Effective noise removal in graylevel image using joint bilateral filter

8/18/2019 Effective noise removal in graylevel image using joint bilateral filter

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EFFECTIVE NOISE REMOVAL IN

GRAYLEVEL IMAGE USING JOINT

BILATERAL FILTER

P.Karthikeyan

Department of Electronics and

Communication Engineering,

Velammal College of Engineering

and Technology,

Madurai, India

S.Vasuki




and Technology,

Madurai, India

R.Boomadevi




and Technology

Madurai, India

Abstract — Natural images are mostly corrupted by Gaussian

noise. Denoising of these images is even now a challenging task inimage restoration. This paper proposes the removal of Gaussian

noise using spatial filter. The spatial filter employed in this paper

is joint bilateral filter. The Bilateral Filter is a nonlinear filter

that does spatial averaging without smoothing edges; it has

shown to be an effective image denoising technique. For

parameter estimation the Joint Bilateral Filter requires a

reference image. In the proposed scheme, noise-free image is

taken as the reference image. The performance is evaluated in

terms of Peak Signal to Noise Ratio, Image Quality Index and

Edge Keeping Index. The experimental results are obtained and

then compared with the results of denoised image using bilateral

filter and BM3D.

Keywords: Image denoising Bilateral filter Joint bilateral filter

I. I NTRODUCTION

The aim of image denoising algorithm is to reduce

the noise with the preservation of image features as much as

possible. The images are corrupted by different types of

noises. For example, dark current noise is due to the thermally

generated electrons at sensor sites. Shot noise is due to the

quantum uncertainty in photoelectron generation; and it is

characterized by a Poisson distribution. Amplifier noise and

quantization noise occur during the conversion of the number

of electrons generated to pixel intensities.

The overall noise characteristics in an image dependson many factors, including sensor type, pixel dimensions,

temperature, exposure time, and ISO speed. Images are often

corrupted by additive noise, which is mostly modelled as

Gaussian, during acquisition and transmission. Several

methods have been proposed to remove noise and try to

recover the “true” image. Bilateral Filter is a nonlinear, edge-

preserving, smoothing filter [4].The intensity value at each

pixel in an image is replaced by a weighted average of

intensity values from nearby pixels. This weight is based on a

Gaussian distribution. Joint Bilateral Filter is an extension ofBilateral Filter based on the concept of combining the

strengths of flash and no-flash images [1]. In the

multiresolution bilateral image denoising scheme, Bilateral

Filter is applied on the approximation band of wavelet

coefficients and wavelet thresholding is applied on the detail

subbands [10]. In a new hybrid image denoising scheme,

Bilateral Filter is employed as pre-filter and post-filter for

wavelet thresholding [11]. In a multiresolution multilateral

filtering, Gaussian noise is reduced based on the idea of

regional similarity [12]. A variant of Bilateral Filter,

Joint/Cross Bilateral Filter, which uses a second image to

shape the filter kernel and operate on the first image, and vice

versa was proposed in [1,8]. Both of these papers address the problem of combining the details of images captured with and

without flash under ambient illumination.

The performance is evaluated in terms of Peak Signal

to Noise Ratio (PSNR), Image Quality Index (IQI) [2] and

Edge Keeping Index (EKI) [3].

. The rest of the paper is structured as follows:

Section II describes theoretical background, Section III

describes the proposed image denoising algorithm, Section IV

illustrates the experimental results and Section V concludes

the paper.

II. THEORITICAL BACKGROUND

A .GAUSSIAN FILTER Gaussian filter is a linear, smoothing filter whose impulse

response is a Gaussian function and it is not edge-preserving.

[] = σ(‖ − ‖) () (1)

where G(x) = πσ e σ (2)

Gaussian filtering is a weighted average of the intensity of

the adjacent positions with a weight decreasing with the

International Journal of Applied Engineering Research, ISSN 0973-4562 Vol. 9 No. 21, 2014© Research India Publications http://www.ripublication.com/ijaer.htm

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spatial distance to the centre position p. This distance is

defined by G(‖p− q‖) where σ is a parameter defining theextension of the neighbourhood. As a result, image edges are

blurred.

B. BILATERAL FILTER

Bilateral filter overcomes gaussian filter problem by

filtering the image in both range and domain (space). Bilateral

filter is a local, nonlinear and non-iterative technique whichconsiders both gray level (color) similarities and geometric

closeness of the neighboring pixels. Mathematically, the

bilateral filter output at a pixel location p is calculated as

follows

[] = ∑ Gσ(‖p− q‖)Gσ(|I(p) − I(q)|)∈ I(q) (3)where Gσ(‖p− q‖) = e

σ (4)

is a geometric closeness function,

Gσ(|I(p) − I(q)|) = e|()()|

σ (5)

is a gray level similarity function,W=∑ Gσ(‖p− q‖)Gσ(|I(p) − I(q)|)∈ (6)is a normalization constant ,

‖p− q‖ is the Euclidean distance between p and q, and S is aspatial neighborhood of p.

The two parameters σ s and σ r control the behaviour of

the bilateral filter. As range parameter σr increases, the

bilateral filter gradually approaches Gaussian convolution

more closely because the range Gaussian widens and flattens,

which means that it becomes nearly constant over the intensity

interval of the image. On increasing the spatial parameter σd ,

the larger features get smoothened.

Let the image pixel to be replaced is g, and g, be the neighboring pixels of (2 M + 1) × (2 M + 1)window, where (i, j ) and (i + s, j + t) be the locations of g, and g,respectively. Each pixel is replaced by the newvalue calculated using Eq. (7).

g, =∑ ∑ (,).(,).,

∑ ∑ (,). (,) (7)

where the Gaussian filter W G is defined in Eq. (8)

(,) = (()())/ (8)

and the range filter W R is defined in Eq. (9)

(,) = (,,)/ (9)where σ d and σ r are geometric spread and photometric spread,

used to control the performance of the Bilateral Filter.

C. JOINT BILATERAL FILTER

Using digital photography, a pair of images can be

taken in low-light environments: one with flash (flash image)

to capture detail and another one without flash (no-flash

image) to capture ambient illumination. Flash images are

noise-free and have a higher signal to noise ratio. Therefore, it

can resolve in detail that would be hidden in the noise in an

ambient (no-flash) image. The flash image is assumed as a

good local estimator of high-frequency content in the ambient

image. Based on this concept, the Joint Bilateral Filter is

designed to reduce the noise in the no-flash image using the

relatively noise-free flash image. It is designed by modifying

the basic Bilateral Filter. The main problem of traditionalBilateral Filter in image denoising is that the range filter W R

could not be accurately designed based on noisy image

[5].Since the flash image contains a much better estimate of

the true high-frequency information than the ambient image,

the range filter is designed using the flash image. The intensity

distance of range filter is calculated using the flash image.

The range filter in Joint Bilateral Filter is defined as

(,) = (,,)/ (10)where f is the flash image [1].

The Gaussian filter is designed as in the case of

Bilateral Filter. The output of the Joint Bilateral Filter is

defined in Eq. (1) with the value of W R (s, t) obtained from Eq.(4).

III. PROPOSED DENOISING ALGORITHM

Let { xi, j , i, j = 1 , 2 . . . , N } be the N × N image,

where N is some integer power of two. The image x is

degraded by independent and identically distributed (iid) zero

mean white Gaussian noise with standard deviation σ n during

transmission.

The image observed at the receiver end is

, = , + , (11)

The image is recovered from noisy observation by applying joint bilateral filter and parameter is estimated in terms of

PSNR ,EKI and IQI.

In the proposed scheme, it is assumed that the noise-

free image is known, and it is used to estimate the noisy pixels

in the noisy image. The noise-free image x is used in the range

filter of Joint Bilateral Filter as shown in Eq. (12).

W(s,t) = e(,,)/σ (12)

The major problem with Bilateral Filter is the

selection of the parameters photometric spread σ r and

geometric spread σ d . The problem is analyzed in [6]. They

confirmed the values of σ d = 1.8 and σ r = 2 × σ n, to give better performance in terms of PSNR. Hence, the experiments with

Bilateral Filter are carried out using these values. The work

done by Yu et al. [8] concluded that the value of = 3+ in the design of Joint Bilateral Filter to get better

performance in terms of PSNR. Thus, in this proposed image

denoising scheme, the Joint Bilateral Filter is designed with

the same σ r value.The performance of this image denoising

scheme is evaluated using PSNR, IQI and EKI.


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TABLE I PSNR Comparison of various denoising methods versus proposed method for different standard deviations

Test images with

pixel size Existing method Proposed method

BM3D BILATERAL JBF

peppers

512x512

10 32.15 49.78 57.08

20 28.78 48.21 56.93

30 26.77 47.87 54.84

40 26.88 47.59 53.3

50 25.70 47.14 52.70

House

512x512

10 29.49 34.52 54.15

20 26.13 34 53.36

30 23.77 33.50 53.00

40 22.67 31.34 52.89

50 21.89 30.56 52.56

Cameraman

512x512

10 28.6 28.38 51.99

20 25.91 28.01 51.34

30 23.78 27.27 50.89

40 21.45 26.25 50.12

50 21.54 25.10 49.56

IV. R ESULTS AND DISCUSSION

Experiments are carried out on various standard

grayscale images of size 512 × 512 which are corrupted by a

simulated Gaussian white noise with zero mean and five

different standard deviations σ n [10 , 20 , 30 , 40 ,

50].Denoising process have been performed on these images

using Joint bilateral filter and the PSNR, EKI,IQI results are

calculated. Figure 1 shows the result of image obtained by

applying JBF.The experimental results are then compared with

results of denoising image using bilateral filter and

BM3D[9].figure2 shows the result obtained using different

filters.Peak signal-to-noise ratio, often abbreviated PSNR

This ratio is often used as a quality measurement between the

original and a compressed image. The higher the PSNR, better

the quality of the compressed or reconstructed image.

The Mean Square Error (MSE) and the Peak Signal to Noise

Ratio (PSNR ) are the two error metrics used to compare image

compression quality. The MSE represents the cumulative

squared error between the compressed and the original image,

whereas PSNR represents a measure of the peak error. The

lower the value of MSE, the lower the error. The PSNR (dB)

is defined as

PSNR(dB) = 10log (13)

where Mean Squared Error (MSE) is defined as

MSE = ×∑ ∑ x, − x,

(14)

Table I gives the PSNR Comparison of various denoising

methods versus proposed method for different standard

deviations.

Edge Keeping Index is abbreviated as EKI.The edges

are recognised to be most informative in this particular

application. The motive behind using this criterion is to

evaluate and establish how well the edges are maintained

during the denoising process. EKI is calculated using Eq. (15)

= ∑ ∑ ∆,∆μ(∆,∆μ) ∑ ∑ ∆,∆μ∑ ∑ (∆,∆μ)

(15)

where ∆,and ∆,are the high pass filtered noise-free image and denoised image. ∆ and ∆⃖ are the meanvalues of high pass filtered noise-free image and denoisedimage [3]. High pass filtered versions of the images are

obtained with the Laplacian operator. EKI is based on the

correlation between the coefficients. Thus, EKI value is close

to unity, if the denoised image is similar to the noise-free

image.TableII gives the EKI Comparison of various denoising


deviations.

Any image distortion can be modeled as IQI in terms

of three parameters such as loss of correlation, luminance

distortion and contrast distortion [2]. IQI is calculated as given

by

IQI = .

μμμμ .

(16)

Table III gives the IQI Comparison of various denoising


deviations.

Among these methods, JBF gives the nice denoisingresult in terms of PSNR, IQI and EKI, since it incorporates

noise-free image to implement range filter.Figure3 shows the

graph that represent comparison of filters in terms of

PSNR,EKI,IQI.


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TABLE II EKI Comparison of various denoising methods versus proposed method for different standard deviations

TABLE III IQI Comparison of various denoising methods versus proposed method for different standard deviations

test images with

pixel size

Existing method Proposed methodBM3D BILATERAL JBF

Peppers512x512

10 0.6543 0.7785 0.8426

20 0.6533 0.7234 0.8356

30 0.6234 0.6282 0.8134

40 0.5983 0.6154 0.7873

50 0.5654 0.5982 0.7567

house512x512

10 0.6754 0.7543 0.8345

20 0.6543 0.7324 0.8245

30 0.5839 0.7212 0.7654

40 0.5641 0.6548 0.7456

50 0.5423 0.6432 0.7444

cameraman512x512

10 0.6123 0.7122 0.7653

20 0.5932 0.7006 0.7456

30 0.5643 0.6542 0.7339

40 0.5456 0.6265 0.6543

50 0.4567 0.6223 0.6765

Figure1: Result of Joint BilateralFilter on candlelit setting of

the wine cave image.

(a) Flash image

(b) No Flash image

(c) Output

(a) (b) (c)

(a) (b)(c)

Test images with

pixel size Existing method Proposed method

BM3D BILATERAL JBF

Peppers512x512

10 0.7124 0.7867 0.9765

20 0.6954 0.6777 0.8675

30 0.6754 0.4688 0.8376

40 0.6166 0.3898 0.7994

50 0.567 0.3743 0.7687

house512x512

10 0.7444 0.7333 0.9223

20 0.6890 0.6315 0.9002

30 0.6100 0.5256 0.8945

40 0.5679 0.3163 0.7795

50 0.5466 0.2098 0.6567

cameraman512x512

10 0.5789 0.5654 0.8456

20 0.4432 0.4390 0.8400

30 0.4100 0.3789 0.8190

40 0.3678 0.2654 0.787750 0.2345 0.2234 0.6455


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Figure 2: Denoised results of peppers

images.(a) original image, (b) noisy

image(σ=50),(c) BMD3, (d) Bilateralfilter , (e) Joint Bilateral filter

(a) (b) (c)

(d) (e)

(a)

(b)

0

10

20

30

40

50

60

10 20 30 40 50

P S N R

sigma (σn)

COMPARISON OF PSNR

BM3D

BILATERAL

JBF

0

0.5

1

1.5

10 20 30 40 50

E K I

sigma (σn)

COMPARISON OF EKI

BM3D

BILATERAL

JBF


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(c)

Figure 3: Comparison of BM3D, BF and JBF in terms of (a) PSNR, (b) EQI, (c) IQI

V. CONCLUSION AND FUTURE WORK

In this paper, joint bilateral filter is proposed for denoising

an image. This method exploits the edge-reserving property of

JBF. The proposed method gives outperformed results than

BM3D and bilateral filter in terms of PSNR,EKI and IQI.The

proposed framework will inspire further research towards

understanding and eliminating noise in real images and help

better understanding of the joint bilateral filter. Further, the

work can be extended by combing JBF with non subsampled

contourlet transform.

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1 (2012).

0

0.2

0.4

0.6

0.8

1

10 20 30 40 50

I Q I

sigma (σn)

COMPARISON OF IQI

BM3D

BILATERAL

JBF


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Effective noise removal in graylevel image using joint bilateral filter