image denoising by utilizing bilateral filter via box ...€¦ · keywords: bilateral filtering,...

IJRRAS 32 (3) September 2017 www.arpapress.com/Volumes/Vol32Issue3/IJRRAS_32_3_02.pdf

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IMAGE DENOISING BY UTILIZING BILATERAL FILTER VIA BOX

FILTERING APPROACH

Sheeraz Ahmed Solangi 1,*, Qunsheng Cao1 & Shumaila Solangi2

1 Nanjing University of Aeronautics and Astronautics (NUAA), Nanjing 211106, China 2 IMCS, University of Sindh, Jamshoro 76080, Pakistan

ABSTRACT

Box and Gaussian filters are suitable and typically perform well in applications where amount of smoothing required

is small. These types of filters are quite optimum in eliminating small amount of noise from natural images. However,

when the floor of the noise is large, and one is essential to average more pixels to suppress the noise, so these type of

filters begin to over smooth sharp image features such as corners and edges. To overcome this shortcoming the bilateral

filter has been proposed. In this paper we have presented new approach by utilizing bilateral filter via box filter

method. The proposed method significantly improve the bilateral filter performance by simply implementing pre-

processing step of box filtering at almost no additional cost.

Keywords: Bilateral filtering, Box filtering, Image denoising, Edge-preserving

1. INTRODUCTION

The bilateral filter (BF) is a kind of non-linear weighted averaging filter [1]. The methodology of bilateral filter is that

the weights of the filter is totally depend on the spatial distance and the photometric similarity distance with respect

to the center pixel. While doing the spatial smoothing the bilateral filter have the capability to preserve the edges that

is the main characteristic of this filter. The performance of bilateral filter is relatively effective in denoising images

degraded with small amounts of Gaussian noise. The bilateral filter perform very well in denoising images, though,

images degrade quickly as increase in noise level. To overcome this shortcoming of the filter there are a lot of modified

versions of the bilateral filter have been suggested in the literature, but often at an extensive computational overhead.

There are wide range of applications in computer vision and image processing has found for bilateral filter. The prompt

application of bilateral filter is as it can do spatial averaging in images without smoothing edges. Other applications

of the bilateral filter comprise of image denoising multiresolution addition [2], contrast enhancement [3], 3-D mesh

denoising [4], estimation of depth map [5], illumination and texture separation [6], tone mapping [7], enhancement of

video [8], compression artifact reduction [9], estimation of optical flow [10] and fusion of flash and no-flash images

[11].

In this paper we have utilized bilateral filter that can significantly improve the bilateral filter performance by

implementing simple pre-processing step. There is no additional cost of this filter. The performance of the filter is

significant at high noise levels as compare to the existing bilateral filter but at certain noise threshold it tends to

perform poor. Both the numerical and visual denoising results on standard test images have been reported in this paper.

In the experimental results, we have verified that, by utilizing bilateral filter via box filter the performance over the

existing bilateral filter is significant both visually and numerically in terms of PSNR. Additionally, the denoising

performance of the proposed filter is competitive with the anisotropic diffusion (AD) [12], total variation (TV) [13]

and non-local means filter (NLM) [14] in terms of visual and computational process.

2. STANDARD PROBLEM OF DENOISING

The images degraded with the white Gaussian noise that is the standard problem of denoising grayscale images in

image processing and computer vision [15], [13], [16]. In this method, we are given the noisy image as:

𝑢(𝒊) = 𝑢°(𝒊) + 𝜎 ∙ 𝑤𝑖 (𝒊 ∈ 𝐾) (1)

where K is finite rectangular domain of ℤ2, 𝑢°(𝒊) ∶ 𝒊 ∈ 𝐾 is the unknown original clean image, 𝑤𝑖: 𝒊 ∈ 𝐾 are

independent and identically distributed as N (0, 1), and the noise level is σ.

The main aim is to discover an estimate denoised (𝒊) of the original clean image from the degraded samples. So the

goal is to denoised an image that should be visually similar to original clean image. By using mean-squared-error

(MSE) we can calculate the resemblance rate of image which is defined to be:

IJRRAS 32 (3) September 2017 Solangi et al. Image Denoising by Utilizing Bilateral Filter

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MSE = 1

|𝐾| ∑(

𝒊∈𝐾

(𝒊) − 𝑢° (𝒊))𝟐 (2)

So, in this paper, we have used the peak signal-to-noise ratio (PSNR) which is given by PSNR = 10log10(2552/MSE).

Edge-preserving bilateral filter in the applications of image denoising is the current interest in our paper [1], [17],

[18]. In this case we have designed the denoised image as:

1(𝒊) =Σ𝒋єΩ 𝑔𝜎𝑠

(𝒋) 𝑔𝜎𝑟(𝑢(𝒊 − 𝒋) − 𝑢(𝒊)) 𝑢(𝒊 − 𝒋)

Σ𝒋єΩ 𝑔𝜎𝑠(𝒋) 𝑔𝜎𝑟

(𝑢(𝒊 − 𝒋) − 𝑢(𝒊)) (3)

where,

𝑔𝜎𝑠(𝑖) = exp (−

‖𝑖‖2

2𝜎𝑠2 ) and 𝑔𝜎𝑟

(𝑡) = exp (− 𝑡2

2𝜎𝑟2 ) (4)

The spatial and range kernels are given in Eq. (4) which refers for Gaussian kernels. The domain Ω, in practice is

limited to some neighborhood of the origin. Usually, the square of the neighborhood is Ω, which refers to Ω = [-W;

W] × [-W; W], where W = 3𝜎𝑠[1].

3. BOX FILTERING APPROACH

A box filter is kind of spatial averaging filter in which all coefficients are must be equal. Spatial averaging filters are

mostly used for smoothing and for image denoising. The output of the each pixel in the resulting image has a value

equal to the average value of its neighboring pixels in the input.

The idea behind spatial averaging filters is straight forward. By replacing every pixel value in an image by the mean

of the intensity levels in the neighborhood of the filter mask. So, in this method the results in an image with reduced

‘sharp changes’ in intensity levels. Hence, the noise reduction is the most noticeable application of smoothing. The

main drawback of these filters is they blur edges of the image.

Box filtering in its simplest form can be described as [19]:

ℎ𝑘𝑙𝐾𝐿 =

1

(2𝐾 + 1)(2𝐿 + 1) (5)

where, ℎ𝐾𝐿 with real samples ℎ𝑘𝑙𝐾𝐿.

4. UTILIZING BILATERAL FILTER VIA BOX FILTERING

We have demonstrated in this section that how bilateral filter denoising performance can be improved at high noise

levels. So, by integrating a simple pre-processing step into the framework at almost no additional cost.

We have noted that in Eq. (3) the range filter operates on the noisy samples.

It means that the degraded image is used not just for averaging but also to control the smoothing via range filter.

The approach in this regard is to apply range filter directly on the original clean image so it can consider some

form of proxy for the original clean image. In this scheme we use the box filter as a proxy for the noisy image. In particular, proposed bilateral filter can be written as:

2(𝒊) =Σ𝒋єΩ 𝑔𝜎𝑠

(𝒋) 𝑔𝜎𝑟((𝒊 − 𝒋) − (𝒊)) 𝑢(𝒊 − 𝒋)

Σ𝒋єΩ 𝑔𝜎𝑠(𝒋) 𝑔𝜎𝑟

((𝒊 − 𝒋) − (𝒊)) (6)

where,

(𝑖)1

(2𝑅 + 1)2 ∑ 𝑢(𝑖 − 𝑗)

𝑗∈−𝑅,𝑅2

(7)


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We have set the parameter R in which can we can control the amount of smoothing induced by the box filter. We have

performed number of simulations in this regard. The number of simulation results recommend that R=1 (3 × 3) is ideal

for most of output results. By doing this we can explain this as the small blur can suppress the noise but also can keep

features of the image. We have performed denoising on both original bilateral filter and proposed method and obtained

results of test images are shown in Table 1. So the results of these filters can be tuned independently with respect to

𝜎𝑠 and 𝜎𝑟. The tuning of these filters can get the best PNSR results.

4. EXPERIMENTAL RESULTS

We have used MATLAB R2013a (8.1), CPU: 1.70GHz, Memory: 4GB and Windows 10 platform and performed

simulations for anisotropic diffusion (AD), total variation (TV), bilateral filter (BF) and proposed method. We have

taken standard test images of Lena, Pepper, Goldhill and Barbara of dimension of 512×512 for simulation purpose.

These images are degraded with Gaussian noise of standard deviation 𝜎n = 10, 20, 30, 40, and 50. The execution time

and PSNR are taken as performance measures.

In Table 1 various images of PNSR values for different filters and proposed filter are given. In this we have highlighted

the best PNSR value for these various images as given in Table 1.

The visual results shown in figures: Figure1, Figure 2, Figure 3 and Figure 4. It is suggest that beyond a certain noise

level depending on the type of image the proposed filter starts to perform better. Adding up the box filtering into the

bilateral filter can perform better at high noise levels but brings down the overall PSNR due to the blurring of the

image. Certainly, the degraded image is already a good proxy for the original clean image when the noise ratio is

small. Moreover, we have noted that the improvement in peak-signal-to-noise-ratio is often as large as 8 dB at high

noise levels as compare to the original bilateral filter.

In Table 2 is execution time of these filters are given. For online and real time applications the less execution time

filter usually preferred. The minimum execution time is highlighted in this text. Hence, this filter is powerful tool used

in today’s applications.

(a) Original Lena image (b) Noisy image (c) Denoised by AD

(d) Denoised by TV (e) Denoised by BF (f) Proposed method

Figure 1. Denoising performance of various filters and proposed method for Lena test image with noise = 30.

Original Image Noisy Image, PSNR = 18.60 Noisy Image, PSNR = 28.13

Denoised image Original Bilateral Filter, PSNR = 24.79

Improvement = 6.1908

Improved BF, PSNR = 29.50


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(a) Original Lena image (b) Noisy image (c) Denoised by AD


Figure 2. Denoising performance of various filters and proposed method for Lena test image with noise = 50.

(a) Original Goldhill image (b) Noisy image (c) Denoised by AD


Figure 3. Denoising performance of various filters and proposed method for Goldhill test image with noise = 20.

Original Image Noisy Image, PSNR = 14.15 Noisy Image, PSNR = 18.59

Denoised image Improved BF, PSNR = 27.47

Noisy Image, PSNR = 22.11 Noisy Image, PSNR = 28.13

Denoised image Standard Bilateral Filter, PSNR = 27.74 Improved BF, PSNR = 28.86

Original Bilateral Filter, PSNR = 18.37



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(a) Original Pepper image (b) Noisy image (c) Denoised by AD


Figure 4. Denoising performance of various filters and proposed method for Peppers test image with noise = 30.

Noisy Image, PSNR = 18.62 Noisy Image, PSNR = 22.11

Denoised image Original Bilateral Filter, PSNR = 25.43


Improved BF, PSNR = 30.03


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Table 1. Filtering performance of various filters and proposed method in terms of PSNR (dB) operated on different

test images under various noise conditions (𝜎𝑛 varies from 10 to 50).

Peak-Signal-To-Noise-Ratio, PSNR (dB)

Test Images Denoising

Filters

Standard deviation of noise

10 20 30 40 50

Lena

AD 31.36 29.26 27.21 25.39 23.92

TV 33.23 30.25 27.84 25.86 24.11

BF 33.53 28.02 24.79 22.37 18.37

Proposed 33.28 30.90 29.50 28.44 27.47

Pepper

AD 30.67 28.80 26.84 25.10 23.62

TV 31.20 29.09 27.11 25.30 23.75

BF 33.70 28.73 25.43 20.71 18.79

Proposed 33.14 31.64 30.03 28.28 27.04

Goldhill

AD 29.87 28.26 26.49 24.82 23.39

TV 31.29 29.12 27.19 25.42 23.77

BF 31.83 27.74 25.23 22.65 21.52

Proposed 30.41 28.86 27.70 26.99 26.16

Barbara

AD 26.05 25.34 24.36 23.31 22.27

TV 26.46 25.47 24.41 23.32 22.30

BF 31.20 27.05 24.12 22.02 20.75

Proposed 26.06 25.07 24.19 23.76 23.27


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Table 2. Filtering performance of various filters and proposed method in terms of PSNR (dB) operated on different

test images under various noise conditions (𝜎𝑛 varies from 10 to 50).

Denoising Filters Execution time (𝑇𝐸), (seconds)

Lena Pepper Goldhill Barbara

AD 6.55 6.77 7.01 7.21

TV 9.26 9.61 9.33 8.66

BF 4.31 3.73 4.73 5.26

Proposed method 3.11 3.42 3.18 3.85

5. CONCLUSION

The performance of AD, TV, BF and proposed method are studied under low, moderate and high noise conditions.

From Table 1, it is observed that the proposed method perform better in terms of PSNR as compare to the original

bilateral filter and also competitve with the other filters depending on the type of image. As increasing of noise in

these filters the performance of filters reduces in terms of PNSR and as well as makes image more blurry. The proposed

filter perform quite well and preserve the edges in low and high noise conditions. The original bilateral filter perform

well in low noise conditions only. The execution time of these filters is shown in the Table 2 which suggests the

execution time of proposed method is better than the other filters.

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image denoising by utilizing bilateral filter via box ...€¦ · keywords: bilateral filtering,...

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