1. ISSN: 2277 – 9043
International Journal of Advanced Research in Computer Science and Electronics Engineering
Volume 1, Issue 2, April 2012
MODIFIED POINTWISE
SHAPE-ADAPTIVE DCT FOR
HIGH-QUALITY DEBLOCKING OF
COMPRESSED IMAGES
Chandan Singh D. Rawat, Rohan K. Shambharkar, Sukadev Meher
 from digital camera manufacturers and software developers.
Abstract— Blocking artifact is one of the most annoying As a matter of fact, the classic JPEG still dominates the
artifacts in the image compression coding. In order to improve consumer market and the near-totality of pictures circulated
the quality of the reconstructed image several deblocking on the internet is compressed using this old standard.
algorithms have been proposed. A high-quality modified image
deblocking algorithm based on the shape-adaptive DCT
Moreover, the B-DCT is the work-horse on which even the
(SA-DCT) is shown. The SA-DCT is a low-complexity latest MPEG video coding standards rely upon. There are no
transform which can be computed on a support of arbitrary convincing indicators suggesting that the current trend is
shape. This transform has been adopted by the MPEG-4 about to change any time soon. All these facts, together with
standard and it is found implemented in modern video the ever growing consumer demand for high quality imaging,
hardware. This approach has been used for the deblocking of makes the development of advanced and efficient
block-DCT compressed images. In this paper we see modified
pointwise SA-DCT method based on adaptive DCT threshold
post-processing (deblocking) techniques a very actual and
coefficient instead of constant DCT threshold coefficient used relevant application area.
by the original pointwise SA-DCT method. Extensive
simulation experiments attest the advanced performance of the In this paper a modified pointwise SA-DCT method
proposed filtering method. The visual quality of the estimates is for the restoration of B-DCT compressed grayscale images is
high, with sharp detail preservation, clean edges. Blocking proposed. It is based on the pointwise shape-adaptive DCT
artifacts are suppressed while salient image features are
(SA-DCT) [14] approach and its characterized by a high
preserved.
quality of the filtered estimate.
Index Terms— Anisotropic, DCT threshold coefficient. The SA-DCT [1, 2] is a generalization of the usual
Deblocking, SA-DCT. separable block-DCT (B-DCT) which can be computed on a
support of arbitrary shape. It is obtained by cascaded
application of one-dimensional varying-length DCT
I. INTRODUCTION transforms first on the columns and then on the rows that
constitute the considered support. Thus, it retains the same
The new JPEG-2000 image compression standard solved computational complexity of the B-DCT. The SA-DCT has
many of the drawbacks of its predecessor. The use of a been originally developed for coding non-rectangular image
wavelet transform computed globally on the whole image, as patches near the border of image objects, in such a way to
opposed to the localized block-DCT (B-DCT) (employed e.g. minimize the stored information and to avoid the ringing
by the classic JPEG), does not introduce any blocking artifacts (Gibbs phenomenon) that would appear in
artifacts and allows it to achieve a very good image quality correspondence with strong edges. Because of its low
even at high compression rates. Unfortunately, this new complexity, the near-optimal de-correlation and energy
standard has received so far only very limited endorsement compaction properties (e.g. [1], [5]), and its backward
compatibility with the B-DCT, the SA-DCT has been
included in the MPEG-4 standard [3], where it is used for the
coding of image segments that lie on the video-object’s
Chandan Singh D. Rawat, Phd Scholar, Electronics and
Communication Engineering Department, National Institute of Technology,.
boundary. The recent availability of low-power hardware
Rourkela, Orrisa, India, 9029067260. SA-DCT platforms (e.g. [2], [6]) makes this transform an
appealing choice for many image-and video-processing
Rohan K. Shambharkar, M.E. Student, Electronics and tasks.
Telecommunication Engineering Department V.E.S.I.T Mumbai, India,
9920835523.
The first attempt to use of SA-DCT for image
Sukadev Meher, Professor and Head, Electronics and Communication denoising was reported by the authors in [7]. The original
Engineering Department, National Institute of Technology, Rourkela,
Orissa, India, Tel: +919437245472 version of the method has been adapted for image
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International Journal of Advanced Research in Computer Science and Electronics Engineering
Volume 1, Issue 2, April 2012
deblocking. These algorithms demonstrate a remarkable shown. The developed anisotropic estimates are highly
performance, typically outperforming the best methods sensitive with respect to change points, and allow to reveal
known to the authors. The SA-DCT estimates have also been fine elements of images from noisy observations.
shown to achieve one of the highest subjective visual quality
[8].
The paper is organized as follows. In the sections 2 to 5
a brief overview on the basic anisotropic LPA-ICI in
conjunction with SA-DCT method [14] is shown. In section 6
we see the proposed modified pointwise SA-DCT method
Fig. 1. Anisotropic LPA-ICI. From left to right: Sectorial structure of the
based on adaptive DCT threshold coefficient. In Section 7 the anisotropic neighborhood achieved by combining a number of adaptive-scale
adaptation of the denoising algorithm to deblocking [14] is directional windows; some of these windows selected by the ICI for the noisy
seen and to relate the quantization table with the value of the Lena and Cameraman images [14].
variance to be used for the filtering. The final Section is
devoted to extensive experimental results by considering III. SHAPE-ADAPTIVE DCT
different types of quantization tables, several level of
compression, for grayscale images. SA-DCT [1, 2] is computed by cascaded application of
1-D varying-length DCT transforms first on columns and
II. ANISOTROPIC LPA-ICI then on rows that constitute the considered region as shown
in Fig 2. This approach concerns normalization of transform
Noisy observations z of the form is given by,
and subtraction of the mean and which have a fundamental
impact on the use of the SA-DCT for image filtering.
z(x) = y(x) + η(x)
(1)
where y is the original image, is
independent
Gaussian white noise, x is a spatial variable belonging to the
image domain . we restrict ourself to grayscale
images (and, thus, scalar functions).
Here only a brief overview on the original method
developed for image denoising is shown and refer the reader
to [14] (and references therein) for a more formal, complete,
and rigorous description.
The use of a transform with a shape-adaptive support Fig. 2. Illustration of the shape-adaptive DCT transform and its inverse.
involves actually two separate problems: not only the Transformation is computed by cascaded application of 1-D varying-length
transform should adapt to the shape (i.e. a shape-adaptive DCT transforms, along the columns and along the rows [14].
transform), but the shape itself must adapt to the image
features (i.e. an adaptive shape). The first problem has found A. Orthonormal Shape-Adaptive DCT
a very satisfactory solution in the SA-DCT transform [1, 2].
The second problem is essentially application-dependant. It The normalization of the SA-DCT is obtained by
must be noted that conventional segmentation (or normalization of the individual 1-D transforms that are used
local-segmentation) techniques which are employed for for transforming the columns and rows. In terms of their basis
video processing (e.g. [10]) are not suitable for degraded elements, they are defined as
(noisy, blurred, highly compressed, etc.) data. In this
approach, the SA-DCT in conjunction with the anisotropic
LPA-ICI technique [11, 12, 13] is used. The approach is
based on a method originally developed for pointwise (2)
adaptive estimation of 1-D signals [12, 13]. The technique Here, L stands for the length of the column or row to be
has been generalized for 2-D image processing, where transformed. The normalization in (2) is, indeed, the most
adaptive-size quadrant windows have been used [16]. natural choice, since in this way all the transforms used are
Significant improvement of this approach has been achieved orthonormal and the corresponding matrices belong to the
on the basis of anisotropic directional estimation [7, 11]. orthogonal group. Therefore, the SA-DCT—which can be
Multidirectional sectorial- neighborhood estimates are obtained by composing two orthogonal matrices—is itself an
calculated for every point. Thus, the estimator is anisotropic orthonormal transform. A different normalization of the 1-D
and the shape of its support adapts to the structures present in transforms would produce, on an arbitrary shape, a 2-D
the image. In Fig. 1, some examples of these anisotropic
neighborhoods for the Lena and Cameraman images are
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International Journal of Advanced Research in Computer Science and Electronics Engineering
Volume 1, Issue 2, April 2012
transform that is nonorthogonal (for example, as in [1] and
the neighborhood is the octagon
[2], where and cm=2/L for m>0).
constructed as the polygonal hull of
Here is the orthonormal SA-DCT transform
obtained for a region , where . Such neighborhoods are shown
and are in Fig. 4.
function spaces and indicates the domain of the
transform coefficients. is the inverse
transform of . The thresholding (or quantization) operator
is indicated as γ. Thus, the SA-DCT-domain processing of
the observations on a region U is written as
. From the
orthonormality of T and the model (1) follows that
Fig. 4. The anisotropic neighborhood is constructed as the polygonal hull of
, where is again the adaptive-scale kernels' supports. One-dimensional ―linewise‖ kernels are
Gaussian white noise with variance σ2 and zero mean. used [14].
V. THRESHOLDING IN SA-DCT DOMAIN
B. Mean Subtraction
There is an adverse consequence of the normalization (2).
An illustration of the SA-DCT-domain
Even if the signal restricted to the shape is constant, the
hard-thresholding,
reconstructed is usually non constant. In [5] this behavior is
performed according to (2) is given in Fig. 5.
termed as ―mean weighting defect,‖ and it is proposed there
to attenuate its impact by applying the orthonormal SA-DCT
on the zero-mean data which is obtained by subtracting from
the initial data its mean. After the inversion, the mean is
added back to the reconstructed signal
(3)
where is the mean of z on U.
IV. POINTWISE ANISOTROPIC LPA-ICI + SA-DCT
The anisotropic adaptive neighborhoods defined by
the LPA-ICI as supports for the SA DCT, as shown in Fig. 3 Fig. 5. Hard thresholding in SA-DCT domain. The image data on an
is used. By demanding the local fit of a polynomial model, arbitrarily shaped region is subtracted of its mean. The zero-mean data is then
the presence of singularities or discontinuities within the transformed and thresholded. After inverse transformation, the mean is
transform support cab be avoided. In this way, it can be added back [14].
ensured that data are represented sparsely in the transform
domain, significantly improving the effectiveness of A. Thresholding in SA-DCT domain: Local Estimate
thresholding.
For every point x Є X, a local estimate
of the signal y is constructed by thresholding in SA-DCT
domain as in (3)
(4)
where γx is a hard thresholding-operator based on the
universal threshold,
Fig. 3. From left to right: Detail of the noisy Cameraman showing an
adaptive-shape neighborhood determined by the Anisotropic LPA-ICI
procedure and the image intensity corresponding to this region before and
after hard thresholding in SA-DCT domain [14]. (5)
A. Fast implementation of the LPA-ICI anisotropic B. Thresholding in SA-DCT domain: Global Estimate
neighborhoods All the local estimates (4) are averaged together using
Narrow 1-D ―linewise‖ directional LPA kernels adaptive weights (7) that depend on their local variances and
gh, k h{1, 2,3,5,7,9} on the size of the corresponding adaptive-shape regions.
are used for k = 8 directions, and after
the ICI-based selection of the adaptive-scales
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where TU is the orthonormal SA-DCT transform for a
region U and γ is the thresholding coefficient and is
its mean.
(6) From the above relation we conclude that is dependent
on γ (or γx) and .
We propose to use value of γx dependent on MSE (Mean
Squared Error) of image and MAX (Maximum Absolute
Difference).
(7) First we calculate the value of MAX and MSE. Several
experiments were carried out using Lena, Peppers and
Barbara image of size 512 × 512 on MATLAB platform on a
C. Wiener filtering in SA-DCT domain: Local Estimate 1.6 GHz Intel(R) CPU. For B-DCT quantization, if the value
Once a global estimate of the signal is available, it is used of MAX and MSE is less than 90 then thresholding
as a reference signal in order to perform Wiener filtering in coefficient is 0.9. If the value of MAX is greater than 90 and
SA-DCT domain which is given by, the value of MSE is between 100 to 120 or greater than 250
then thresholding coefficient is 0.9. If the value of MAX is
greater than 90 and the value of MSE is greater than 120 or
less than 80 then the thresholding coefficient is 1.01. For
(8) JPEG compression if the value of MSE is less than 90 then
the thresholding coefficient is 0.9 or else it is 1.01. Thus in
our modified case the DCT threshold coefficient
DCTthrCOEF = 1.01 or 0.9 depending on MSE and MAX.
D. Wiener filtering in SA-DCT domain: Global Estimate
All the local Wiener estimates (8) are averaged together VII. POINTWISE SA-DCT FOR B-DCT ARTIFACTS
using adaptive weights (10) that depend on the size of the REMOVAL
corresponding adaptive-shape regions.
More sophisticated models of B-DCT-domain
quantization noise have been proposed by many authors, here
we model this degradation as some additive Gaussian white
noise. In this section we restrict our attention to the
(9) grayscale/single-channel case and thus assume the
observation model
z=y+n
(13)
where y is the original (non-compressed) image, z its
(10) observation after quantization in B-DCT domain, and n is
independent Gaussian with variance σ2, n (·) ∼N (0,σ2).
We estimate a suitable value for the variance σ2 directly
VI. PROPOSED MODIFIED POINTWISE SADCT ALGORITHM from the quantization table Q = [qi,j]i,j = 1,…,8 using the
following empirical formula:
From (4), the threshold coefficient for DCT for local
estimate is calculated as
(14)
γx = DCT threshold coefficient × This formula uses only the mean value of the nine table
(11) entries which correspond to the lowest-frequency DCT
harmonics (including the DC-term) and has been
where σ is the standard deviation and is an experimentally verified to be quite robust for a wide range of
adaptive-shape neighbourhood as shown in Figure 3. different quantization tables and images. A higher
The author has used DCT threshold coefficient compression obviously corresponds to a larger value for the
DCTthrCOEF = 0.925 (constant). We propose a more variance.
adaptive method. The reconstructed image yU which is The σ2 which is calculated by (14) is not an estimate of
restricted to the shape z|U (Figure 3) from hard thresholding is the variance of compressed image, nor it is an estimate of the
given by variance of the difference between original and compressed
images. Instead, it is simply the variance of the white
Gaussian noise n in the observation model (13). It is the
variance of some hypothetical noise which, if added to the
(12) original image y, would require- in order to be removed - the
same level of adaptive smoothing which is necessary to
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suppress the artifacts generated by the B-DCT quantization therein) in order to simulate various types of B-DCT
with the table Q. compression. For identifying the considered quantization
tables, the first row of each table is shown below:
Q1(1···8,1) = [50 60 70 70 90 120 255 255],
Q2(1···8,1) = [86 59 54 86 129 216 255 255],
Q3(1···8,1) = [110 130 150 192 255 255 255 255].
The values of the standard deviation σ corresponding to these
three tables - calculated using formula (4) - are 12.62, 13.21,
Figure 6: Details of the JPEG-compressed grayscale Lena (Q=6,
PSNR=28.24dB) and Pointwise SA-DCT estimate (PSNR=29.8671dB) and and 22.73, respectively.
of the corresponding modified Pointwise SA-DCT estimate
(PSNR=29.8679dB). The estimated standard deviation for this highly In terms of image degradation, they correspond to a medium
compressed image is σ=17.6. to high compression level, similar to what can be obtained by
using JPEG with Q = 11 (Q1), Q = 9 (Q2), or Q = 5 (Q3).
Figures 6, and 7 shows the JPEG compressed grayscale Lena
image obtained for two different compression levels (JPEG
In Table 1 we present results for deblocking from B DCT
quality Q=6 and Q=15) as used in original SADCT method
quantization performed using these specific quantization
[14] and the corresponding SA-DCT filtered estimates and
tables. We compare the results obtained by the SA-DCT
our modified estimates. For these two cases the estimated
algorithm against the best results obtained by any of the
standard deviations are σ=17.6 and σ=9.7.
methods [17, 18, 19, 20, 21, 22], as reported in [17]. We use
Lena, Peppers and Barbara image of size 512 × 512 for
comparison our modified SA-DCT algorithm against the
VIII. EXPERIMENTAL RESULTS original SA-DCT algorithm. The results are in favor of our
proposed technique.
Extensive simulation experiments were carried out.
Consequently, we present comparative numerical results Further positive results are shown in Table 2 for the case
collected in two separate tables. The two tables contain of deblocking from JPEG-compression. In this second table
results for grayscale images obtained using particular comparison is shown between SA-DCT against the best
quantization tables found in the literature (Table 1) and JPEG result obtained by any of the methods [23, 24, 25, 26, 27, 19],
(Table 2). as reported in [23] and we compare the modified pointwise
SA-DCT method against the original pointwise SA-DCT
method. Also in this comparison, our modified Pointwise
SA-DCT method is found to be superior to all other methods.
IX. CONCLUSION
We proposed a new method of selecting DCT threshold
coefficient depending on the MSE (Mean Squared Error) of
the image and MAX (Maximum Absolute Difference)
instead of taking it constant as in the original pointwise
Figure 7: Details of the JPEG-compressed Lena (Q=15, PSNR=31.95dB) and
Pointwise SA-DCT estimate (PSNR=33.2144dB) and of the corresponding SA-DCT method. Our modified pointwise SA-DCT
modified Pointwise SA-DCT estimate (PSNR=33.2148dB). The estimated approach with adaptive DCT threshold coefficient gives
standard deviation for this compressed image is σ=9.7. better result than the original pointwise SA-DCT method
with constant DCT threshold coefficient.
Three quantization tables - usually called Q1, Q2, and Q3
- have been used by many authors (e.g. [15] and references
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Table 1: PSNR (dB) comparison table for restoration from B-DCT quantization for three different quantization matrices. The values of best
results correspond to any of the methods[17, 18, 19, 20, 21, 22] as reported in [17] and the value of original Pointwise SA-DCT method is
compared with our modified Pointwise SA-DCT method.
Lena Peppers Barbara
Best Deblocked Best Deblocked Best Deblocked
Deblocked Deblocked Deblocked
Table Compressed result Modified Compressed result Modified Compressed result Modified
SA-DCT SA-DCT SA-DCT
image from SA-DCT image from SA-DCT image from SA-DCT
image image image
[14] image [14] image [14] image
Q1 30.70 31.63 32.1256 32.1293 30.42 31.33 32.0149 32.023 25.94 26.64 26.7903 26.8026
Q2 30.09 31.19 31.5572 31.5593 29.82 30.97 31.4408 31.4532 25.59 26.32 26.453 26.4641
Q3 27.38 28.65 29.03307 29.037 27.22 28.55 29.13359 29.1436 24.03 24.73 25.12925 25.1301
Table 2: PSNR (dB) comparison table for restoration from JPEG compression of grayscale images. The values of best results correspond to
any of the methods[23, 24, 25, 26, 27, 19] as reported in [23] and the value of original Pointwise SA-DCT method is compared with our
modified Pointwise SA-DCT method.
Qua Lena Peppers Barbara
l JPEG Best SA-DCT Modifie JPEG Best SA-DCT Modifie JPEG Best SA-DCT Modified
result result result
d d SA-DCT
from from from
[1] SA-DCT [1] SA-DCT [1]
4 26.46 27.63 28.07731 28.0818 25.61 26.72 27.40472 27.4359 23.48 24.13 24.65214 24.6549
6 28.24 29.22 29.8671 29.8679 27.32 28.22 28.96882 28.9925 24.50 25.08 25.50203 25.5176
8 29.47 30.37 30.9860 30.9868 28.40 29.28 29.9023 29.9222 25.19 25.71 26.10794 26.11986
10 30.41 31.17 31.8447 31.8461 29.16 29.94 30.5068 30.5213 25.79 26.27 26.61224 26.6260
12 31.09 31.79 32.4774 32.4786 29.78 30.47 31.0064 31.0203 26.33 26.81 27.10363 27.1174
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[14] Alessandro Foi, Vladimir Katkovnik, and Karen Egiazarian, Chandan Singh D. Rawat received B. E degree in the department of
―Pointwise Shape-Adaptive DCT for High-Quality Electronics and communication engineering from Nagpur University. He
Denoising and Deblocking of Grayscale and Color Images‖, also received M.E degree from Mumbai University. He is currently
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