , j )

W ( s , t )W ( s , t )

= =

+ += − = −

= =

= − = −

=∑ ∑

∑ ∑

(12)

2 2)

G 2s

( s ( j )W ( s ,t ) exp2

− + −= −σ

(13)

2i s , j t

S R 2R

( P x )W ( s , t ) e x p2

+ +−= −σ

(14)

It is difficult for a bilateral filter to remove impulse noise

because the difference between the noisy pixel and its

neighbors is huge. This makes the radiometric weighting function too small to change the noisy pixel. By replacing x i, j with RM of the window in a bilateral filter, we can remove impulse noise without adding another weighting function. The difference between neighbors and median would not be too large, and thus, the edges and details can be preserved while removing the noise. Our proposed SBF provides a sharper image than a median filter. The experiments showed that SBFim function gives better noise removal results than the median function alone. The noise detector deals with a large number of Gaussian noise pixels and noise-free pixels, which cannot be always precisely identified. Therefore, SBFga has to be capable of keeping the details and edges in an image when noise is detected. Our proposed SBF removes not only Gaussian noise but also impulse noise while keeping the details and the edges.

A. Noise Detector Switching Scheme In the switching scheme, the noise detector searches for

noisy pixels in a corrupted image and tries to distinguish them from uncorrupted ones. The filter is applied to the noisy samples only, thus preventing blurred edges or removal of fine details. The most difficult part in the process is to accurately discriminate the noise from the image details. Two critical situations may occur; the image detail may be falsely treated as the noise and, therefore, filtered from the image; and the noisy pixel can be interpreted as the image detail and, thus, left unchanged. We propose an extension to the standard switching-scheme, which uses an additional detector to identify edge or detail in a current window. The noise detection is done in two stages. In this scheme, the reference median is used for noise identification. The noise detector also decides whether a current pixel should be filtered by using an SBF or whether it should bypass the SBF If │x i, j - RM│ ≥ Tk1 SW1=1 and SW2=1 (x i, j is corrupted by Impulse noise) Else If │x i, j - RM│ ≥ Tk2 SW1=1 and SW2=0 (x i, j is corrupted by Gaussian noise) Else SW1=0 andSW2=0 (x i, j is noise free)

V. RESULTS AND DISCUSSION Simulations are carried out to verify the noise removing

capability of the ASBF and the results are compared with several exiting filters. Images are mixed with noise at different densities for evaluating the performance of the algorithm. A quantitative comparison is performed between several filters and the proposed algorithm in terms of Peak Signal to Noise Ratio (PSNR), Mean Square Error (MSE), Mean Absolute Error (MAE), Image Enhancement Factor (IEF) and Mean Structure SIMilarity (MSSIM) Index Our method produced results superior to other methods in both visual image quality and quantitative measures.

The performance of the algorithm for Lena image for different noise is studied and results are shown in Figure.1. The quantities for comparison are defined as follows and Tables [I] – [V] display the quantitative measures.

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( )2P S N R 1 0 lo g 1 0 2 5 5 / M S E= (15)

( )M N 2

i j i ji 1 j 1

M S E1 r - y

M N = == ∑ ∑ (16)

M Ni j i j

i 1 j 1

1M AE |r - y |M N = =

= ∑ ∑ (17)

( )( )

M N 2ij ij

i 1 j 1M N 2

ij iji 1 j 1

x ? rIEF y ? r

= =

= =

∑ ∑

∑ ∑= (18)

( ) ( )yr 1 x y 2

2 2 2 2y yr 1 r 2

(2 μ μ + C ) (2 σ + C )SSIM ( r , y )

μ + μ + C σ + σ + C= (19)

G

p pp 1

1MSSIM ( R,Y ) SSIM ( r ,y )

G == ∑ (20)

rij is the original image, yij is the restored image, xij is the corrupted image. The simulation results show that our approach provides a visually appealing output. The proposed Adaptive Switching Bilateral Filter can restore an image

corrupted with mixed noise, which is demonstrated by two cases. A lena image is corrupted by uniform Gaussian noise of variance= 20 and salt and pepper noise of different noise densities from 10 % to 60 %. Fig. 1 shows the simulation results for lena .jpg image corrupted by Gaussian noise of variance 20 and impulse noise with noise density p=40%. The results of the proposed Switching Bilateral Filter (PA) are compared with Standard Median Filter (SMF), General Adaptive Median Filter (GAMF), Lins Adaptive Median Filter (LAMF), Progressive Switching Median Filter (PSMF), Decision Based Algorithm (DBA), Robust Estimation Algorithm (REA), Alpha Trimmed Mean Filter (ATMF), Bilateral Filter, Mean Filter and Wiener filter. Table [I]-[V] gives the quantitative measures for lena image. Fig. 2 shows the comparison graph of various quantitative measures of lena image.

a b c d e f g

h i j k l m

a b c

d e

Figure. 3 (a) Comparison graph of PSNR at different noise densities of lena image. (b) Comparison graph of MSE at different noise densities of lena image. (c) Comparison graph of MAE at different noise densities of lena image. (d) Comparison graph of IEF at different noise densities of lena image. (e) Comparison graph of MSSIM at different noise densities of lena image.

Figure. 2 Simulation results of different filters. (a) Original Lena.jpg image. (b) Corrupted image. (c) Output of SMF. (d) Output of GAMF. (e) Output of LAMF. (f) Output of PSMF. (g) Output of DBA. (h) Output of REA. (i) Output of ATMF. (j) Output of Bilateral Filter. (k) Output Mean filter. (l) Output of wiener Filter. (m) Output of PA.

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As for uniform impulse noise, the noise detection rate is

good up to 70% noise density. Compared with the original image, it is clear that the proposed Switching Bilateral Filter can eliminate noise while preserving the edge and fine details.

VI. CONCLUSION This paper proposes a new non-linear Switching Bilateral

Filter for detection and removal of mixed Gaussian and impulse noise. A new Quadrant Median Vector scheme is proposed for the detection of impulse and Gaussian noise. Many noise removal algorithms tend to treat impulse noise as edge pixels and end with unsatisfactory results. The proposed algorithm uses a new scheme called as Reference Median (RM) to process impulse noise and edge pixels differently. The Quadrant Median Vector scheme is incorporated in to Bilateral filter for replacing the corrupted pixel with a proper median value. The new filter is called Switching Bilateral Filter. The noise detector shows good performance in

identifying noise even in mixed noise models. The proposed filter has excellent performance in simultaneous removal of both impulse noise and Gaussian noise using the existing bilateral filter without adding another weighting function.

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