A Detail Preserving Filter for Impulse Noise Detection and Removal

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					                                   ICGST-GVIP Journal, Volume 7, Issue 3, November 2007

         A Detail Preserving Filter for Impulse Noise Detection and Removal
                           S. Md. Mansoor Roomi , T. Pandy Maheswari , V. Abhai Kumar
                         Dept of ECE, Thiagarajar College of Engineering. Madurai, TN, India

Abstract                                                           schemes, by applying “no filtering” to preserve true
It is imperative to remove impulse noise corrupted pixels          pixels and Simple Median filter to remove impulse noise.
in images, in order to facilitate the subsequent processing        In [23], Manglem singh et al. have proposed adaptive
such as image analysis, segmentation, pattern recognition          rank ordered median filter(AROM) that employs two
etc. Many linear and non linear filtering techniques have          stage switching schemes utilizing rank-conditioned
been proposed earlier to remove impulse noise, however             median       filter(RCM)[10]      and     center-weighted
the removal of impulse noise is often accomplished at the          median(CWM) filter[6]. The shortcoming of impulse
expense of blurred and distorted features of edges;                detection and switching scheme is that they employ
therefore it is necessary to preserve the edges and fine           different optimizing parameters: four thresholds in SD-
details during filtering. In this paper a no reference blur        ROM in [12], a set of fuzzy rules and membership
metric based iterative edge preserving filtering technique         functions, etc. Additionally, methods such as fuzzy filters
has been proposed, that is selective on noisy and edge             [13-15], and the neural network method [15], were also
pixels. Experimental results show that the proposed filter         developed but their performances depend on previous
is superior over the state of art filters in maintaining           training. In this context, a detail preserving, least
higher peak signal to noise ratio (PSNR), near ideal               blurring, noise removal technique becomes essential.
structural similarity index measurement (SSIM) and                 This paper proposes an iterative, selective, filtering
lower blur.                                                        technique the uses blur metric (BM) [19] in its frame
                                                                   work to remove impulse noise. The outline of the paper is
Keywords:                                                          as follows. Section 2, reviews impulse noise model,
Impulse noise, SSIM, PSNR, Perceptual blur metric                  Section 3, presents the novel iterative, adaptive filtering
                                                                   scheme. Section 4, provides the experimental results and
1. Introduction                                                    discussion.
A robust image enhancement technique has to suppress
the noise while preserving natural information in the              2. Impulse noise model
images. A large number of linear and non linear filtering          Consider an image I and an observation image X of same
algorithms [1] have been proposed to remove impulse                size
noise from corrupted image to enhance image quality.
Most of the linear filters generally have a neighborhood                  ⎧ N i , j with probabilty p
                                                                          ⎪                                 ⎫
                                                                   X ij = ⎨                                 ⎬
averaging mechanism to remove impulse noise and tend                      ⎪ I i, j with probabilit y 1 -
                                                                          ⎩                                p⎪
                                                                                                            ⎭             (1)
to destroy all high frequency details like edges, lines and
other fine image details. This led to the development of           Where i=1,2,…..s1 and i=1,2,…..s2 and 0<p<1.
nonlinear median-type filters such as stack filters [3],            Iij and Nij denotes the pixel values at location (i,j) of the
multistage median [5], weighted median [6,7], rank                 original image and the noisy image, respectively and Nij a
conditioned median [10], and relaxed median [11].                  noise value independent from Iij.For gray level images
However, most of these filters are implemented                     with 8 bits per pixel ,when the images are contaminated
uniformly across the image and thus tend to modify both            by fixed value impulse noise, Nij the corrupted pixel is
noisy and noise-free pixels. Consequently, the removal of          equal to 0 or 255 each with equal probability (p/2).
impulse noise is often accomplished at the expense of
blurred and distorted features, thus removing fine details
in the image. Therefore, a noise-detection process to              3. Proposed work
discriminate the uncorrupted pixels from the corrupted             In an impulse detection based noise filtering technique,
pixels prior to applying nonlinear filtering is highly             the first step is to find the position of impulse from the
desirable. Raymond H.Chan and Nikolova [16] and                    corrupted image to apply filtering on the noisy pixels
Florencio and Schafer [17] have proposed switching                 alone, while preserving other noise free pixels. There is a

                                        ICGST-GVIP Journal, Volume 7, Issue 3, November 2007

tendency for any impulse detection scheme to misclassify                            edge(local minima and local maxima)
the edge pixels in the corrupted image as noise and vice                        •   Calculate edge width (local blur)
versa, since the nature of the noise and edge in an image                       •   Blur measure=sum of all edge width        (2)
appear to be similar due to their sudden transition in the                                           No of edges
gray level value. It becomes imperative to differentiate
between noisy and edge pixels. Extracting the edges from
the corrupted image is also a difficult task without having                                       Corrupted Image f’(x,y)
prior knowledge about the edge information. The issue of
identifying noise free, noisy and edge pixels still looms
large, which has a direct implication on preserving details                                        Noise detection N(i,j)
in an image during filtering. The proposed iterative,
selective detail preserving filter (DPF) takes these issues
into account and tends to isolate pixels belonging to                                             Edge detection e(i,j)
edge, noise, and noise free even at higher noise levels as
discussed below.                                                                       Noise filtering along edge direction

3.1 Selective Filtering
One of the main properties of the classical filters [1] is
that all input samples X are unconditionally affected by                               Yes                      If
the filtering process. In the presence of impulse noise                                                  BM(i+1)<BM (i)
model stated above, this approach is not optimal in
contrast to continuous noise distributions, only certain
samples of the original Image I are corrupted and others                                                   No
remain unchanged. The concept of selective filtering is
accomplished by,
1. Deciding whether the input sample considered (centre                                                      Stop
pixel in the processing window) is corrupted by an
impulse.                                                                            Figure 2.Framework for Detail Preserving Filter
2. If so, replace it by a value estimated from its neighbors
in the window; otherwise pass it to the output                       3.2.1 Impulse noise Detection
unprocessed. as shown in figure 1                                    As a first step in DPF, Adaptive Median Filter based
                                                                     impulse detector [16] is applied for finding the position of
                                                                     impulses. Consider a (2m+1) x (2m+1) window W around
                     Noisy     Image
                                                                     a pixel Xp, q given by,
                                                                                  ⎧ X i, j | p − m ≤ i ≤ p + m , ⎫
                                                                                  ⎪                              ⎪         (3)
                                                                     W   p ,q   (X ) = ⎨                             ⎬
                                                                                       ⎩            q − m ≤ j ≤ q + m⎪
                          Is pixel
                           Noisy                                     Where p,q denotes the index of the current pixel. It could
                                                                     be observed that the corrupted pixels belong to the set
                                                                     {Wmin ,Wmax}, where Wmin is the minimal pixel value in
               Yes                                                   the defined window and Wmax is the maximum pixel
                                                                     value. A pixel may be corrupted and assigned to a flag
                 Detail preserving filter                            matrix ‘N’ as,
                         (DPF)                                               ⎧1 if {( Χ i , j ≠ M i , j ) & Χ i , j ∈ { min,Wmax }}
                                                                                                                      W             (4)
                                                                      N (i, j ) = ⎨
                                                                                  ⎩0       else
                                                                       Where X and M are the corrupted and filtered images
                                                                     respectively. This impulse detection scheme detects
        Figure 1 Selective filtering scheme                          impulse noise even at higher corruption levels setting the
                                                                     flag matrix N(i.j) values as 1 wherever noise exists.
3.2 Detail Preserving Filter (DPF)
 It is necessary to extract noise and edge information from          3.2.2 Edge detection
the corrupted image before filtering. Locations of noisy             In order to isolate the noisy pixels present on the edge,
pixels are obtained by applying adaptive impulse noise               edge information from the noisy image is necessary.
detection. The knowledge of the rough estimate of edge               Extracting edges from the corrupted image is a difficult
positions from the corrupted image is obtained by                    task, since the noisy edges will also be detected. So
filtering and detecting edges. Such a DPF framework is               median filtering is applied on the corrupted image f’(x,y),
given in figure 2, where the final filtering is oriented             Canny edge detector is applied on the median filtered
towards the edge direction which ultimately tends to                 output m(i,j) since Canny detects true edges at higher
reduce the blur metric (BM) given by the algorithm[19],              level corruption also. In Canny, location of edges are
                                                                     identified using non maximal suppression (eqn 5)
    •    Find strong vertical edges in the filtered image             ∂                                                   (5)
    •    For each corresponding edge in the processed                    (G * I ) = 0
         image: Find the start and end positions of the

                                                  ICGST-GVIP Journal, Volume 7, Issue 3, November 2007

 e(i, j ) = ∇(G * I )
                                                                            (6)              In the above figure, an example noisy edge flag, Ne(i,j) of
                                                                                             size 7x7is shown ,where Z is a noisy edge pixel . Shaded
Where G is a Gaussian function of standard deviation
                                                                                             regions indicate the direction of edge, Here noisy edge
  and I(i,j) is obtained from the median filtered output
                                                                                             pixels indicated by the 1’s and 0’s represent either noise
m(i,j). Edge matrix e(i,j), will have the value 1 if there is
                                                                                             free or non- edge pixels. The proposed method tends to
an edge pixel and value 0 for pixels not on edge. Initially
                                                                                             replace ‘Z’ by median of nearest non noisy pixels
edge is detected from the median filtered output, and then
                                                                                             contained in the vector ‘Y’ along the direction of the edge.
edge is detected from the iterative filtered result.
            ⎧ m (i , j )
I (i, j ) = ⎨
                                   when k = 1
                                   when k > 1
                                                                           (7)                             {
                                                                                             S1 i , j = med ( Y ) i , j = s , t ∀ Ne       i, j   = 1              (11)
            ⎩ s k −1 (i, j )

Where k is the order of iteration                                                            Here the corrupted pixel position x(i,j) indicated by the
                                                                                             flag matrix of noisy edge Ne(i,j) and S1(i,j) is filtered
 m (i , j ) = adaptive median filtered output
                                                                                             output of the noise other than on edge. If the population
 sk (i , j ) = proposed filtered output at kth iteration                                     of non noisy pixel along the edge is less, then a greater
 I(i, j) = input image for canny edge detection                                              window of size [s,t] along the direction of edge is
3.2.3 Categorization of noisy pixels
                                                                                                        In second filtering scheme, the noisy pixels
Categorization of a noise pixel as “Noise on Edge” or                                        indicated by flag Ne’(i,j) are filtered by applying median
“Noise but not on Edge” is accomplished by comparing                                         filter on the non noisy neighborhood as given below.
the noise(Ne) and edge(Ne’ ) flag, obtained from section
3.2.1 and section 3.2.2 respectively and given by,.                                          S2   i, j   = {med (V ) i , j = s , t ∀ Ne ' i , j = 1
               ⎧1         if e(i, j) = 1 & N(i, j) = 1 ⎫                    (8)
 N e (i, j ) = ⎨                                       ⎬                                     where S2(i,j) is filtered output of the noisy edge pixels.
               ⎩0         otherwise                    ⎭
                                                                                             And ‘V’ is vector containing non noisy pixels present in
                                                                                             its neighborhood. Here again the window size varies
              ⎧1         if e(i, j) = 0 & N(i, j) = 1 ⎫                    (9)
N ' (i, j ) = ⎨                                       ⎬                                      depending on the population of non noisy pixels in ‘V’. A
              ⎩0         otherwise                    ⎭                                      filtered pixel at location (i, j) is included in the estimation
where                                                                                        next noisy pixel thus making the method Recursive. The
N(i,j)=noise matrix                                                                          final filtered image S(i,j) is obtained as,
e(i,j)=edge matrix                                                                            S ( i , j ) = S 1i, j ∪ S 2 i, j                         (13)
Ne(i,j)=Noise on Edge
                                                                                             The entire filtering scheme functions with median filtered
Ne’ (i,j)=noise other than edge
                                                                                             image as its input which is not completely reliable to
Thus Ne(i,j) gives the location of noisy pixels present
                                                                                             obtain all the edge details of the original image. In order
only on edge is and Ne’ (i,j) gives the remaining noisy
                                                                                             to compensate this, an iterative procedure is adopted
pixels .
                                                                                             which improves the quality of image by minimizing the
                                                                                             blur. In all iterations, the output filtered image is given as
3.2.4 Filtering schemes
                                                                                             an input to the next iteration for edge detection. This
Two filtering schemes are presented here, one for noise                                      process depends on the blur metric (eqn 1) and repeats
indicated on edge pixels by Ne(i,j)and other for noisy                                       until there is no further significant improvement as given
pixels not on edge indicated by Ne’(i,j). During the                                         in eqn 14.
filtering of the noisy edges, each noisy edge pixel is                                                     ⎧k = k + 1    if blur metric( sk +1 (i, j ) < sk (i, j ))
replaced by taking the median of closest non noisy edge                                       sk (i, j ) = ⎨
                                                                                                           ⎩sk (i, j)     if blur metric( sk +1 (i, j ) ≥ sk (i, j ))
pixel present along the direction of the edge which is
described in Figure 3. The direction of edge is found by
using the connectivity of the edge pixels.                                                                                                            (14)
                                                                                             Where‘k’ is the number of iteration k=1,2 ,3 ,4---------N,
 N8 ( P) = N4 ∪ {(i + 1, j + 1), (i + 1, j − 1), (i − 1, j + 1), (i − 1, j − 1)} (10)
                                                                                             ‘N’ is the last iteration ,the iteration stops when blur
Where N8(P) and N4(P) is 8 connected and 4 connected                                         metric of ‘N-1’ iteration is less than the Nth iteration. Thus
neighbors for the pixel N’(i,j).                                                             filtering is done efficiently on the corrupted image
                                                                                             preserving the sharpness of edges.
                        0      1   0    1 0 0 1
                        1      0   1    0 1 0 0                                              4. Experimental Results
                        0      0   1    0 0 0 0                                              In this section, extensive experimental results with
                        0      0   0    Z 1 0 0                                              commonly used gray-scale test images of size        256 x
                                                                                             256 are presented to assess the performance of the
                        1      0   0    0 0 0 0
                                                                                             proposed impulse noise removal technique. These images
                        0      1   0    1 0 1 1                                              including Lena, boat have distinctly different features in
                        1      0   0    0 0 0 0                                              terms of details as shown in figure 4d. These images are
                                                                                             corrupted by various levels of salt and pepper noise. The
                        Figure 3 .Edge direction                                             performance of the proposed method is compared with
                                                                                             that of many other well-known algorithms. such as

                                             ICGST-GVIP Journal, Volume 7, Issue 3, November 2007

adaptive median filter, progressive switching median                            5(b).The above results clearly depicts that (figure 5(d) is
filter, Central weighted median filter. The performance of                      sharper when compared to figure 5(b) and figure 5(c)
each filter is validated in terms of quality metrics                            respectively, hence sharper the image, lower the blur
PSNR,SSIM and BM                                                                metric.
          M N
 MSE = ∑ ∑ ( S (i, j ) − I (i , j )) 2              (15)
          ii = 1 j = 1

                         ⎛         ⎞
                         ⎜ 255 2   ⎟
 PSNR = 10 log 10        ⎜         ⎟                               (16)
                         ⎜         ⎟
                         ⎜ MSE     ⎟
                         ⎝         ⎠

I--- Original input image
S --- Output filtered image
                                                                                 (a) 40% corrupted image                        (b)         1st Iteration output
The Structural Similarity (SSIM)[20] index is a method
for measuring the similarity between two images.                                                                                            Blur metric= 3.2632

SSIM (x, y ) = [l (x, y )]α .[c(x, y )]β .[s(x, y )] γ (17)

where α , β , γ are positive values used to adjust the
relative importance of the three components. Amount of
blur can be measured by applying blur metric (eqn 2)                            ( c) 2nd Iteration output                            (d) 3rd Iteration output
algorithm [19].
                                                                                  Blur metric=2.8140                                        Blur metric= 2.5485

             Results & Discussions                                                           Figure5. Comparison of Iterative Results

                                                                                                            Table1. Blur Metric Analysis
                                                                                                 10%           20%    30%           40%        50%      60%        70%
                                                                               Iteration 1           2.13      2.03   2.74          3.26        3.17     3.68      2.95
                                                                               Iteration 2       2.08         2.09    2.42       2.81          2.17     2.81*      2.74*
                                                                               Iteration 3       2.10         2.21    2.42       2.54          2.44*    2.94       3.22
(a) Original image             (b) 50% corrupted Image                         Iteration 4       2.10*        2.17*   2.21       2.16*         2.47     2.35       4.62
                                                                               Iteration 5       2.08         2.18    2.15*      3.02          2.56     2.41       4.28

(c) Adaptive Median filtered d)Detail preserving filtered output                             1
Blur Metric= 2.5166,                   Blur Metric= 2.4269                              0.5
SSIM=0.8691                             SSIM=0.8923,                                         0
                                                                                                 1               2              3                  4               5
    Figure 4 Comparison of filtered output
                                                                                                                         i t e r a t i on
The figure (4a) shows the original Image figure (4b)
shows the 50% (salt & pepper) noise corrupted boat
image of size (256x256) and the adaptive median filtered
image is shown in (4c) has the blur metric value of
                                                                                         Figure 6 Blur metric Vs Number of Iteration
2.5166 and proposed Detail preserved filtered image is
shown in the figure (4d) and has the blur metric value of
2.4269 which is lesser than adaptive median filtered                            The above table shows the blur metric analysis of various
image figure (4c).                                                              iterative output of the filtered image for different levels of
                                                                                corruption. It can be seen from figure 6 that blur reduces
Similarly other results are shown for Lena image for all                        gradually till it reaches the minimum value.
iterations considered. From the above results the
proposed filter blur metric value for the 2nd iteration
output shown in figure 5(c) is 2.8140 which is less than
the 1st iteration output blur metric 3.2632 shown in figure

                                                ICGST-GVIP Journal, Volume 7, Issue 3, November 2007

       Table 3       SSIM Comparisons For different filters
   Filter        10%         20%     30%    40%      50%     60%     70%
                                                                                                      1                                     SD[12]
  SD[12]         0.96        0.88    0.70    0.44    0.23    0.11    0.05
   SM[2]         0.83        0.78    0.65    0.44    0.24    0.12    0.06                           0.8

                                                                                      SSIM Values
PSM[8]           0.95        0.91    0.87    0.81    0.70    0.49    0.25                                                                   CWM[6]
CWM[6]           0.89        0.77    0.52    0.30    0.15    0.08    0.04                                                                   PWMAD[9]
PWMAD[9]            0.94     0.83    0.57    0.32    0.16    0.09    0.04                           0.4                                     MF[2]

   MF[2]         0.98        0.95    0.92    0.88    0.83    0.77    0.68                                                                   AM[4]
  AM[4]          0.98        0.96    0.93    0.90    0.86    0.80    0.74
    DPF          0.98        0.96    0.94    0.91    0.89    0.85    0.79
                                                                                                          10   20 30   40   50 70
                                                                                                                Noise level in %

    Table 2 PSNR Comparisons For Iterative Results
Noise                                                                                     Figure8. SSIM Vs Noise level in % With Different
             10%           20%      30%     40%      50%      60%      70%
Level ->                                                                                                     Filters
             30.42         27.49    22.99   18.74    15.15   12.31     9.96
Iterative                                                                           Table 2 shows the PSNR comparison for the Iterative
 Results     37.81         34.53    32.09   30.24    28.13   26.10     24.17        filter results.* indicates the highest PSNR value. It can be
    1                                                                               seen that the PSNR value increases after each iteration.
   2         37.96         34.68    32.57   30.82    29.15   27.29     25.36        Table 3 Shows the Structural similarity based image
                                                                                    quality assessment [20], For an Ideal Image Quality
   3         38.03         34.83    32.83   31.05    29.16   27.43     25.44        index of the SSIM value=1, the above Table 3 depicts
                             *        *       *                *                    clearly that proposed filters values are approaching
   4         38.14         34.65    32.69   30.87    29.22   27.30     25.62
                                                                                    towards quality index of an ideal image. In Figure 8, the
               *                                       *                 *          varying noise level in percentage Vs. SSIM values are
   5         37.98         34.84    32.84   30.98    29.28   27.51     25.60        plotted for different filtered results, we can see that for
                                                                                    the proposed filter Q approaches nearly to 1 and the
                                                                                    value is high when compared to other filters.

                                                                                    The proposed Filtering technique applies Iterative,
                                                                                    selective and directional filtering on the corrupted image
                                                                                    to reduce the blur. The results shows that this method
                                                                                    removes impulse noise, also simultaneously preserves
                                                                                    edges at higher levels of noise as is evident from
                                                                                    comparison with existing filters.
(a) 70% noise filtered                        (b) 70% noise filtered
       boat image                               Barbara image
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                                    ICGST-GVIP Journal, Volume 7, Issue 3, November 2007

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