Non-local Means using Adaptive Weight Thresholding
Asif Khan and Mahmoud R. El-Sakka
Computer Science Department, The University of Western Ontario, London, Ontario, Canada
Keywords:
Image Denoising, Additive Gaussian Noise, Non-local Means, Two-stage Non-local Means, Spatial Domain
Denoising.
Abstract:
Non-local means (NLM) is a popular image denoising scheme for reducing additive Gaussian noise. It uses
a patch-based approach to find similar regions within a search neighborhood and estimates the denoised pixel
based on the weighted average of all pixels in the neighborhood. All weights are considered for averaging,
irrespective of the value of the weights. This paper proposes an improved variant of the original NLM scheme
by thresholding the weights of the pixels within the search neighborhood, where the thresholded weights are
used in the averaging step. The threshold value is adapted based on the noise level of a given image. The
proposed method is used as a two-step approach for image denoising. In the first step the proposed method is
applied to generate a basic estimate of the denoised image. The second step applies the proposed method once
more but with different smoothing strength. Experiments show that the denoising performance of the proposed
method is better than that of the original NLM scheme, and its variants. It also outperforms the state-of-the-art
image denoising scheme, BM3D, but only at low noise levels (σ 80).
1 INTRODUCTION
Image denoising is the process of reducing noise ar-
tifacts from a digital image and it is one of the most
fundamental problems in image processing. Noise is
a random signal which affects the signal from the ac-
tual source by adding unwanted information to the
signal. In digital image, noise causes random varia-
tion of brightness or color. It is usually produced dur-
ing the image acquisition phase, caused by the sen-
sors of digital cameras or scanners. Modern digital
cameras have come a long way in using high quality
sensors which have significantly reduced the presence
of noise during image acquisition, but still noise can
affect an image especially in low light conditions.
Noise in digital images can be categorized either
as additive or multiplicative noise. Additive noise
gets added with the image signal. It is modeled as:
v(i) = u(i) + η(i) (1)
where v(i) is the observed intensity value at pixel i,
u(i) is the actual raw intensity value and η(i) is the
random noise affecting pixel i. Multiplicative noise
signal gets multiplied in the original image source. It
is modeled as:
v(i) = u(i) × η(i) (2)
The main challenge of a denoising model is to re-
duce noise while preserving the texture, fine details
and edges of an image. A model which is able to re-
duce significant noise artifacts but completely blurs
the entire image, to a point where only minimal visual
information can be extracted, is not ideal. Similarly, a
denoising method which preserves the textures in the
image but fails to reduce the noise to a satisfactory
level is not an effective model as well.
The denoising methods can be generally catego-
rized as either spatial domain approaches or trans-
form domain approaches. The term spatial domain
refers to the image plane itself (Gonzalez and Woods,
2008) and the methods under this domain uses the raw
intensity of the pixels to generate a denoised image.
In transform domain approaches, the image is trans-
formed to another domain, e.g., frequency domain us-
ing, for example, Fourier transform or wavelet trans-
form. The transform domain decomposes smooth re-
gions in an image into low frequencies, while edges
and subtle information into high frequencies, thus
making it easier to target and enhance certain regions
in an image.
Among the various noise types, additive white
Gaussian noise has attracted significant interest
among researchers in the past few decades. Our work
will focus only on this type of noise reduction. Ad-
ditive white Gaussian noise is referred to noise sig-
nals with a zero-mean Gaussian distribution, having
Khan, A. and El-Sakka, M.
Non-local Means using Adaptive Weight Thresholding.
DOI: 10.5220/0005787100670076
In Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2016) - Volume 3: VISAPP, pages 69-78
ISBN: 978-989-758-175-5
Copyright
c
2016 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
69
uniform power across the frequency band. Initial ap-
proaches to reduce the additive Gaussian noise in-
cluded the use of basic linear filters, namely mean
filter, median filter and Gaussian smoothing (Gonza-
lez and Woods, 2008). These filtering approaches use
only the raw pixel values in a small local neighbor-
hood around each pixels to determine the denoised
image. These methods does not take into account
the extent to which the neighborhood overlaps with
smooth or textured regions. Thus the use of such lin-
ear filters are detrimental for edge and texture preser-
vation, resulting in blurry denoised images. To ad-
dress this problem, Perona and Malik proposed an
iterative edge preserving method called Anisotropic
Diffusion (Perona and Malik, 1990). It attempts to
determine whether a pixel is part of a smooth or a tex-
tured region and applies differentdegree of smoothing
based on the characteristics of its locality.
Most of the earlier spatial domain denoising meth-
ods used pixel intensities within a defined local
neighborhood around each pixel for estimating a de-
noised version of a noisy image. In recent years,
Buades et el. proposed a non-local, patch based
approach called Non-Local Means (NLM) (Buades
et al., 2005a)(Buades et al., 2005b). It takes advan-
tage of the fact that similar local regions can be spread
through out the entire image. Each of the pixels are
denoised using a weighted average of all the pixels
within a defined search area. The weights are as-
signed based on the local characteristics of the pixels
used in the weighted averaging step. It uses weighted
euclidean distance of the local region around the pixel
being denoised, also referred to as the reference patch,
and the local regions around each of the the pixels
within the search area. The patches with smaller eu-
clidean distance, i.e., patches similar to the reference
patch are assigned higher weights.
The concept of non-local based approach has also
been applied to denoising methods in frequency do-
main. Dabov et el. proposed Block Matching and 3D
Filtering (BM3D) (Dabov et al., 2007), using patch
based concept for image denoising. It is a two-step
process, where the first step groups similar patches
into blocks, followed by a transform operation and
hard thresholding of the transform coefficients to gen-
erate a basic estimate of the denoised image. The
basic estimate is used in the second step to generate
the actual denoised image. BM3D is one of the state-
of-the-art approaches for denoising additive Gaussian
noise.
In the field of spatial domain denoising, non-local
means demonstrated significant improvement in de-
noising images affected with additive Gaussian noise
and researchers have continued further work on the
method and have proposed improvements for it. The
exhaustive search nature of non-local means makes
it computationally expensive. To improve the com-
putation cost, several methods have been proposed.
Tasdizen used principal component analysis (PCA) in
conjunction with non-local means (Tasdizen, 2008).
The image neighborhoods are projects to a lower di-
mension space using PCA and the reduced subspace
is used for computing similarities. A similar dimen-
sion reduction approach has also been proposed by
Maruf and El-Sakka (Maruf and El-Sakka, 2015),
where the image neighborhood are projected to a
lower dimension by using t-test.
Along with the research focused on improving the
computation performance of non-local means, work
has also been done on improving the denoising perfor-
mance as well. Rehman and Wang proposed SSIM-
based non-local means (Rehman and Wang, 2011),
utilizing structural similarity instead of euclidean dis-
tance when comparing local characteristics between
patches. Chaudhury and Singer proposed Non-Local
Euclidean Medians (Chaudhury and Singer, 2012),
replacing the use of mean with median. Zhu et el.
proposed a two-stage non-local means approach with
adaptive smoothing parameters (Zhu et al., 2014). It
generates a basic denoised image by applying NLM
in the first stage and the basic image is refined one
more time in the second stage by using NLM but with
smaller smoothing strength.
Non-local means and its variants have been used
in variousimaging applications such as medical imag-
ing, including MRI brain images (Iftikhar et al.,
2013), CT scan imaging (Kelm et al., 2009) and 3D
ultrasound imaging (Hu and Hou, 2011). It is also
used in video denoising (Basavaraja et al., 2010) (Xu
et al., 2010), surface salinity detection (Zhao and
Liu, 2012) and metal artifact detection (Mouton et al.,
2012).
Although much work has been done to improve
non-local means, there are still possibilities for further
improvements. In the weighted averaging step, non-
local means considers all the pixels within a defined
search area. The pixel patches having significantly
different details than the patch of the reference pixel
being denoised are likely to deviate the estimated de-
noised value of the reference pixel from its true noise-
free pixel intensity, even with their smaller weights.
In our proposed method we have thresholded the pixel
weights and only the pixels with weight higher than
the cut-off weight are considered for weighted aver-
aging. The threshold is adapted based on the noise
level of the given noisy image. The proposed method
is applied in a two-step approach, where the first step
applies the proposed method to generate a basic de-
VISAPP 2016 - International Conference on Computer Vision Theory and Applications
70
noised image and in the second step the image gen-
erated from the first step is again denoised, using
a smaller smoothing parameter. Experiments have
illustrated better denoising performance of the pro-
posed method compared to existing methods, e.g., the
original NLM, a variant of NLM and BM3D, both
in terms of objective measurements and visual image
quality.
2 NON-LOCAL MEANS (NLM)
Buades et el. proposed a non-local based approach for
image denoising (Buades et al., 2005a)(Buades et al.,
2005b). Images have redundant or similar patterns in
them and the Non-Local Means (NLM) approach at-
tempts to take advantage of such self-similarities to
estimate the denoised gray level value of each pixel.
Instead of using only a local region around each pixel
for estimating the actual intensity of the pixel, NLM
uses a non-local approach by searching for similar
patches, within a certain search-bound, in the im-
age. The center pixel of each patch contributes to a
weighted averaging based on the similarity between
the reference and search patches.
When comparing the reference patch to a search
patch, a variation of the euclidean distance is mea-
sured. The euclidean distance measures the sum of
squared difference between each pixel in a patch. To
give more importance to pixels near the center of the
patch, a Gaussian weight distribution is used, thus re-
sulting in the final measurement being the weighted
euclidean distance, kN(i) N( j)k
2
2,a
, where a is the
standard deviation of the Gaussian kernel and N(i)
and N( j) are the patches around pixel i and j, respec-
tively. The weight associated with each of the search
patches is based on the similarity with the reference
patch. After calculating the euclidean distance be-
tween the patches, the weight is assigned using Equa-
tion (3),
w(i, j) =
1
Z(i)
e
kv(N
i
)v(N
j
)k
2
2,a
h
2
, (3)
where v(N
i
) and v(N
j
) are the gray values of the pixels
in the patch centered on i and j respectively. Z(i) is
the normalizing constant as defined in Equation (4),
Z(i) =
j
e
kv(N
i
)v(N
j
)k
2
2,a
h
2
(4)
The constant, h, controls the decay rate of the expo-
nential weight function. Given a noisy image, the es-
timated value NL[v](i), for pixel i, is computed as a
weighted average of the center pixels of the patches
in a certain search area, see Equation (5),
NL[v](i) =
jI
w(i, j)v( j), (5)
where w(i, j) is the weight calculated based on the
similarity of neighborhood around pixel i and j.
3 NON-LOCAL MEANS USING
ADAPTIVE WEIGHT
THRESHOLDING
Non-local means method defines a search area of size
S × S centered on the pixel, i, being denoised. The
similarity of all the patches defined around each of
the pixels within the search area is considered during
the weighted averaging process, where higher weights
are assigned to patches which are more similar, as de-
termined by lower euclidean distance to the reference
patch. The goal of the weighted averaging process is
to estimate the true noise-free intensity value of pixel
i, based on the similarity of the patches within the de-
fined search area of the given noisy image. The inclu-
sion of the center pixels of patches which are not very
similar to the reference patch is likely to move the re-
sulting estimate further from the true pixel intensity
value of the noise-free image.
In our proposed method, only a subset of the avail-
able patch centers are considered for the final estima-
tion of the denoised pixel. The patches are selected
based on the similarity measure compared to the ref-
erence patch. Effectively, a cut-off weight, w
thresh
is
selected using a defined percentile position, w
percentile
among the availablepatch weights within the bounded
search area and the weights of the patches are thresh-
olded against w
thresh
. All weights above w
thresh
are
unchanged and weights below w
thresh
are reduced
to zero, thus removing their pixel centers from the
weighted averaging process. The selected percentile
position is determined based on the noise level in a
given image. In real systems, the actual amount of
noise in a noisy image cannot be known beforehand.
The noise can be estimated in digital image using
fuzzy processing (Russo, 2001), image filters (Mou-
ton et al., 2007) and local variance estimate (Lim,
1990) methods.
For low noise levels, a higher cut-off weight,
w
thresh
, is selected for thresholding the patch weights
and as the noise level of a given image increases,
w
thresh
is lowered to include more patch centers for
averaging. For lower noise levels, only the patches
with high similarity measure to a reference patch can
be used to estimate a denoised image. The remaining
Non-local Means using Adaptive Weight Thresholding
71
patches can be considered as outliers. So, a higher
cut-off threshold is selected for low noise levels. In
high noise, the euclidean distance measurement may
not give a true measure of patch similarity as it will
end up comparing, to some extent, the noise between
patches along with the structures of the patches. So,
considering only the higher weighted patch centers,
by keeping the threshold value high, can in fact devi-
ate the denoised estimation from the true value. To
mitigate this effect, the threshold value is lowered
so that more pixels are averaged for attenuating the
noise. The denoised image is calculated as shown in
Equation (6),
NL[v](i) =
jEI
ˆw(i, j)v( j), (6)
where ˆw(i, j) is the thresholded weight between patch
at pixel i and patch at pixel j as shown in Equation
(7),
ˆw(i, j) =
(
w(i, j), if w(i, j)>w
thresh
0, otherwise
(7)
The proposed method is applied in two-step approach.
In the first step, proposed method is used to generate
a basic estimate of the denoised image. In the basic
estimate, most of the noise is reduced but still some
visible noise artifacts remain, especially for stronger
noise levels and it is necessary to further denoise the
basic image for better denoising (Zhang et al., 2010).
As most of the noise is reduced in the basic image,
similar regions can be identified more easily which
helps to generate better denoised images in the sec-
ond step. In the second step, the basic image is de-
noised using similar method used in the first step, but
with a smaller smoothing parameters. To verify that
the two-step approach is good enough, we conducted
experiments to measure the improvement in the de-
noising performance with further steps and found the
amount of improvements to be negligible, and even
less in some cases.
Non-local means has two key parameters, namely
the patch size and the search size. In our proposed
method we have attempted to select the optimal patch
and search window sizes based on the noise level in
the image. We have empirically defined a model for
selecting the patch size and the corresponding search
window size for a noise level, σ, see Section 4.1
4 EXPERIMENTAL RESULTS
In this section we will report the experimental results
of our proposed method. All the experiments were
carried out on the standard Kodak gray-scale image
set. It comprises of 24 gray-scale images of dimen-
sions 768 × 512 and 512 × 768. The Kodak image
set is shown in Figure 1. For the purpose of our
experimentation, the standard noise free image were
contaminated by additive Gaussian white noise, ran-
domly distributed throughout the image. The final
intensity values were kept within the maximum in-
tensity value of gray-scale images. The noise lev-
els, determined by σ, ranges from 10 to 100, with
a step size equals 10. The performance of our pro-
posed method is compared with the original non-
local means (NLM), the two-stage non-local means
(TS-NLM) and the Block Matching and 3D Filtering
(BM3D) methods.
4.1 Parameter Selection
The patch size and search window size for a given
noise level was determined empirically, using an iter-
ative learning approach on a training image set. The
training image set is shown in Figure 2. At first, the
patch size was fixed and the search window size was
varied, for each noise levels, to select the best search
window size. The noise levels, σ, ranged from 10
to 100, with a step size equals 5. Next, the patch
size was varied for each noise levels, while using the
best search window size for each noise as determined
in the previous step. The best patch size for each
noise level was used to find the correspondingoptimal
search window sizes one more time. This process was
repeated until an iteration was reached where updat-
ing the optimal search window size for a noise level
did not change the corresponding best patch size and
vice versa.
From our experiments, we have selected a patch
size of 7 × 7 when the noise strength is, σ 80 and
for σ>80 the patch size is increased to 9×9. For high
noise levels, the larger patch size is needed to reduce
the effect of noise in patch similarity measurement.
From our experiments, we also determined a
model for selecting the search window size for a noise
level, σ. The model used to select the search size S×S
for a given noise, σ, is shown in Equation (8),
S = round
odd
(0.117σ + 9.758), (8)
where, round
odd
() rounds a decimal value to its near-
est odd integer. As the search window is centered on
pixel, i, being denoised, the search window size needs
to be an odd integer.
For thresholding the weights, the percentile posi-
tion of the weight to be used as the cut-off weight is
given by Equation (9),
w
percentile
= ceil(100× e
σ
100
), (9)
VISAPP 2016 - International Conference on Computer Vision Theory and Applications
72
(a) Boat2 (b) Lighthouse (c) Woman (d) Sail (e) Statue (f) Model
(g) Beach (h) Bike (i) Bridge (j) Cottage
(k) Door (l) Flower (m) Raft (n) Girl
(o) Hats (p) House2 (q) Houses (r) Windows
(s) Island (t) Lake (u) Landscape (v) Lighthouse2
(w) Parrot (x) Plane
Figure 1: Test Image set (Kodak Image set).
where ceil() rounds a decimal value to the smallest
following integer. The thresholding model defined
by Equation (9) was also empirically found through
learning on the training image set. We applied differ-
ent linear and exponential models to select the thresh-
old. The model which provided the best denoising
Non-local Means using Adaptive Weight Thresholding
73
(a) Lena (b) Barbara (c) Baboon (d) Boats (e) Peppers
Figure 2: Train Image set.
performance was finally selected.
The smoothing parameter, h, for the first step of
the denoising approach is set as h
basic
= 10σ. For the
second step, h
final
= σ is used as the smoothing pa-
rameter value.
4.2 Performance Measure
To measure the performance of our proposed method
in comparison to other existing denoising methods,
we have used the Peak Signal to Noise Ratio (PSNR)
and the Mean Structural SIMilarity (MSSIM) mea-
sure. These measures are generally used for objec-
tive evaluation and measurement of various denois-
ing methods. We also evaluated subject comparison
between our proposed method and existing denoising
methods.
4.2.1 Peak Signal to Noise Ratio (PSNR)
The Peak Signal to Noise Ratio measures the ratio
between the maximum possible power of a signal to
the power of the noise which affects the quality of
the original signal. The PSNR is usually expressed
as the logarithmic decibel scale. A higher value in
PSNR represents better reconstructed or denoised im-
age. The PSNR is measured using Equation (10),
PSNR = 10log
10
(
MAX
2
I
MSE
), (10)
where MAX
I
represents the maximum intensity of the
image (255, for grayscale image) and MSE measures
the mean squared error between the original image
and the degraded image, as defined in Equation (11),
MSE =
1
M × N
M
i=0
N
j=0
(u
ij
v
ij
)
2
, (11)
where u
ij
is the original image, v
ij
is the degraded
image and the size of the images is M × N.
4.2.2 Mean Structural Similarity (MSSIM)
One of the drawbacks of the PSNR measure is that it
relies on the mean square error for calculating the ra-
tio. Mean squared error considers only the differences
between isolated data points. To evaluate the perfor-
mance of a denoising method based on the degree of
structural similarity between the original and the re-
constructed image, the Structural SIMilarity (SSIM)
measure is used. The SSIM measure provides a bet-
ter assessment of an image restoration or denoising
method. The SSIM between two blocks is defined in
Equation (12),
SSIM =
(2µ
x
µ
y
+ c
1
)(2σ
xy
+ c
2
)
(µ
2
x
+ µ
2
y
+ c
1
)(σ
2
x
+ σ
2
y
+ c
2
)
, (12)
where, x and y are two identical sized window or
patch, µ
x
and µ
y
are the averages of x and y, σ
2
x
and σ
2
y
are the variance of x and y and σ
xy
is the co-variance.
The mean SSIM (MSSIM), averaged over all SSIM,
is used as for the quality measurement of a denoising
method.
4.3 Performance Evaluation using
PSNR
Table 3 shows the PSNR comparison of the proposed
method, the original non-local means, the variant of
non-local means and BM3D, on the Girl image. Ta-
ble 2 shows the average PSNR values over all images
in the Kodak image set, for various noise levels. The
performance of the proposed method is better than
the original non-local means method and its variant
for all noise levels. Yet, when compared to BM3D,
our proposed method managed to produce better re-
sults only when σ 80. The proposed method also
demonstrated better performance than existing meth-
ods on the average of all the noise levels used in our
experiments.
4.4 Performance Evaluation using
MSSIM
Table 3 shows the MSSIM comparison of the pro-
posed method, the original non-local means, the vari-
ant of non-local means and BM3D, on the Girl image.
Table 4 shows the MSSIM comparison over all im-
ages in the Kodak image set, for various noise levels.
VISAPP 2016 - International Conference on Computer Vision Theory and Applications
74
Table 1: PSNR comparison of the Girl image for the pro-
posed method and existing methods.
Noise NLM TS-NLM BM3D Proposed
10 33.92 33.93 35.42 35.61
20 31.83 32.01 33.46 33.60
30 29.43 29.70 31.03 31.12
40 28.47 28.96 29.88 30.04
50 26.64 27.20 28.21 28.27
60 25.12 25.77 26.53 26.60
70 24.78 25.24 25.88 26.03
80 23.69 24.46 25.33 25.50
90 23.15 24.04 24.95 24.81
100 22.91 23.88 24.43 24.28
Average 26.99 27.52 28.51 28.59
Table 2: PSNR comparison of the proposed method with
existing methods.
Noise NLM TS-NLM BM3D Proposed
10 32.61 32.63 34.05 34.27
20 30.77 30.94 32.25 32.43
30 28.58 28.83 29.80 29.95
40 27.02 27.47 28.19 28.33
50 24.88 25.54 26.07 26.09
60 23.93 24.66 25.38 25.46
70 23.24 24.02 24.74 24.91
80 22.90 23.56 24.46 24.65
90 22.21 23.18 24.25 24.13
100 21.98 22.83 23.97 23.84
Average 25.81 26.36 27.36 27.41
In terms of MSSIM, the performance of the proposed
method is consistent with PSNR, which means it is
better than the original non-local means and its vari-
ant for all noise levels. When compared to BM3D,
our proposed method managed to produce better re-
sults only when σ 80. On average across all noise
levels, the performance of proposed method has been
found to be better than existing methods.
4.5 Visual Quality
Figure 3 and Figure 4 shows the visual compari-
son of the proposed method with the original non-
local means (NLM), the two-stage non-local means
(TS-NLM) and the Block Matching and 3D Filtering
(BM3D) methods for noise level, σ = 20 and σ = 70
respectively. Figure 5 and Figure 6 shows the visual
comparison by zooming in on a particular region, the
face. From Figure 6, it can be noticed that the de-
noised output from the proposed method has fewer
noise artifacts remaining when compared to the other
methods. The blurring is also less in the denoised out-
Table 3: MSSIM comparison of the Girl image for the pro-
posed methods with existing methods.
Noise NLM TS-NLM BM3D Proposed
10 0.919 0.922 0.927 0.936
20 0.875 0.882 0.889 0.897
30 0.849 0.855 0.857 0.862
40 0.818 0.822 0.832 0.834
50 0.790 0.797 0.811 0.813
60 0.761 0.767 0.780 0.784
70 0.728 0.731 0.747 0.750
80 0.713 0.717 0.738 0.741
90 0.692 0.694 0.724 0.720
100 0.678 0.683 0.713 0.708
Average 0.782 0.787 0.802 0.804
Table 4: MSSIM comparison of the proposed methods with
existing methods.
Noise NLM TS-NLM BM3D Proposed
10 0.916 0.918 0.921 0.932
20 0.871 0.876 0.882 0.891
30 0.843 0.847 0.851 0.857
40 0.815 0.817 0.826 0.829
50 0.786 0.792 0.801 0.806
60 0.755 0.760 0.772 0.778
70 0.724 0.726 0.742 0.744
80 0.709 0.714 0.734 0.735
90 0.689 0.691 0.712 0.709
100 0.672 0.678 0.708 0.704
Average 0.777 0.782 0.795 0.798
put of the proposed method compared to NLM, TS-
NLM and BM3D.
4.6 Intensity Profile
The image intensity profile can help analyze how sim-
ilar the profile of a denoised image is to that of the
original noise-free image. Figure 7 shows the chosen
horizontal scan line 100 from the Girl image. Figure
8 shows the intensity profiles of the true image, the
noisy image at noise level, σ = 70 and the profiles
of denoised images produced by the original NLM
scheme, the variant of NLM, BM3D and the proposed
method. The Pearson correlation coefficient between
the original intensity profile and the profile of the
noisy and each of the denoised images is shown in
Table 5 (for σ = 70).
The intensity profile of the proposed method
shows better preservation of edges and textures, rep-
resented as sharp changes in profile graph. The origi-
nal non-local means method and its variant have more
noise artifacts remaining, as represented by the more
Non-local Means using Adaptive Weight Thresholding
75
(a) Noise Free (b) Noise (c) NLM (d) TS-NLM (e) BM3D (f) Proposed
Figure 3: Visual comparison of proposed method with existing method (σ = 20).
(a) Noise Free (b) Noise (c) NLM (d) TS-NLM (e) BM3D (f) Proposed
Figure 4: Visual comparison of proposed method with existing method (σ = 70).
(a) Noise Free (b) Noise (c) NLM (d) TS-NLM (e) BM3D (f) Proposed
Figure 5: Visual comparison (zoomed) of proposed method with existing method (σ = 20).
(a) Noise Free (b) Noise (c) NLM (d) TS-NLM (e) BM3D (f) Proposed
Figure 6: Visual comparison (zoomed) of proposed method with existing method (σ = 70).
Figure 7: Row number 100 of Girl image used for generating intensity profile. Scan line shown as a black line.
Table 5: Pearson correlation coefficient comparison of the
proposed method, the noisy image, the NLM method, vari-
ant of NLM and BM3D denoising scheme for noise σ = 70.
Noise NLM TS-NLM BM3D Proposed
0.680 0.975 0.980 0.988 0.990
jagged lines in the profile graph, closer to the ori-
gin. When comparing the Pearson correlation coef-
ficient, the correlation between the intensity profile of
the original image and the proposed method is higher
compared to those of the other existing methods. It
shows that the proposed method has the closest re-
semblance to the intensity profile of the original im-
age.
5 CONCLUSION
This paper proposed an improvement over the non-
local means method, the patch-based approach for
VISAPP 2016 - International Conference on Computer Vision Theory and Applications
76
(a) Original (b) Noise
(c) NLM (d) TS-NLM
(e) BM3D (f) Proposed
Figure 8: Intensity profile comparison for the Girl image at scan line 100 (σ = 70).
denoising additive Gaussian noise in the spatial do-
main. The proposed method thresholds the weights
of the pixels defined around a search area of the pixel
being denoised. The thresholded weights are used for
weighted averaging, whereby pixels below a defined
cut-off weight are ignored. The cut-off weight is de-
Non-local Means using Adaptive Weight Thresholding
77
termined based on the noise level estimation of an
image. For a noise level, the patch and search win-
dow size are determined by a model, which is empir-
ically defined through a learning approach. The pro-
posed method is applied in a two-step approach for
image denoising. The proposed method has demon-
strated better objective and subjective denoising per-
formance, compared to the original non-local means
algorithm and its variant. When compared to BM3D,
the state-of-the-art approach for image denoising, the
proposed method demonstrated better results when
σ 80.
ACKNOWLEDGEMENTS
This research is partially funded by the Natural Sci-
ences and Engineering Research Council of Canada
(NSERC). This support is greatly appreciated.
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