Gaussian Noise Filter

IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 19, NO. 9, SEPTEMBER 2010 2307

Switching Bilateral Filter With a Texture/NoiseDetector for Universal Noise Removal

Chih-Hsing Lin, Jia-Shiuan Tsai, and Ching-Te Chiu

Abstract—In this paper, we propose a switching bilateral filter(SBF) with a texture and noise detector for universal noise removal.Operation was carried out in two stages: detection followed byfiltering. For detection, we propose the sorted quadrant medianvector (SQMV) scheme, which includes important features such asedge or texture information. This information is utilized to allo-cate a reference median from SQMV, which is in turn comparedwith a current pixel to classify it as impulse noise, Gaussian noise,or noise-free. The SBF removes both Gaussian and impulse noisewithout adding another weighting function. The range filter in-side the bilateral filter switches between the Gaussian and impulsemodes depending upon the noise classification result. Simulationresults show that our noise detector has a high noise detection rateas well as a high classification rate for salt-and-pepper, uniformimpulse noise and mixed impulse noise. Unlike most other impulsenoise filters, the proposed SBF achieves high peak signal-to-noiseratio and great image quality by efficiently removing both typesof mixed noise, salt-and-pepper with uniform noise and salt-and-pepper with Gaussian noise. In addition, the computational com-plexity of SBF is significantly less than that of other mixed noisefilters.

Index Terms—Gaussian noise, image restoration, impulse noise,mixed noise, nonlinear filters, switch bilateral filter, switchingscheme.

I. INTRODUCTION

N OISE is introduced into images during acquisition, signalamplification and transmission [6], [27]–[31]. An impor-

tant problem of image processing is to effectively remove noisefrom an image while keeping its features. Noise removal is a dif-ficult task because images may be corrupted by different typesof noise, such as additive, impulse or signal dependent noise[27]–[29]. The solution depends upon the type of noise addedto the image [28]–[30]. Linear filtering possesses mathematicalsimplicity and offers satisfactory performance on images withadditive Gaussian noise [29]–[31]. However, linear techniquesblur edges and fail for non-Gaussian and/or impulse noise. This

Manuscript received September 02, 2009; revised March 02, 2010; acceptedMarch 20, 2010. First published April 08, 2010; current version published Au-gust 18, 2010. The associate editor coordinating the review of this manuscriptand approving it for publication was Prof. Kiyoharu Aizawa.

C.-H. Lin is with the Institute of Communications Engineering, NationalTsing-Hua University, Hsinchu, Taiwan. R.O.C. (e-mail: [email protected]).

J.-S. Tsai is with the Department of Computer Science, National Tsing-HuaUniversity, Hsinchu, Taiwan, R.O.C. (e-mail: [email protected]).

C.-T. Chiu is with the Department of Computer Science and Instituteof Communications Engineering, National Tsing-Hua University, Hsinchu,Taiwan, R.O.C. (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIP.2010.2047906

disadvantage leads to the use of nonlinear filtering in image pro-cessing [29]–[31].

In this paper, we propose a filtering scheme that can removeboth the additive Gaussian noise and the impulse noise. Addi-tive Gaussian noise is characterized by adding to each imagepixel a value with a zero-mean Gaussian distribution [6], [27].Such noise is usually introduced during image acquisition [27].The zero-mean distribution property allows such noise to beremoved by averaging pixel values locally [27]. Traditionallinear filters can remove noise effectively but with the sideeffect of blurring edges and details significantly [6], [31],[32]. The more advanced methods for noise removal aim atpreserving edges and details in images while removing thenoise [25], [32]. Tomasi and Manduchi propose a bilateral filterthat uses weights based upon spatial and radiometric similarity[1]. The bilateral filter has good results in removing noise whilepreserving edges in images [1], [32]. In addition, this methodis noniterative, local and simple [1], [32].

Impulse noise is characterized by replacing a portion ofan image pixels with noise values, leaving the remainder un-changed [29]. Such noise is introduced due to acquisition ortransmission errors [27], [29], [30]. Nonlinear filters have beendeveloped for removing impulse noise such as the traditionalmedian filter [29]. Extensions of the median filter [2], [5],[14]–[21], [23], [24], [26] are proposed to meet various criteria,e.g., robustness, preservation of edge, or preservation of details.The learning algorithm [7] and the switching noise filters[14], [16], [17], [19], [22]–[24], [26] are also proposed. Thegenetic programming (GP) filter [7] is based upon the learningalgorithm that is used to build two detectors, and this methodrequires a training procedure to arrive at an optimal classifi-cation based upon the measure of pixels and their neighbors.Methods that require training are less easily controlled andmore unpredictable than traditional methods. The switchingscheme detects impulse noise pixels before filtering and re-places them with estimated values while leaving the remainingpixels unchanged [14], [16], [17], [19], [22]–[24], [26].

Filters that can remove Gaussian or impulse noise, or anymixture thereof, have also been proposed [3], [4], [6], [8]–[11],[13]. The median-based signal-dependent rank ordered mean(SDROM) filter can remove impulse noise rather effectively, butwhen applied to images with Gaussian or mixed noise, it oftenproduces a visually disappointing output [8]. This is becausethe rank-ordered mean gets corrupted in a high noise inten-sity window. Another median-based filter, the adaptive center-weighted median filter (ACWMF), uses a comparison of thecenter weighted medians and adaptive thresholds for detection[9]. When applied to Gaussian or mixed noise images, it cre-ates blur and removes the details. The directional weighted me-

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2308 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 19, NO. 9, SEPTEMBER 2010

Fig. 1. (a) Bright region contaminated with pepper-like impulse noises.(b) Dark region corrupted by salt-like impulses. (c) Lower window is noise-freeand the upper window is corrupted by 20% uniform noise.

dian (DWM) filter uses an iterative filtering approach, and thedetector is based upon absolute differences within the filteringwindow [10]. The estimation is done using an adaptive weightedmedian filter. For ensuring high accuracy of detection, iterativefiltering is applied, which takes a longer total processing timebut removes more details with each iteration.

The fuzzy impulse noise detection and reduction method(FIDRM) filter is a fuzzy filter that consists of two consecu-tively applied filters [13]. The FIDRM filter effectively removessalt-and-pepper noise, but its performance in the case of uni-form impulse noise is not satisfactory, as some of the uniformimpulse noise may not produce large gradient values. Tomasiand Manduchi’s bilateral filter cannot adequately remove im-pulse noise because the difference between the noise pixel andsurrounding pixels are too large. Therefore, local weightingis too small to change the noise value. The trilateral filter is amodification of the bilateral filter with incorporated rank-orderabsolute difference (ROAD) statistics for impulse noise de-tection [1], [6]. It has been especially designed for uniformimpulse and Gaussian noise removal. The ROAD value couldbe false under the case that half of the pixels in the processingwindow are corrupted.

In this paper, we propose a universal noise removal filterbased upon the “detect and replace” methodology. To detectnoise, the absolute difference between a current pixel value andthe reference median is computed. If the absolute difference islarge, then the current pixel is considered as impulse or Gaussiannoise. On the other hand, when the absolute difference is small,the current pixel may be considered as noise-free pixel. It is veryimportant to find a proper reference median in the window, be-cause a nonproper one would lead to false detection. In order tofind the proper reference median, we have to understand prop-erties such as edge or texture in the current window. We define

Fig. 2. Four quadrant blocks in a single 5� 5 window.

a sorted quadrant median vector (SQMV) and present an ap-proach to recognize edge and texture. Based upon the edge/tex-ture content in the window, a proper reference median can beselected.

To achieve good visual image quality, it is important that thenoise filter not only replaces noisy pixels but also preserves theedge. The bilateral filter can achieve this, but it cannot removeimpulse noise. Therefore, we propose a switching bilateralfilter (SBF) for removing both Gaussian and impulse noise.From the noise classification result in the noise detector, SBFswitches between the Gaussian and impulse modes. SBF showsvery good results in removing salt-and-pepper noise, uniformimpulse noise and Gaussian noise. It efficiently removes bothtypes of mixed noise, salt-and-pepper with uniform impulsenoise and salt-and-pepper with Gaussian noise.

This paper is arranged as follows. In Section II, we proposethe SQMV scheme, and the features of SQMV and the approachfor detecting noise are discussed. Section III presents the two-stage detection method and the switching bilateral filter for uni-versal noise removal. Section IV presents the simulations onnoise detection and noise removal, with visual examples and nu-merical results. Finally, a brief conclusion is given in Section V.

II. SORTED QUADRANT MEDIAN VECTOR (SQMV)FOR NOISE DETECTION

A. Noise Models

When an image is corrupted by impulse noise, a portion of thepixel values are replaced with random values. Let anddenote the intensity values of a noise-free image and the cor-rupted image at the pixel location . Then the noisy imagecan be described as follows:

(1)

The value of indicates the probability that a noise-freeimage is corrupted by impulse noise, and is the intensityvalue of the impulse noise at the location . The valueof is in the range of maximum luminance valueand minimum luminance value . When only takesvalues of either or , the noise model is calledsalt-and-pepper noise. And when takes random valuesfrom the interval with a uniform distribution,

LIN et al.: SWITCHING BILATERAL FILTER WITH A TEXTURE/NOISE DETECTOR FOR UNIVERSAL NOISE REMOVAL 2309

Fig. 3. (a) Uniform region. (b) Diagonal edge in dark side. (c) Diagonal edge in bright side. (d) Vertical edge. (e) Horizontal edge. (f) Diagonal line. (g) Gradualchange edge. (h) Texture.

the model is called uniform impulse noise. For the case ofadditive Gaussian noise, each noise value is produced froma zero-mean Gaussian distribution and the noisy image isrelated to the original image by

(2)

In this paper, mixed impulse noise containing either salt-and-pepper noise or uniform impulse noise or both of them is con-sidered. In addition, impulse noise mixed with Gaussian noiseis also considered. Gaussian noise is independent of impulsenoise; therefore, it is processed in a separate path.

B. Motivation of the Noise Detection Scheme

Existing two-state noise detectors fail in several conditionswhen a portion of the pixels in an image is contaminated withimpulse noise. For example, when the number of pixels withimpulse noise is equal to or larger than half of the size of a pro-cessing window, the median of the processing window falls tothe value of the impulse noise. The central pixel and its halfneighboring pixels exhibit all salt-like or all pepper-like impulsenoise, as shown in Fig. 1, where Fig. 1(a) shows a bright re-gion contaminated with pepper-like impulse noise and Fig. 1(b)shows a dark region corrupted by salt-like impulses noise. Theabsolute difference between the median and the central pixel iszeros, and the central pixel is, thus, identified as a noise-freepixel.

Another case occurs when adding uniform impulse noise intoimages with fine texture or details. For finely textured or de-tailed images, the difference between pixels is larger than usual.Since the uniform impulse noise value could be any value be-tween maximum and minimum, it is hard to tell the differencebetween a texture and a uniform impulse noise. Fig. 1(c) shows

a portion of Lena’s hair which is corrupted by 20% uniform im-pulse noise. There are two 3 3 windows in the figure where thelower one is not corrupted and the upper one is contaminated.The medians of the lower and upper windows are 83 and 118,respectively. The absolute differences between the median andthe central pixel are 34 and 32 for the lower and upper window.Since the absolute differences are so close, it is difficult to distin-guish between the fine texture and the noise corrupted window.

One of the reasons that previous approaches fail to detectthese cases is because the processing window size is too small toprocess information to distinguish texture or noise. For imageswith fine details, a processing window of size 3 3 may fail todistinguish between noise and detail. For a larger window size,such as 5 5, the resulting median value drifts from the medianvalue of a small-size window because new textures are addedinto the larger window. Using a median value from a largerwindow may cause false noise detection and blur the imageduring filtering.

C. Definition of Sorted Quadrant Median Vector (SQMV)

To overcome the previous problems, we propose a sortedquadrant median vector (SQMV). We start from a larger windowbut observe medians from subwindows in the larger one. Themedians in the subwindows are sorted and the result vector iscalled SQMV, and it reveals edge and texture information inthe larger window. With the median values in the subwindowand edge/texture information in the larger window, the mediandrifting problem in the larger window or lack of texture infor-mation problems can be avoided. For a window with size

, we divide the window into four subwin-dows of size , with the central pixel as thecorner pixel in the four subwindows (Fig. 2; ). Let bethe luminance of the central pixel located at the position in


Fig. 4. Example of �� and �� for the three cases: (a) without edge, (b) weak edge, and (c) strong edge or texture.

Fig. 5. (a) Original image: part of an airplane. (b) Noise-free image edge drawn by the edge detector. (c) Edge drawn by the edge detector for an image withGaussian noise �� . (d) Edge drawn by the edge detector for an image with salt-and-pepper noise �� %.

a window. Then, the set of points in a window can be expressedas

(3)

The set of pixels in the four subwindow blocks of sizeare defined as

(4)

(5)

(6)

(7)

In the following discussion, we discuss the case andthe window size is 5 5, with its four quadrant blocks of size3 3. Each quadrant block has a median value expressed as

(8)

where , and denote the medians of the topright, top left, bottom left, and bottom right of the four quadrantblocks. These four median values are sorted in an increasingorder and the SQMV is defined as

(9)

Here, , and are the medians, and sorted in an ascending order such that

.

D. Features of SQMV

After sorting the medians of the four subwindows, someof the medians value are very similar while others are dif-ferent, leading to the formation of clusters. The clusters of

, and and the order of the fourmedians , and , which are mapped into theclusters, include important features of the window such asdetail and edges. From the SQMV clusters and geometric shapein the window, we obtain seven different patterns, listed in thefollowing.

Fig. 6. Direction average: the pixels in the window that are needed in eachcase. The four pixels of (a) vertical, (b) horizontal, and (c) diagonal directionsare located in the black box.

Fig. 7. Switching scheme detection with two detectors.

1) Uniform Region: When the pixel values in windoware similar, the values of the four medians are

close to each other. The SQMV falls into a single clusteras shown in Fig. 3(a).

2) Diagonal Edge: When there is a diagonal edge in window, the values of the four sorted medians are divided into two

unequal clusters such asin Fig. 3(b) or in Fig. 3(c),depending upon whether the majority of pixels in the windowis dark or light. Four types of patterns (I, II, III, and IV) existdepending upon the direction of the edge for both cases. Themapping of the four medians to the clusters are also listedin Fig. 3(b) and (c). For example, case I in Fig. 3(b) showsthat the value of is higher than the others, and therefore,

is associated with . and are mapped into


TABLE IIMPULSE DETECTION RATIO

Fig. 8. Pseudo-code of noise detector.

cluster , and the order of ,and does not matter. The mapping of in other casesin Fig. 3(b) and (c) are obtained in a similar way.

3) Vertical Edge: When there is a vertical edge in window, the values of the four sorted medians are divided into

two equal clusters .Two patterns exists depending on whether the right handside or left hand side is darker. When the left hand side isdarker than the right hand side, is associatedwith and is associated with

, as shown in Fig. 3(d), case II. Fig. 3(d),case I shows the other pattern.

Fig. 9. Optimal � values and � are linearly related in the Gaussian noisemodel.

4) Horizontal Edge: Similar to the case of a vertical edge,a horizontal edge divides the SQMV into two equal clusters

and . The associa-tions of SQMV with the corresponding unsorted medians

and are shown in Fig. 3(e) for thetwo patterns.

5) Diagonal Line: When there is a diagonal line in window, the values of the four sorted medians are divided into two

equal clusters and . Thediagonal lines in the middle of the window have similar mediansand the two triangles on the side of the window have similar


TABLE IICLASSIFICATION ACCURACY

medians. The unsorted medians andare associated with the two clusters as shown in Fig. 3(f).

6) Gradual Change Edge: Gradual change edge is similar tothe diagonal line mentioned in case (5) except that the two trian-gles on the side of the window have different median values. Thevalues of the four sorted medians are divided into three clusters

and and their associatedmedians as shown in Fig. 3(g).

7) Texture: When there is a complex texture in window ,the values of the four sorted medians are quite different fromeach other, as shown in Fig. 3(h). The SQMV is divided intofour clusters. In a natural image, very few have this kindof property.

E. Edge/Texture Identification With the Clusters of SQMV

The clusters of SQMV provides edge and texture informationwithin a window for an image. Although there are seven patternsfor classifying the geometric shape and clusters from SQMV,we can condense the previously mentioned seven patterns intothree edge/texture cases based upon the cluster distribution. Todetermine the cluster distribution, we define as thedifference between the two boundary values (or the maximumand minimum) of the sorted quadrant medians

(10)

In addition, is defined as the difference between thetwo center values of the sorted quadrant medians

(11)

and provide a measure of the similaritybetween the four quadrant blocks. Based upon the informationof and , three edge/texture cases withoutedge, weak edge, and strong edge or texture are obtained asshown in Fig. 4. The without edge case occurs whenis small (i.e., the difference between the maximum and min-imum median is small). It means that the pixel values in thewindow are similar so there is no edge in it, such as the caseof Fig. 3(a). When is large but is small,such as the patterns in Fig. 3(b), (c), and (g), there is a weakedge in the window. The case of strong edge or texture happenswhen both and are large, as shown inFig. 3(d), (e), (f), and (h).

Based upon the information of and , wepropose the edge/texture detector summarized in the following:

Edge/Texture DetectorWithout edgeweak edge

strong edge or texture

(12)


Fig. 10. (a) Part of the original Lena image. (b) Image corrupted with mixed-noise (Salt-and-Pepper and Uniform, � � ��%). (c) Trilateral filter. (d) GP filter.(e) ACWMF filter. (f) Median 3� 3 filter. (g) SDROM filter. (h) DWM filter. (i) Proposed filter.

Using the edge/texture detector to classify SQMV into threesimple cases, we can analyze the texture information in thewindow. SQMV is an efficient and robust edge detection schemefor a noisy image. We found through experimentation that agood value of lies in the interval [25–40]. Fig. 5(a) shows a partof an airplane and Fig. 5(b) contains the edge drawn by the pro-posed edge detector for weak edge detection withand . Here, is set to 40. Then a Gaussian noisewith a variance of 10 is added to the noise-free image; the sameedge detection is applied to this noisy image and the detectededges are plotted in Fig. 5(c). The same procedure is applied forthe case of Fig. 5(d) with 20% salt-and-pepper noise. For noisyimages with Gaussian and impulse noise [Fig. 5(c) and (d)], theproposed edge detector works as well as in the noise-free image.

F. Reference Median

When the number of medians inside a cluster is more than thatinside other clusters, e.g., cases in Fig. 3(a)-(c), and (g) (withoutedge or weak edge cases), the cluster with the most number ofmedians represents the majority feature in this window. Thiscluster is defined as a major cluster and the average ofand is used as the reference median value for compar-ison. When the difference between the current pixel value and

the reference median in the major cluster is large, then the cur-rent pixel is not similar to the majority of the block and is verylikely to be a noise pixel.

For the cases in Fig. 3(d), (e), (f), and (h)(strong edge or tex-ture), there is no major cluster in the SQMV. Under this situ-ation, it is necessary to decide which cluster the current pixelfalls into. From the order of four values, the pattern in thiswindow can be classified into the three cases: vertical edge, hor-izontal edge, diagonal line or texture. A direction average ap-proach is adopted to determine which cluster is more similar tothe current pixel. Depending upon the case, the four pixels inthe major pattern are averaged, represented by

(13)

As shown in Fig. 6, the four pixel values of the major pat-tern within the block are averaged. For example, in the case ofa vertical edge, if is close to , thenis chosen as the reference median value in the window. On theother hand, if is close to , then we choose

as the reference median value. Even if there is a com-plex texture in the window, as shown in Fig. 3(h), the filteringresult would be less artificial when the value of a current pixel


Fig. 11. (a) Part of the original Lena image. (b) Image corrupted with mixed-noise (Salt-and-Pepper and Gaussian noise; � � ��%� � � ��). (c) Trilateral filter.(d) GP filter. (e) ACWMF filter. (f) Median 3� 3 filter. (g) SDROM filter. (h) DWM filter. (i) Proposed filter.

is similar to or . The reference median (SQMR)is defined as

(14)

The comparison between the reference median and a currentpixel is adopted for detecting whether a current pixel is noisy ornot.

III. SWITCHING BILATERAL FILTER

A. Bilateral Filter

The bilateral filter proposed by Tomasi and Manduchi is anonlinear filter which removes Gaussian noise while preserving

edges. Each pixel is replaced by a weighted average of theintensities in the window. The weighting function gives highweighting to those pixels that are both near the central pixeland similar to the central pixel.

Let be the current pixel, and let be the pixels ina window that surrounds and

are the location of and . The outputof bilateral filter is defined as follows:

(15)

where

(16)

and

(17)


TABLE IIICOMPARATIVE RESTORATION RESULTS IN PSNR (dB) FOR SALT-AND-PEPPER NOISE

The Gaussian filter and range filter are defined in (16) and (17),respectively. In the Gaussian filter, the Euclidean distance be-tween and is calculated and the difference of lu-minance is computed in the range filter.

The bilateral filter shows great results in removing Gaussiannoise while keeping the edge, but it is difficult to removeimpulse noise. Because the noisy pixel is very different fromits neighbors, the surrounding weights are too small to changethe noisy pixel in the range filter. In order to remove impulsenoise and Gaussian noise using a bilateral filter, we propose aswitching bilateral filter, discussed in the following.

B. Switching Scheme

In the switching scheme, the noise detector searches for noisypixels in a corrupted image and tries to distinguish them fromuncorrupted ones. The filter is applied to the noisy samples only,thus, preventing blurred edges or removal of fine details. Themost difficult part in the process is to accurately discriminatethe noise from the image details. Two critical situations mayoccur; the image detail may be falsely treated as the noise and,therefore, filtered from the image; and the noisy pixel can beinterpreted as the image detail and, thus, left unchanged. If thenoise detector is good enough, the first type of error is not crit-ical, because only a small part of the image would be unneces-sarily filtered. On the other hand, the second type of error canproduce a negative effect on the output image quality, becauseonly a small percentage of noisy pixels are sufficient to decreasethe image quality.

We propose an extension to the standard switching-scheme,which uses an additional detector to identify edge or detail ina current window. The noise detection is done in two stages,and therefore, the filter is called a two-stage filter (Fig. 7). Inthis scheme, the edge detector shown in (12) identifies the edgeexistence in the window. This information is used in the noisedetector to decide the reference median for noise identification.The noise detector also decides whether a current pixel shouldbe filtered by using an SBF or whether it should bypass the SBF.There are two kinds of SBF, and . The former isa bilateral filter for impulse noise and the latter is for Gaussiannoise. Let and denote the noisy pixel and the filteredpixel, respectively. Also, let and denote binary controlsignals generated by the noise detector. The filtered image isdefined as follows:

(18)

The filtered image contains the original pixels only if bothdetectors identify the pixels as noise-free. If the noise detectoridentifies a pixel as an impulse noise, then the pixel is pro-cessed by the SBF . When the pixel is not identified as an im-pulse noise, but the difference between the current pixel and thereference median is still large than a threshold, then pixelis identified as Gaussian noise and is filtered by . Theswitching scheme is implemented in a recursive manner, similarto [7] and [8]. Thus, half of the samples in the current filteringwindow are composed of the results from the previous steps.


TABLE IVCOMPARATIVE RESTORATION RESULTS IN PSNR (dB) FOR UNIFORM IMPULSE NOISE

Noise in the pixels processed in the previous step are likely tobe moved and, thus, recursive implementation produces betterresults than nonrecursive implementation.

C. Noise Detector Design

A noise detector is used in the proposed filter to determinewhether or not the current pixel is corrupted. This decision ismade using the features of SQMV, which can show the propertyof the background and is more reliable than only one medianvalue. We obtain the reference median for noise identificationfrom SQMV. If the reference median is improper, it can leadto lost detection or over detection. The lost noisy pixels have agreat negative effect on the results and the undesired filteringremoves the details. When a current pixel is very different fromthe reference median, it is identified as an impulse noise. Whenthe difference between the current pixel and reference median isnot too much, it may be a Gaussian noise or a noise-free pixel.Because the image background can give four different SQMvalues, the reference median can be selected from SQMV asdescribed in Section II. The decision making mechanism is real-ized by employing a reference median and two thresholds (and ) and the noise detection algorithm is shown Fig. 8.

and are thresholds for identifying impulse noise orGaussian noise. From simulations on a large variety of images,

excellent results were obtained using thresholds selected fromthe following set of values:

(19)

The salt-and-pepper impulse noise contains either the max-imum or minimum value so it is easy to detect. The selectionof yields satisfactory results in fil-tering salt-and-pepper impulse noise, while the setting of

consistently performs well in removinguniform impulse and Gaussian noise.

D. Switching Bilateral Filter

In this section, we propose a new universal noise removalalgorithm: the switching bilateral filter (SBF). Let be thecurrent pixel, and let be the pixels in a

window surrounding . Finally, the SBF is definedas follows:

(20)

where

(21)


TABLE VCOMPARATIVE RESTORATION RESULTS IN PSNR (dB) FOR GAUSSIAN NOISE

and

(22)

It is difficult for a bilateral filter to remove impulse noisebecause the difference between the noisy pixel and its neigh-bors is huge. This makes the radiometric weighting function toosmall to change the noisy pixel. The trilateral filter adds a newweighting function which is based upon ROAD statistic to re-move the impulse noise. However, the trilateral filter has to beimplemented iteratively. For an image with impulse noise, thetrilateral filter processes each pixel individually and it takes toomuch processing time and creates a blurred result.

By replacing with SQMR of the window in a bilateralfilter, we can remove impulse noise without adding anotherweighting function. The difference between neighbors andmedian would not be too large and, thus, the edges and detailscan be preserved while removing the noise. Our proposed SBFprovides a sharper image than a median filter. The experimentsshowed that function gives better noise removal resultsthan the median function alone. The noise detector deals witha large number of Gaussian noise pixels and noise-free pixels,which cannot be always precisely identified. Therefore,has to be capable of keeping the details and edges in an imagewhen noise is detected. Our proposed SBF removes not onlyGaussian noise but also impulse noise while keeping the detailsand the edges.

E. Parameter Selection for the Switching Bilateral Filter

There are two parameters and that control the bilateralfilter. There is no single set of and that is optimal for allimages. In the switching scheme, we take different values forthe two parameters in the different noise models.

Through our experiment, when an edge is detected by theedge detector, we take , and otherwise. In theGaussian noise model, the relationship between and the stan-dard deviation of Gaussian noise has been presented [11], [12].For the proposed filter, better for each standard deviationvalue is shown in Fig. 9. For the impulse noise model, we alsofound through experimentation that a good initial value ofis 40 and any value in the interval [30, 50] should work well toremove both impulse noise and mixed impulse noise.

IV. RESULTS

Simulations are carried out to verify the noise removing ca-pability of the SBF and the results are compared with severalexiting filters. Our method produced results superior to othermethods in both visual image quality and quantitative measures.Simulations were made on several 512 512 8-bit grayscale testimages corrupted with salt-and-pepper noise, uniform impulsenoise, mixed impulse noise, and Gaussian noise.


TABLE VICOMPARATIVE RESTORATION RESULTS IN PSNR (dB) FOR MIXED-NOISE

A. Implementations and Testing Procedures

We implement the proposed SBF based upon the dataflowshown in Fig. 7. Testing is divided into two parts, one for noisedetection and the other for noise removal. In the noise detectiontesting, only impulse noise is considered. A corrupted imageis passed through the edge and noise detector. Pixels are pro-cessed row by row from top to bottom and, in each row, fromleft to right. The processed pixel is the central pixel of its asso-ciated 5 5 window, which is adopted for the edge detection, asshown in Fig. 2. The edge detection is based upon (12). Here, theparameter is set to 40. Equation (14) is used for finding the ref-erence median in this window. The dataflow in Fig. 8 is used to

detect noise. The selection of yields satis-factory results for salt-and-pepper impulse noise, while the set-ting of consistently performs well for uni-form and mixed impulse noise. Various kinds of impulse noise,generated randomly, are used to corrupt images with differentnoise ratio. For each noise ratio in the corrupted image, simula-tions are repeated a number of times and the average results arereported. The detection rate and classification accuracy of eachimage are compared with the results of the SDROM and GP.

In the noise filtering testing, impulse, Gaussian andmixed noise are considered. Images are corrupted withsalt-and-pepper, uniform impulse, Gaussian, and mixed noisewith different noise ratio. Pixels are processed in the same


order and the same window size as those in the noise detectiontesting. Pixels are processed by the edge and noise detectorfirst and then filtered by SBF if the current pixels are detectedas noise pixels. When an edge is detected by the edge detector,we set , and otherwise in (16). For the impulsenoise model, we also find through experimentation that a goodinitial value of is 40 and any value in the interval [30, 50]should work well to remove both impulse noise and mixedimpulse noise in (21).

The noniteration SBF is adopted and the results are comparedwith other filters. For those filters used in our comparison, theirparameters are set as suggested by authors to obtain optimalresults. For example, we adopt a 3 3 window for the tradi-tional median filters since the PSNR and visual image qualityare better than those of a 5 5 median filter. The detail results,observation and discussion are described in the following.

B. Comparison of Noise Detection

In Table I, the ratios of the noise impulse detection for twoimages (Lena and Boats) are shown for three different filters,SDROM, GP, and our proposed SBF. This ratio presents thenumber of detected impulses divided by the total number of im-pulses. Three noise models, salt-and-pepper, uniform impulse,and mixed impulse noise, are simulated. Our proposed SBFfilter has the highest detection rate for all three cases. Comparedwith other methods for salt-and-pepper noise, the detection ra-tios are slightly higher when the noise level ranges from 10% to40% and performs better with a noise level of 50%. For uniformimpulse noise, our SBF outperforms the other methods for noiselevels from 10% to 50%.

For the same test sets used in Table I, Table II shows the com-parison for classification rate, which presents the number of cor-rectly classified pixels (correctly detected noise plus correctlydetected noise-free pixel) divided by the total number of pixels.For salt-and-pepper noise, our proposed filter gives a better clas-sification rate than GP. Although the classification rate is lowerthan SDROM, our detection rate is higher (Table I). As for uni-form impulse noise, the classification rate of our proposed filteris lower than SDROM and GP. The reason is that due to thehigh detection rate compared with the other two methods, somepixels are wrongly marked as noise. In the high ratio of impulsenoise, the classification ratio is as good as the others.

C. Image Quality

The following simulations show that our approach providesa visually appealing output. The SBF can restore an imagecorrupted with mixed noise, as demonstrated by two cases.One is the Lena image corrupted by mixed salt-and-pepper anduniform impulse noise with %. The other is the boatimage contaminated by mixed salt-and-pepper and Gaussiannoise with % and . The original, noisy image andthe one filtered by our proposed SBF are compared with thetrilateral filter, GP filter, ACWMF filter, Median filter, SDROMfilter, and DWM filter (Figs. 10 and 11). Compared with theoriginal image, it is clear that the SBF filter can eliminate noisewhile preserving the edge and fine details.

The visual quality of images restored by the SBF filter hasbeen demonstrated in the previously shown figures. Quantitative

measures of signal restoration are discussed in the following.The peak-to-noise ratio (PSNR) is used as a quantitative mea-sure for comparison. If is an original image and isa restored image of , the PSNR of is given by

(23)

The proposed SBF filter is compared with implementationsof the standard median filter whose filter window is 3 3 andthe ACWMF [9], SDROM [8], bilateral [1], trilateral [6], DWM[10], and two-stage GP [7] filters. Table III compares the PSNRvalues on impulse noise (salt-and-pepper) for % and in

%. The SBF shows better PSNR than other filters ex-cept the SDROM. Table IV shows the PSNR value for uniformimpulse noise; for %, the SBF and SDROM filter showthe best results, but SBF and the trilateral are better than theSDROM filter for %.

Table V shows the PSNR values corrupted with Gaussiannoise ( and ); and the SBF produces nearly thesame results with the bilateral and trilateral filters. Finally, thethree kinds of mixed noise: salt-and-pepper and Gaussian with

% and ; uniform impulse and Gaussian with% and ; and salt-and-pepper and uniform im-

pulse with % are compared with the other filters and theresults are listed in Table VI. In Table VI (a), the SBF shows thebest values followed by the trilateral filter. In Table VI (b), thetrilateral shows better results in most of the images and the SBFis very close to it. In Table VI (c), the SBF filter consistentlyyields the highest PSNR for each image.

V. CONCLUSION

The major contribution of this paper is to propose SQMV foredge/texture detection, noise detection and the switching bilat-eral filter. The edge detector, with a simple structure, obtains athe reference median value for noise detection, which detectsimpulse and Gaussian noise. Both detectors are based upon ro-bust estimators of SQMV. Many noise removal algorithms, suchas bilateral filtering, tend to treat impulse noise as edge pixels,and end up with unsatisfactory results. In order to process im-pulse pixels and edge pixels differently, we introduce two de-tectors based upon SQMV in a neighborhood of a pixel. We in-corporate SQMV into switching bilateral filtering by replacingthe current pixel with a proper median value in the range filterfunction. The new nonlinear filter is called the switching bilat-eral filter and the switching control signal is from the noise de-tector. With regard to the impulse detection rate and classifica-tion rate, the noise detector shows a good performance in iden-tifying noise even in mixed noise models. In most of the noisemodel cases, the proposed filter outperforms other filters, both inPSNR and visually. Moreover, it shows excellent performancein the simultaneous removal of both impulse and Gaussian noiseand without adding another weighting function. A mathematicalmodel based upon this work can be developed to better under-stand the SQMV and SBF. A theoretical development also helpsto gain an insight for the connection between the SBF and otherrelated filters. A mathematical model and theoretical develop-ment will be pursued in our future work.


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Chih-Hsing Lin was born in I-Lan, Taiwan, R.O.C.,in 1977. He received the B.S. degree in electricengineering from Ming Hsin of Science and Tech-nology University, Hsinchu, Taiwan, in 2000, andthe M.S. degree in electric engineering from ChungYuan Christian University, Chung-Li, Taiwan,R.O.C., in 2002, and is currently working towardthe Ph.D. degree in the Institute of Communica-tions Engineering, National Tsing Hua University,Hsinchu.

His research interests are delay-locked loops, fre-quency synthesizers, low power, and image filter design.

Jia-Shiuan Tsai was born in I-Lan, Taiwan, R.O.C.,in 1983. He received the B.S. degree in technologyapplication from National Taiwan Normal University,Taipei, Taiwan, in 2006, and the M.S. degree in com-puter science from National Tsing Hua University,Hsinchu, Taiwan, in 2009.

His research interests are image filter, HDR imagesynthesis.

Ching-Te Chiu received the B.S. and M.S. degreefrom National Taiwan University, Taipei, Taiwan,R.O.C., in 1986 and 1988, respectively, and the Ph.D.degree from University of Maryland, College Park,Maryland, in 1992, all in electrical engineering.

She was an Associate Professor with NationalChung Cheng University, Chia-Yi, Taiwan from1993 to 1994. From 1994 to 1996, she was memberof technical staff with AT&T, Murray Hill, NJ,and at Lucent Technologies, Murray Hill, from1996 to 2000, and with Agere Systems, Santa

Clara, CA, from 2000 to 2003. Since 2004, she has joined Department ofComputer Science and Institute of Communications Engineering, NationalTsing Hua University, Hsinchu, Taiwan. Her research interests are videoand communication integrated circuit design. She has been working on highdynamic range tone mapping processor chip design, high speed switch fabricIC design and SERDES interface design. Her previous chip designs includehigh definition television video decoder, the standard television demodulation,the SONET/SDH mapper and framer, the ATM core/edge switch, 10 Gbps I/Prouter traffic management, and FEC decoder.

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Gaussian Noise Filter