Nonlocal-Means Image Denoising Technique ... - Semantic Scholar

Peter DJ, Govindan VK, Mathew AT et al. Nonlocal-means image denoising technique using robust M-estimator. JOURNAL OF COMPUTER SCIENCE AND TECHNOLOGY 25(3): 623–631 May 2010

Nonlocal-Means Image Denoising Technique Using Robust M-Estimator Dinesh J. Peter1 , V. K. Govindan1 , and Abraham T. Mathew2 1

Department of Computer Science, National Institute of Technology Calicut, Calicut, 673 601, India

2

Department of Electrical Engineering, National Institute of Technology Calicut, Calicut, 673 601, India

E-mail: [email protected]; {vkg,atm}@nitc.ac.in Received April 1, 2009; revised November 6, 2009. Abstract Edge preserved smoothing techniques have gained importance for the purpose of image processing applications. A good edge preserving filter is given by nonlocal-means filter rather than any other linear model based approaches. This paper explores a different approach of nonlocal-means filter by using robust M-estimator function rather than the exponential function for its weight calculation. Here the filter output at each pixel is the weighted average of pixels with surrounding neighborhoods using the chosen robust M-estimator function. The main direction of this paper is to identify the best robust M-estimator function for nonlocal-means denoising algorithm. In order to speed up the computation, a new patch classification method is followed to eliminate the uncorrelated patches from the weighted averaging process. This patch classification approach compares favorably to existing techniques in respect of quality versus computational time. Validations using standard test images and brain atlas images have been analyzed and the results were compared with the other known methods. It is seen that there is reason to believe that the proposed refined technique has some notable points. Keywords

1

image processing, denoising technique, nonlocal-means filter, robust M-estimators

Introduction

Denoising is the technique of removing noise from an image. Most of the denoising techniques seem to be very similar regardless of the image being processed. All denoising algorithms are based on the noise framework and the relative smoothing framework. Due to the fixed estimations of all denoising methods on the original image, fine structures are smoothed out since they act like noise. So the implementation of these techniques must be greatly contingent on the type of images and the analytic knowledge of the characteristics of an output image. A linear Gaussian smoothing function[1] reduces noise in piecewise constant area but blurs edges. But nonlinear models handle edges much better than any other linear models. Total variation filter[2] gives good edge preserving smoothing scheme but tends to generate mask effect in flat regions on the output image. Bilateral filter is another nonlinear filter proposed by Tomasi et al.[3] to smooth images while preserving edges. Here the output of each pixel is the weighted average of its neighbors. When compared to anisotropic diffusion, bilateral filtering is not flat to blocky artifacts since it does not depend on shock information. Since it is nonlinear and its process is computationally expensive, conventional acceleration will not be

applicable. Buades et al. in [4] pointed out that Nonlocal-means filter is a special case of bilateral filter which gives better edge preserving denoising results. The output of the filter at each pixel is replaced by the weighted average of pixels with surrounding neighborhoods using Gaussian function as the smoothing function. This method gives good results but it is too slow to be manageable. A fast approach of nonlocal-means algorithm was already proposed in [5-10]. In [5], two different filters have been introduced to eliminate uncorrelated neighborhoods from the weighted average of its mean and gradient. Similarity between the pixels by averaging the gray values in the neighborhood is measured by one filter and the average gradient orientation between two neighborhoods is found by another filter. But there are few disadvantages of using these filters which are briefly explained in [5]. In [6], the identification of the similar neighborhoods is based on the first and second order moments of the neighborhoods of each pixel. This will give better results than the other fast approaches since the standard deviation is not much sensitive to noise. A more realistic image model assumes that images are made of smooth regions, separated by sharp edges containing more duplicated structures. On averaging the duplicated structures, noise is impressively reduced when compared with the averaging of pixels in the same

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J. Comput. Sci. & Technol., May 2010, Vol.25, No.3

structure, so the computation of nonlocal neighborhoods give better results than the local neighborhood computation. This paper proposes a refined approach in which it says that the reconstructed pixel value is obtained by the weighted average of all pixel values in an image using some robust function from robust statistics. But each weight is related to the similarity between nonlocal neighborhood pixels. The selection of smoothing and similarity function is an important attempt here for getting good results. Comparison has been made to find out the best robust M-estimator function which will be very well suited for nonlocal-means denoising algorithm. To make the algorithm work faster, similar neighborhoods are classified using the method proposed in Subsection 2.3, thereby reducing the effect of uncorrelated neighborhoods for the weight calculation. The rest of this paper deals about the following. In Section 2, the methodology of the robust nonlocalmeans method is introduced. In this, the inside information of various robust M-estimator functions (edge arresting functions) are examined and the selection of best robust M-estimator function has been exercised. In order to accelerate the algorithm, a new patch classification scheme is proposed in this section. In Section 3, the results are compared with other edge preserved smoothing techniques and its details are discussed briefly. Section 4 concludes the paper. 2

Ismooth = min I

X

ϑσ (Nj − Ni ).

(1)

i,j∈I

Here ϑσ represents the M-estimator function which is also called edge arresting smoothing model, σ is a scale parameter, Nj and Ni are the neighborhoods of the pixels i and j of the image I. A suitable ϑσ -function permits us to minimize the consequence of the noises. And the derivative of the given ϑσ -function (which is also called influence function) examines its behavior. To increase the robustness and refuse noises, the ϑσ function must be more forgiving about noises. Black et al.[16] compared some robust functions and suggested Tukey’s biweight M-estimator function since it contributes larger potential to outliers. But here, one needs to determine the best robust M-estimator function which will be very well suited for nonlocal-means algorithm. The classical nonlocal-means method used exponential function for its weight calculation. Since this function has a wide symmetric bell-shaped probability density function, the influence function of this (see in Fig.1) symbolizes that this is rather robust to outliers. Fig.2 plots the weight functions of various robust M-estimator functions and their formulas are given

Methodology

A different interpretation of nonlocal-means filtering is presented here. A different formation has been made to form the kernels for smoothing function and to calculate the weight for similarity functions. Here the similarity function is the decreasing function of weights for the neighborhood of each pixel in an image. 2.1

Robust M-Estimator Function Selection

Estimation function is the function of intensities of the image. The properties that will satisfy the estimation function for edge preservation have been defined in various papers. Geman et al.[11] recommends functions having a finite asymptotic behavior for the edge preserving regularization. In [12-15], the researchers prefer using convex potentials in order to ensure the uniqueness of the solution. The problem of estimating a smooth image from a noisy image can be explained from the area of robust statistics [16] and the review of applications of robust statistics in computer vision can be seen in [17]. Robust approaches for local image smoothing can be seen in [18]. To find such an image I using nonlocal-means algorithm, it satisfies the following criterion:

Fig.1. Influence functions of the robust M-estimator functions in Table 1.

Fig.2. Weight functions of robust M-estimator functions in Table 1.

Dinesh J. Peter et al.: NLMeans Denoising using Robust M-Estimator Table 1. Robust M-Estimator Functions and Its Weight Function Robust M-Estimator Function

Weight Function

Exponential (ϑG σ)

G (x) = e 2σ 2 gσ

Geman-McClure (ϑGM σ )

GM (x) = gσ

Ã Tukey’s Biweight

calculation in nonlocal-means filter and the results show that it has more stable characters for calculating the weights. 2.2

−x2

(ϑT σ)

T (x) gσ

=

1 x )2 )2 (1+( σ 1 [1 2

x 2 2 − (σ ) ]

0

| x |6 σ

625

!

otherwise

in Table 1. This figure shows how the ϑσ -functions act on the outlier noises. All the ϑσ -functions in Table 1 are robust to outlier noises. Fig.1 plots the influence functions of various robust M-estimator functions. These influence functions are otherwise called as redescending norms. While analyzing Fig.1, the exponential influence function (ϑG σ ) not only reduces noise, but also blurs important features such as edges. ϑG σ allows to monotonically increase and decrease the effect of the Euclidean distance (Nj − Ni ). But for large distances, it tends to zero quickly. Thus it is called hard redescending norm. So smoothing may not behave properly but the edges are preserved. Tukey’s biweight M-estimator function (ϑT σ ) is another hard redescending norm which has a reduced normal distribution function than the exponential function for the same scale parameter σ (see Fig.2). In Fig.1, it shows that the outlier noises are influenced more in this norm. Though this norm is more robust to outlier noises, for the case of nonlocal-means filter, the noisy pixels are wrongly interpreted as detailed features and therefore enhanced instead of the smoothed. Due to the fast decay of the exponential and Tukey’s biweight influence function, Euclidean distances outside the fixed point “o1 ” lead to zero weights immediately, so smoothing may not behave properly but the edges are preserved. Hence, we need a function that compromises the effect of smoothness as well as edge preservation. Fig.1 clearly shows that Geman-McClure norm ϑGM gives an optiσ mized redescending behavior than the exponential and Tukey’s biweight error norms. The redescending factor of the Geman-McClure influence function in Fig.1 determines the behavior of the weight calculation in nonlocal-means filter. Even after the fixed point “o2 ”, this function does not descent to zero instead small weight is calculated which smoothes the image well and preserves the edges substantially. For the weight calculation in nonlocal-means filter, the robust weight function gσ· (x) is strictly relying on the similarity of the patches, i.e., similar patches give larger weights and dissimilar patches give smaller weights. Due to the optimized behavior of Geman-McClure norm, our method uses Geman-McClure weight function for the weight

Robust Nonlocal-Means Filter

Let s be the noisy image s = {s(x)|x ∈ Ω } defined over a discrete domain Ω ⊂ R2 and s(x) ∈ R+ is the intensity of noisy observed pixel x ∈ Ω . The estimated value of N L{s(x)} is computed as the weighted average of all pixels in an image s, P y∈N (x) w(x, y)s(y) NL{s(x)} = P (2) y∈N (x) w(x, y) where w(·, ·) are positive weights and N (x) corresponds to a set of neighboring pixels of x which is otherwise called as searching window. The weight w(x, y) measures the similarity between two square patches of the pixels centered on x and y and it is defined as ³X ´ w(x, y) = ϑσs GM σc (t)(s(x + t) − s(y + t))2 ³

t∈Ξ

´ := ϑσs ks(x) − s(y)k22,σ .

(3)

GM σc is the Geman-McClure kernel with closeness parameter σc that is calculated from Geman-McClure weighting function. It is used to take into account the distance between the center pixel and other pixels in the patch. The smoothing function GM σc is defined as 1

GM σc = ³

x + y 2 ´2 σc2 2

1+

.

(4)

(3) is also called as similarity function. ϑσs is a continuous decreasing function (robust M-estimator function) with ϑσs (0) = 1 and ϑσs (+∞) = 0, and Ξ represents the discrete patch region containing the neighboring pixels t. The parameter σs is used to control the amount of filtering. Typical examples of ϑσs are already discussed in Subsection 2.1. Here Geman-McClure Mestimator function is used as ϑσs -function where the exponential function is used in [4]. The robust nonlocalmeans filter NLr , which we will then consider, is defined as X 1 ³ C(x)

s(y) ks(x) − s(y)k22,σ ´2 y∈N (x) 1 + σs2 (5) where k · k is the usual l2 -norm. C(x) is normalizing constant any pixel x we have P such that for 1 C(x) = ¢2 . The usage of y∈N (x) ¡ ks(x)−s(y)k2 2,σ NLr {s(x)} =

1+

2 σs

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Geman-McClure function for the weight calculation of nonlocal-means filter enhances the image much better than the usual exponential function. Because whenever the algorithm faces dissimilar patches, this will not leave the weight to zero value instantly. This is the major reward of using Geman-McClure function and the experimental results depicted this distinctly. Since the proposed refined technique is working on spatial domain, ultimately this will take large CPU time. The nonlocal-means filter is the special case of bilateral filter and both of these are nonlinear in the sense that the weight calculation relies on the image intensities. Since the weight calculation from the nonlocal neighborhoods is still more tedious work and it takes more CPU time than the bilateral filter, a new patch classification scheme is proposed in the next subsection. 2.3

Patch Classification in the Search Space

Many recently proposed methods[5-10] deal with the computational burden of nonlocal-means filter. In [5-6], the methods used low-order statistic called “mean” for preselecting the patches. But it is easy to show that this simplistic pre-filtering method can lead to sub-optimal results. Fig.3 shows the example involving three 7 × 7 binary patches. The mean intensity of the patch centered on x is 0.4286. The two other patches centered on y and z have mean intensities 0.4286 and 0.5714 respectively, therefore favoring the weight computation process for the patches centered on y over z. However, the sample correlation coefficients Corr (x, y) = −0.75

while Corr (x, z) = 0.75, suggesting that z matches x much better than y does. Among those, we select a method to preselect a subset of the most relevant patches in a search space to avoid unnecessary weight computations. We suggest a single measure that is more enough to classify the patches in a search space. It is called structural information that can be calculated from the mean and standard deviation. The structural information of each patch centered on x in a search space is calculated as xi − µx |xi ∈ X σx

(6)

where µx is the mean and σx is the standard deviation of a patch X in nonlocal-means filter, xi is the pixel in the patch X. The patch is normalized by its own standard deviation so that the two patches being compared have unit standard deviation. A circularsymmetric Gaussian weighting function W = {wi |i = 1, 2, · · · , |X|} with unit sum

|X| ³X

´ wi = 1

i=1

is adopted in order to reduce the effect of noise. Here wi is the weight and |X| is the number of elements in the patch X. The estimates of the low-order statistics for the patch X centered on x, µx , σx are then modified accordingly as |X|

1 X µx = wi xi |X| i=1 and σx =

|X| ³ 1 X ´1 2 wi (xi − µx )2 |X| i=1

(7)

(8)

as described in [19]. Here |X| is the number of pixels in the patch X. The correlation (inner product) between any two patches, say X, Y , is a simple and effective measure to quantify the structural similarity. y −µ x and iσy y is equivalent The correlation between xiσ−µ x to the correlation coefficient between the patches centered on x and y respectively. The structural comparison ζ(X, Y ) is conducted on these normalized patches as ³x − µ y − µ ´ i x i y ζ(X, Y ) = ζ |xi ∈ X, yi ∈ Y. (9) , σx σy

Fig.3. A case where the similarity between patches using mean is sub-optimal.

Indeed, the mean structural map ζ between the patches in a search space are pre-computed in order to achieve fast structural comparison. The mean of the inner y −µ x product of xiσ−µ and iσy y is ζ. The actual combined x

Dinesh J. Peter et al.: NLMeans Denoising using Robust M-Estimator

structural map in nonlocal-means filter is found from the neighborhood patches under consideration in an image. And, to bring down the computational needs, the weight function in (5) may be restated as given below:  1 X 1   ³ ´2 ´2 , ³   C(x) ks(x)−s(y)k  y∈N (x) 1 +  h w(x, y) =   ζ>η     0, otherwise, (10) where η is a predefined value. This kind of patch classification leads to the nonlocal-means filter rather reducing the effect of denoising in the flat regions while preserving the detailed regions as well. 3

Experimental Results and Discussion

In this section, the proposed new approach of denoising technique is applied on brain atlas images to demonstrate its superior performance in noise reduction without noticeable loss of overall structures. Performances are also compared with several other edgepreserving denoising techniques in the literature. The test brain atlas images used for our experiments are shown in Fig.4. Fig.5 shows the effect of varying the parameters σc and σs on the resulting output image. Here σs acts as the controlling parameter that controls the weights for every pixel. We observe only a slight blurring effect when both parameters take larger values. Because of the brilliant properties of the GemanMcClure weight function and its influence function, a controllable blurring effect and a better preservation of edges lead to distinctly enhanced image quality. The brain atlas images analyzed here are taken from

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Harvard Medical University website[20] . The brain atlas image in Fig.6(a) represents Pick’s disease(MRI) shown in Fig.4(f). This image contains a lot of structures to preserve. Using the proposed denoising method, the structures are well preserved as shown in Fig.6(c). Shown in Fig.7 is the comparison of the nonlocal-means filters using different weight functions given in Table 1 for the brain atlas image shown in Fig.4(f). An image region is cropped and zoomed from the original, noisy and denoised images. Fig.7(b) is the original cropped and zoomed image. Figs. 7(c) and 7(d) are denoised images of applying exponential norm gσG and Tukey’s biweight norm gσT as the weight functions respectively. Fig.7(e) is obtained by applying Geman-McClure norm gσGM . This clearly shows that Fig.7(e) gives better visual quality than Figs. 7(c) and 7(d). The structures are preserved well and a proper smoothing has been

Fig.4. Test images (MR-PD brain atlas images) used for our experiments. (a) AIDS Dementia. (b) Alzheimer. (c) Cerebrovascular fatal stroke. (d) Huntington chorea disease. (e) Meningioma neoplastic tumor. (f) Pick’s disease. (g) Sarcoma neoplastic tumor (Courtesy to: [20]).

Fig.5. Robust nonlocal-means filtering with various σc and σs parameter values for the atlas image representing Sarcoma Neoplastic Tumor : Fig.4(g).

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nonlocal-means filter gives better PSNR value. But for the other increasing level of variances, nonlocal-means filter contributes lower PSNR values. But one can see that the proposed robust approach gives good PSNR values when compared to other techniques as the variance levels go higher. This shows the power of proposed

Fig.6. (a) Original brain atlas image (Pick’s Disease: Fig.4(f)). (b) Added Gaussian noise with σ 2 = 0.04, (PSNR = 15.6064 dB, RMSE = 42.2885).

(c) Denoised with proposed approach

(PSNR = 20.5267 dB, RMSE = 23.9996).

Table 2. Comparison of Denoising Techniques with Brain Atlas Images (The images are with noise variance σ 2 = 0.04. Best values are highlighted as bold. Brain Atlas Images: Courtesy to [20].) Brain Atlas Image

Denoising Methods

RMSE

SSIM

PSNR

Huntington Chorea (MRI)

Proposed approach Nonlocal-means Bilateral filter FOPDE Anisodiff

22.05 24.79 39.84 33.60 40.98

0.669 0.542 0.304 0.361 0.299

21.09 20.21 16.12 17.46 15.87

Pick’s Disease (MRI)


23.42 27.02 39.86 33.80 40.71

0.709 0.571 0.359 0.420 0.350

20.73 19.49 16.11 17.55 15.93

AIDS Dementia (MRI)


22.02 25.03 39.18 33.02 39.48

0.660 0.496 0.254 0.310 0.250

21.27 20.16 16.26 17.75 16.20

Alzheimer (MRI)


23.34 26.29 39.64 33.81 39.88

0.693 0.553 0.326 0.387 0.323

20.76 19.73 16.16 17.54 16.11

Alzheimer (fMRI)


29.72 31.97 40.93 36.58 41.21 2

0.678 0.627 0.585 0.602 0.584

18.66 18.03 15.88 16.86 15.83

Cerebrovascular Fatal Stroke


22.98 25.60 38.29 33.14 39.51

0.671 0.544 0.330 0.380 0.320

20.90 19.96 16.46 17.72 16.19

Meningioma Neoplastic Tumor


22.27 25.32 39.21 33.02 39.68

0.696 0.534 0.267 0.339 0.273

20.86 19.85 16.26 17.61 16.15

Sarcoma Neoplastic Tumor


21.61 25.43 38.63 32.34 39.67

0.651 0.475 0.243 0.302 0.240

21.43 20.02 16.39 17.93 16.16

Fig.7. Visual quality comparison of various robust weight functions applied on nonlocal-means filter using Pick’s Disease in Fig.4(f). (a) The region of the image to be considered. (b) Original image region. (c) Exponential weight function. (d) Tukey’s biweight function. (e) Geman-McClure weight function.

done. Figs. 7(c) and 7(d) preserve edges but smoothness is unstable. Comparisons have been made in Table 2 with several edge-preserved denoising techniques to show the power of the proposed denoising approach. For the purpose of comparison, apart from the classical metrics called PSNR (Peak Signal to Noise Ratio) and RMSE (Rooted Mean Square Error); SSIM measure (Structural SIMilarity) by Wang et al.[19] is included. SSIM is the only metric that measures two scenes with the assumption of human beholding property. Table 2 shows the comparison of the following other edge-preserved denoising techniques with various brain atlas images: classical nonlocal-means, classical bilateral filter, fourth order PDE-based denoising technique (FOPDE)[21] , Anisotropic diffusion[22] and the refined approach that is proposed. Fig.8 shows the visual quality of the various edge preserved denoising techniques for the Cerebrovascular Fatal Stroke image shown in Fig.4(c). Fig.9 shows the PSNR values of various edge preserving denoising techniques with the increasing level of variances. For low level variance,


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image of the proposed method is more or less similar to the original image. Table 3 shows PSNR values of various fast approaches of nonlocal-means filter applied on 512 × 512 barbara test noisy image. This standard textured test image is chosen to do comparison with various other approaches. The other PSNR values are taken from the respective publications. The proposed

Fig.8. Denoised images of various denoising methods. (a) Bilateral filter. (b) Anisotropic diffusion. (c) FOPDE. (d) Nonlocalmeans filter. (e) Proposed refined filter. The image is Cerebrovascular Fatal Stroke: Fig.4(c) degraded by Gaussian noise with σ 2 = 0.04.

approach in the way that how much information it preserves. To demonstrate the accuracy of the proposed method, comparison between the histograms of the denoised images of various techniques with the original image (for Alzheimer disease: Fig.4(b)) is made as shown in Fig.10. It is seen from Fig.10 that the denoised

Fig.9. PSNR values of various edge preserving denoising techniques with the proposed one. Original image representing Huntington’s Chorea Disease: Fig.4(d).

Fig.10. Historgam comparison of various denoising techniques. The histogram of proposed technique matches better with the original image. (Original image representing Alzheimer Disease: Fig.4(b) with noise variance: 0.04.) (a) Noisy image. (b) Bilateral filter. (c) Anisotropic diffusion. (d) FOPDE. (e) Nonlocal means filter. (f) Proposed refined nonlocal means. (e) Nonlocal means filter. (f) Proposed refined nonlocal means.

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refined nonlocal-means filter without patch classification gives good PSNR values than the same with the proposed patch classification technique since the prior one does not cause blurring effects or any other systematic artifacts. Generally, the patch classification approach to speedup the nonlocal-means algorithm works poor in detailed regions of an image, for example, 512 × 512 barbara test image contains several fine textural details. Hence, smaller number of similar pixels in the detailed region are used for weight computation process. Our result outperforms the classical nonlocal-means filter and the recent cluster tree-based patch classification approach[23] . The random sampling method adopted from [24] has been applied for reducing the computational complexity in classical nonlocalmeans filter. Here the samples from the vicinity of the reference patch are preferred. Buades et al.[4] has developed a spatial subsampling (multiscale algorithm) technique in order to accelerate the algorithm. The proposed structural map-based patch classification approach outperforms these fast approaches too. Fig.11 shows the computation time of patch classificationbased nonlocal-means implementations depending on the search window size. Various fast approaches are

J. Comput. Sci. & Technol., May 2010, Vol.25, No.3 Table 3. Qualitative Performance Comparison of Nonlocal Patch-Based Nonlocal-Means Filters When Applied to 512 × 512 Barbara Test Noisy (Gaussian σ 2 = 0.04) Image σ/PSNR Robust NLMeans (without patch classification) Robust NLMeans (with patch classification) Patch classification by mean and variance[6] Cluster trees, overlap ω = 10[23] Random sampling[24] Spatial subsampling[4] Classical nonlocal-means[4]

20/22.18 30.64 30.61 29.80 30.26 29.55 29.51 30.31

applied on 512 × 512 barbara test image. For growing window sizes, the spatial subsampling technique gives lower computation time but fails to produce quality reconstructed (or denoised) image. The second fastest approach for the growing window sizes is the proposed structural-map-based one. We considered the cluster tree-based with overlap parameter ω = 10 since this gives considerably quality denoised image. The proposed structural map-based patch classification approach quantitatively outperforms the computational time of random sampling, cluster tree-based technique, patch classification based on mean and variance fast approaches. Since we are interested only in patch classification-based technique to speed up the weight computation process in nonlocal-means filter, the computational time for the iterated versions of Nonlocalmeans filters is not shown in Fig.11. 4

Conclusion

Although the base of this work imitates the nonlocalmeans algorithm[4] , the results shown in this approach are very well desirable for the given brain atlas images. This proposed method suggests the use of GemanMcClure (ϑGM σ ) robust M-estimator function for finding the smoothing and similarity function. And to speed up this approach, we proposed a new patch classification technique based on the structural map. By doing this, some features of the images are well preserved even better than the classical nonlocal-means technique. The comparisons made for the denoised images from various denoising techniques are presented. This new proposal considerably increases the power of denoising and one can say that the proposed approach achieved the worthy level of pertinence. References

Fig.11. Computational time comparison of the nonlocal patchbased fast nonlocal-means filters depending on the size of the search window.

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Dinesh J. Peter received his M.Tech. degree from Manonmaniam Sundaranar University and is pursuing hid Ph.D. degree in computer science at National Institute of Technology Calicut. His major research interests include image processing and pattern recognition. He has published papers in various international journals and presented international conference papers. V. K. Govindan is a professor in the Department of Computer Science and Engineering, National Institute of Technology Calicut. He obtained his B.Tech. and M.Tech. degrees from National Institute of Technology Calicut and Ph.D. degree from Indian Institute of Science Bangalore. His research interests are image processing, medical imaging, agent technology, pattern recognition, document imaging, operating systems, biometrics based authentication, mobile computing, segmentation, data compression. Abraham T. Mathew is a professor in the Department of Electrical Engineering, National Institute of Technology Calicut. He obtained his Ph.D. degree from Indian Institute of Technology Delhi. His research interests are control systems and image processing.