Denoising Algorithm Based on Anisotropic Diffusion with Vector Median Filtering

Denoising Algorithm Based on Anisotropic Diffusion with Vector Median Filtering

Greeshma. P. V Prof. R. Rajkumar

Department of Electronics and Assistant professor Communication Engineering Department of Electronics and

RVS College of Engineering & Technology Communication Engineering Coimbatore – 641 402. RVS College of Engineering&Technology

Coimbatore – 641 402.

Abstract:- Traditional noise removal techniques couldnt well achieve the trade -off between preserving feature information and removing noise .This project proposed an improved Anisotropic Diffusion (AD) to improve their performance when dealing with multimodal noises in an image. To achieve this goal here propose the inclusion of Vector Median Filtering (VMF) into the formulation of anisotropic diffusion. The main contributions associated with this work are located in the inclusion of a multi-scale edge detector into the formulation of the Perona-Malik (PM) anisotropic diffusion scheme and in the implementation of a new noise removal framework that is able to restore digital images that are corrupted by Gaussian, impulse and photon noise. This noise removal scheme is quantitatively evaluated using standard metrics such as Peak Signal to Noise Ratio (PSNR), edge preservation index.

Keywords: – Anisotropic Diffusion, Vector Median Filtering, multi-scale edge detector, edge preservation index.

1. INTRODUCTION

   Images are frequently corrupted due to the presence of noise and loss of sharpness, during image transmission or acquisition. In the development of noise reduction algorithms basic knowledge about noise distribution is essential (where the most common are the Gaussian distributed and the impulse noise) and the main efforts were focused on the development of optimal strategies that addressed accurate image restoration for one particular noise model. Gaussian Noise is very commonly encountered in image acquisition, and it is characterized by adding a value from a zero-mean Gaussian distribution to each image pixel. The goal of denoising of an image is to remove the noise and to retain the important signal features as much as possible for sharpness enhancement.

   Image noise is random variation of brightness or color information in images. Image is often contaminated by noise in the process of transmission, acquisition and storage, which results in the image degradation of the visual quality. The performance of imaging sensor is affected by variety of factors, such as by the quality of sensing elements themselves and environmental conditions during image acquisition. Images are corrupted during transmission due to interference in the channel used for transmission. It can be produced by the sensor and digital camera or circuitry of a scanner . Noise

   can originate in film grain and in the unavoidable photon noise of an ideal photon detector. Image noise is classified as Gaussian noise, Salt and Pepper noise, Quantization noise, Photon noise, and Film grain noise.

2. RELATED WORKS

   One of the well-known algorithms for image denoising is anisotropic diffusion. Diffusion algorithms remove noise from an image by modifying the image via a partial differential equation. This method able to preserve the edges during denoising, but is not able to produce accurate result on different noises. Other denoising method is median filtering. This method specially designed to eliminate different types of noises but this denoising process has week feature preservation.

   Nonlinear anisotropic diffusion filtering algorithm for multiscale edge enhancement has been explained in [8] by Stephen L. Keeling. This work is to develop nonlinear anisotropic diffusion filters which sharpen edges over a wide range of slope scales and which reduce noise while conserving feature boundaries. To this end, it has been found that while a greater diffusivity decay rate will create sharper edges in a narrower range of edge slopes, a more gradual diffusivity decay rate will sharpen edges over a wider range of edge slopes.

   The basic concept of robustifying vector median filter has been explained in [7] by Samuel Morillas.et.al. This method describes two methods for impulse noise reduction in color images that outperform the vector median filter from the noise reduction capability point of view. But this process has week feature preservation. VMF attempts to minimize the distances between the intensities of the pixels situated within a predefined neighborhood.

3. PROPOSED METHOD

   Many noise reduction schemes are decision-based median filters. This indicates that the noise pixels are first detected and are replaced by the median output or its variants. These techniques are very good because the uncorrupted pixels in a corrupted image will not be modified. The replacement methods in these noise reduction schemes cannot preserve the features of the images. Some other methods preserve edges

   during noise reduction but it has problem in detecting noisy patches.

   In this regard, here propose the implementation of multi

   level smoothing algorithm for three types of noises. The first method able to preserve the edges during noise reduction, but

   choice is as follows

   D( I (x, y, t) ) e( I ( x, y,t ) / c)2

   (4)

   is not able to produce accurate result on different noises. The second method specially designed to eliminate different types of noises but the noise reduction process has week feature

   D( I (x, y, t) )

   1

   1 ( I (x, y, t) / c)2

   preservation. The first method is Multi Scale -Anisotropic Diffusion (MS-AD) [4] and the second method is Vector Median Filtering [5] (VMF). Combining both methods will avoid the drawbacks of either one of them. The aims of this method are to correct images corrupted by multi modal noises and preserve edges in the image.

   Where c is the diffusion parameter that controls the strength of the filtering process.

   C) Multi Scale Edge Detectors

   k

   The structure tensor is calculated for each pixel at the specified scale k in the image as follows

   A) Multimodal noise model

   M (x, y) f (x, y)f (x, y)T

   (5)

   The degraded image can be mathematically expressed by the following formulation

   The next step contains the eigenvector decomposition of the matrix Mk(x, y) to determine the Eigen values 1k and 2k , 1k >> 2k and 1k>> 0, then the pixel is an edge and the

   multi-scale edge response is calculated as follows

   I (x, y) F(x, y) * h(x, y) (x, y)

   (1)

   Where I(x,y) is the degraded image, F(x,y) is the original image, (x,y) is the noisy function, h(x,y) is the spatial representation of the degradation function ,. The noise model consists of three types of noise, Gaussian noise, Impulse noise and Photon noise. The image formation process can be

   E(x, y) sqrt( k )dk

   1

   k0,s

   1

   Where k is the Eigen value.

   1

   k

   k max{eig[M (x, y)]}

   (6)

   (7)

   expressed as follows

   F (x, y) (0, )

   (2)

   1. Vector Median Filtering

      VMF minimize the distances between the intensities of

      I (x, y)

      sup inf

      ( x, y )

      F (x, y)

      F (x, y)

      the pixels situated within a predefined neighborhood in order to implement impulse noise suppression. VMF calculate the

      ( x, y )

      F (x, y) * h N (t, t)

      distances between the intensity values of the pixels situated in

      a neighborhood around the central pixels (x, y) as follows

      were N (0, ) is the Gaussian noise with zero mean and standard deviation , is the probability of impulse noise, inf and sup are the infimum and supremum functions and is

      L( x, y)

      I ( p, q) I (m, n)

      (m,n)

      (8)

      the photon rate respectively, and is the R2 image domain . The strength of the noise component in an image is controlled by two uncorrelated parameters, and .

      B) Anisotropic Diffusion (AD)

      The noise reduction techniques based on anisotropic

      where . defines the L2 norm

      pq

      VMF performs the ordering of the Lpq values in increasing order and the intensity of the central pixels of the neighborhood , I(x, y), is replaced by the intensity of the pixel that has minimum value in the L ( p, q) set.

      diffusion equations, the PeronaMalik (PM) [6] equation provides a better algorithm for image segmentation, edge

      I (x, y) I (arg( p,q) min(Lpq ))

      (9)

      detection, noise removal, and image enhancement. The basic idea behind the PM algorithm is

   2. Combination of MS-AD and VMF noise removal techniques

      I (x, y,t) / t div[D( I (x, y,t) )I (x, y,t)]

      (3)

      In the proposed noise removal scheme the impulse noise estimator (Ne) [8] has been implemented as follows

      where I (x, y) is the image at time t, div(.) represents the divergence operating, I (x, y, t) is the gradient of the image, and D( I (x, y) ) represents the diffusion coefficient denoted

      Ne

      I (x , y ) 1

      c c size() 1

      I (x, y)

      ( x, y )\( xc , yc )

      (10)

      as D(s) . In this model, the diffusion coefficient D(s) is a nonnegative monotonous decreasing function. A typical

      Where size() denotes the cardinality of the neighborhood and (xc, yc) defines the coordinate of the centre of the

      neighborhood . The noise estimator [5] is calculated for each pixel in the image and if the value of Ne is higher than a predefined threshold j (Ne j) then the pixel is assumed to be corrupted by multimodal noise.

      In this method, the output of the noise estimator gives the decision rule that selects the noise removal technique that is applied to each pixel in the image. If the value of noise estimator Ne calculated for the pixel (x, y) is higher than the predefined threshold value j, then the value of the pixel will be updated using the VMF filtering scheme. Otherwise, this will be updated using the MultiScale-AD approach. The value of the threshold parameter j should be set in the interval [140, 250].

4. EXPERIMENTAL RESULTS

   The tests were conducted on different images of size 256×256. All images were corrupted by multimodal noises and the performance of the proposed filtering scheme is quantitatively evaluated using the Peak Signal to Noise Ratio (PSNR).

   Photon noise, (c) shows the result of MS-AD method,(d) shows the result of VMF method, and (e) shows the result of the proposed MS- AD VMF image restoration method. This technique outperforms the VMF and MS-AD noise removal techniques.

5. CONCLUSIONS

The multi-phase noise removing scheme that is able to restore digital images corrupted by multimodal noise has been implemented. The inclusion of VMF into the formulation of AD produced a more robust noise removal scheme that is able to eliminate different types of noises and also preserve feature. This noise reduction scheme was quantitatively evaluated using standard parameters such as PSNR, Epi and its performance has also been assessed when applied to different images. PSNR value of MS-AD VMF method is higher than that of MS-AD and VMF methods. Epi value closer to 1 indicates that accurate edge preservation was attained by this data smoothing algorithm.

The future works will focus on the development of more

10

PSNR 10 log

max

( x, y)

(I (x, y))2

(11)

accurate models that can be applied to detect the pixels that are corrupted by non-Gaussian distributed noise and

(1 / size()) O(x, y) I (x, y) 2 dxdy

( x, y)

where O(x, y) defines the pixel intensities of the original image O and I(x, y) are the pixel intensities resulting after the

pi

data smoothing algorithms were applied to the image that was corrupted by multimodal noise, R2 is the image domain,. The edge preservation index (Epi) is

E (O O, I I ) (12)

(O O, O O)(I I , I I )

where I define the image resulting from smoothing process, O

is the original image, O and I are the mean intensity values calculated from images O and I, respectively and

additional work will be concerned with the removal of noises in a color image.

a b

(q, r)

q(x, y)r(x, y) . The Epi value is

( x, y)

normalized in the interval [0, 1] and a value closer to one indicates accurate edge preservation attained by the data

smoothing algorithm. c d

The experimental tests reported results when the performance of the MS-AD VMF algorithm has been compared against those offered by the MS-AD and VMF techniques. The first set of experiments was conducted on test images corrupted by Gaussian and impulse noise and evaluated using PSNR metric and Epi value. The second set of experiments was conducted on test images corrupted by

Gaussian, impulse and photon noise and evaluated using

PSNR metric and Epi value. The results indicate that the MS- e

AD VMF image restoration strategy outperforms the VMF and MS-AD noise removal methods because of its ability to locally adapt to the characteristics of image noise.

In Figure 1, (a) shows the original image, (b) shows test Image corrupted by Gaussian noise, Impulse noise and

Figure 1 Experimental Results in Presence of Gaussian,

Impulse Noise and Photon Noise – Cameraman Image

1. Original Image

2. Test Image Corrupted by Gaussian Noise ( N( 0, 20)

   ), Impulse Noise

   (- 0.2) and Photon Noise

3. MS-AD Image

4. VMF Image

5. MS-AD VMF Image

Table 1 Quantitative Results n Presence of Gaussian, Impulse Noise and Photon Noise

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