Blocking artifact detection and reduction in compressed data

Abstract

A novel frequency-domain technique for image blocking artifact detection and reduction is presented. The algorithm first detects the regions of the image which present visible blocking artifacts. This detection is performed in the frequency domain and uses the estimated relative quantization error calculated when the discrete cosine transform (DCT) coefficients are modeled by a Laplacian probability function. Then, for each block affected by blocking artifacts, its DC and AC coefficients are recalculated for artifact reduction. To achieve this, a closed-form representation of the optimal correction of the DCT coefficients is produced by minimizing a novel enhanced form of the mean squared difference of slope for every frequency separately. This correction of each DCT coefficient depends on the eight neighboring coefficients in the subband-like representation of the DCT transform and is constrained by the quantization upper and lower bound. Experimental results illustrating the performance of the proposed method are presented and evaluated.

Full text

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 12, NO. 10, OCTOBER 2002 877
Blocking Artifact Detection and Reduction
in Compressed Data
George A. Triantafyllidis, Student Member, IEEE, Dimitrios Tzovaras, and
Michael Gerassimos Strintzis, Senior Member, IEEE
Abstract—A novel frequency-domain technique for image
blocking artifact detection and reduction is presented in this
paper. The algorithm first detects the regions of the image which
present visible blocking artifacts. This detection is performed in
the frequency domain and uses the estimated relative quantization
error calculated when the discrete cosine transform (DCT)
coefficients are modeled by a Laplacian probability function.
Then, for each block affected by blocking artifacts, its dc and
ac coefficients are recalculated for artifact reduction. To achieve
this, a closed-form representation of the optimal correction of the
DCT coefficients is produced by minimizing a novel enhanced
form of the mean squared difference of slope for every frequency
separately. This correction of each DCT coefficient depends on the
eight neighboring coefficients in the subband-like representation
of the DCT transform and is constrained by the quantization
upper and lower bound. Experimental results illustrating the
performance of the proposed method are presented and evaluated.
Index Terms—Blocking artifacts, compressed domain, MSDS
metric.
I. INTRODUCTION
T
and video compression standards including JPEG [1], [2],
H.263 [3], MPEG-1, MPEG-2, MPEG-4 [4], and others, used
in a wide range of applications. The B-DCT scheme takes
advantage of the local spatial correlation property of the images
by dividing the image into 8
8 blocks of pixels, transforming
each block from the spatial domain to the frequency domain
using the discrete cosine transform (DCT) and quantizing the
DCT coefficients. Since blocks of pixels are treated as single
entities and coded separately, correlation among spatially adja-
cent blocks is not taken into account in coding, which results
in block boundaries being visible when the decoded image is
reconstructed. For example, a smooth change of luminance
across a border can result in a step in the decoded image if
neighboring samples fall into different quantization intervals.
HE BLOCK-based discrete cosine transform (B-DCT)
scheme is a fundamental component of many image
Manuscript received May 11, 2000; revised March 20, 2002. This work was
supported by the IST European Project OTELO. This paper was recommended
by Associate Editor O. K. Al-Shaykh.
G. A. Triantafyllidis is with the Information Processing Laboratory,
Aristotle University of Thessaloniki, Thessaloniki 54006, Greece (e-mail:
gatrian@iti.gr).
D. Tzovaras is with the Informatics and Telematics Institute, Thessaloniki
546 39, Greece (e-mail: Dimitrios.Tzovaras@iti.gr).
M. G. Strintzis is with the Information Processing Laboratory, Aristotle
University of Thessaloniki, Thessaloniki 54006, Greece, and also with the
Informatics and Telematics Institute, Thessaloniki 546 39, Greece (e-mail:
strintzi@eng.auth.gr).
Digital Object Identifier 10.1109/TCSVT.2002.804880
Such so-called “blocking” artifacts are often very disturbing,
especially when the transform coefficients are subject to coarse
quantization.
Subjective picture quality can be significantly improved by
decreasing the blocking artifacts. Increasing the bandwidth or
bit rate to obtain better quality images is often not possible or is
too costly. Other approaches to improve the subjective quality
of the degraded images have been published. Techniques which
do not require changes to existing standards appear to be the
most practical solution, and with the fast increase of available
computing power, more sophisticated methods can be imple-
mented. If the blocking effects can be significantly reduced, a
higher compression ratio can be achieved.
Inthispaper,anewmethodisproposedforthedetectionandre-
ductionoftheblockingeffectsintheB-DCT.First,blockswhich
showblockingartifactswiththeneighboringblocksaredetected.
The detection scheme is applied in the subband-like represen-
tation of the modified DCT coefficients which are produced, if
we assume that theDCT coefficients follow the Laplacian prob-
ability model [37] (hereafter, Laplacian corrected DCT coeffi-
cients). Specifically, the presence of visual blocking artifacts of
the B-DCT reconstructed image is inferred from data in the fre-
quencydomain.Then,theblockinessisassumedwhentherelative
difference of two neighboring Laplacian corrected DCT coeffi-
cients in thesubband-like domain is greaterthan a threshold.
Foreveryblockfoundtopresentblockingartifacts,thelowest
frequency DCT coefficients are recalculated by minimizing a
novel enhanced form of the mean squared difference of slope
(MSDS) [33], which involves all eight neighboring blocks. The
minimization is constrained by the quantization bounds and is
performed for every frequency separately, in the subband-like
representation of the DCT transform. Thus, a closed-form
representationisderived,whichpredictstheDCTcoefficientsin
terms of the eight neighboring coefficients in the subband-like
domain.
A first major advantage of the proposed algorithm is that it is
applied entirely in the compressed domain. This is in contrast
to the large majority of the deblocking algorithms which are
applied in the spatial domain.
Compared to other methods of deblocking in the frequency
domain:
• theproposedalgorithm introducesthenovelandenhanced
form of MSDS which involves all neighboring blocks,
including the diagonally located neighboring blocks;
• our algorithm minimizes MSDS in the frequency do-
main, in order to recalculate the DCT coefficients for
blockiness removal. This minimization is performed
1051-8215/02$17.00 © 2002 IEEE

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878IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 12, NO. 10, OCTOBER 2002
for each frequency separately, producing better results
than global minimization. This is intuitively expected
because B-DCT schemes (such as JPEG) use scalar rather
than vector quantization, and also, the DCT transform
(which is an approximation of the Karhuene–Loeve (KL)
transform) produces almost uncorrelated coefficients’;
• furthermore, this paper contains the novelproposition that
the Laplacian corrected DCT coefficients should be used
in place of the simple DCT reconstructed coefficients in
the formula which provides the correction of the DCT
coefficients, because they provide statistically better es-
timates of the original DCT coefficients. This proposition
is supported by the experimental results;
• finally, this paper presents not only a method for the
removal of the blocking artifacts, but also proposes a
novel blockiness detection method which reduces the
time and the computational load of deblocking algorithms
by having the deblocking algorithm applied only where
needed (where there exist disturbing blocking artifacts).
The rest of this paper is organized as follows. In Section II, a
review and discussion of various techniques that have been pro-
posed in the past for the removal of blocking artifacts are given.
Section III describes the mathematical analysis underlying the
concept of blocking artifact detection in the subband-like trans-
form domain, under the assumption that the DCT transform fol-
lows a Laplacian probability density function (pdf). Section IV
presentsindetailtheblockingartifactreductionalgorithmbycon-
strained minimization. Experimental results given in Section V
evaluate visually and quantitatively the performance of the pro-
posed methods. Finally, conclusionsare drawninSection VI.
II. BACKGROUND
Many techniques have been proposed in the literature for the
reduction of blocking artifacts. Two general approaches have
been followed. In the first approach, the blocking effect is dealt
with at the encoding side [5], [6]. The second approach pro-
poses postprocessing at the decoding side, aiming to improve
the visual quality of the reconstructed image without any mod-
ification on the encoding or decoding procedures. Due to this
advantage, most of the recently proposed algorithms follow the
second approach.
The majority of the postprocessing techniques in the litera-
ture are applied in the spatial domain. These techniques may be
classifiedintoseveralcategories:1)thespatialfilteringmethods
[7]–[10];2)methodsbasedonwaveletrepresentation[11]–[14];
3)MRFapproaches[15]–[17];and4)theiterativeregularization
restoration approaches [18]–[21].
In the first category, Jarske et al. [7] test several filters to
conclude that the Gaussian low-pass filter with a high-pass fre-
quency emphasis gives the best performance. Reeves and Lim
[8] apply the 3
3 Gaussian filter only to those pixels along
block boundaries. A similar technique by Tzou [22] applies a
separable anisotropic Gaussian filter, such that the primary axis
of the filter is always perpendicular to the block boundary. A
space-variant filter that adapts to local characteristics of the
signal is proposed by Ramamurthi and Gersho in [23]. The al-
gorithm distinguishes edge pixels from nonedge pixels via a
neighborhood testing and then switches between a one–dimen-
sional (1-D) and a two–dimensional (2-D) filter accordingly to
reduce blocking effects. In [24], an adaptive filtering scheme
is reported, progressively transforming a median filter within
blocks to a low-pass filter when it approaches the block bound-
aries. An adaptive filtering process is also employed in [25].
Theshape and thepositionof theGaussian filteringare adjusted
based on an estimation of the local characteristics of the coded
image. A region-based method is presented in [9], where the
degraded image is segmented by a region growing algorithm,
and each region obtained by the segmentation is enhanced sep-
arately bya Gaussian low-passfilter. Lee etal. in [26] propose a
2-D signal-adaptivefilteringand Chouet al. [27] removeblock-
iness by performing a simple nonlinear smoothing of pixels.
In [10], Apostolopoulos et al. propose to identify the blocks
that potentially exhibit blockiness by calculating the number of
nonzero DCT coefficients in a coded block and comparing it to
a threshold. Then, a filter is applied along the boundaries but
only updating the pixels within the distorted block. However,
the above filtering approaches frequently result in overblurred
recovered images, especially at low bit rates. Another approach
is proposed in [28]–[30], where the optimal filters for subband
coding of the quantized image are efficiently determined for the
reduction of quantization effects in low bit rates.
In the second category, Xiong et al. [12] use an overcom-
plete wavelet representation to reduce the quantization effects
of block based DCT. Other approaches using wavelet represen-
tation are presented in [11], [13], and [14]. In [14] the wavelet
transformmodulusmaxima(WTMM)representationisusedfor
efficient image deblocking.
In the third category, O’ Rourke and Stevenson [15] propose
a postprocessor that can remove blockiness in block encoded
images. To achieve this, they maximize the a posteriori proba-
bility(MAP)oftheunknownimage.Theprobabilityfunctionof
the decompressed image is modeled by an MRF, and the Huber
minimax function is chosen as a potential function. A similar
approach is followed by Luo et al. [16]. In [17], Meier et al. re-
move blocking artifacts by first segmenting the degraded image
into regions by an MRF segmentation algorithm, and then each
region is enhanced separately using an MRF model.
Finally, in the fourth category, iterative image recovery
methods using the theory of projections onto convex sets
(POCS) are proposed in [19], [31], [32]. In the POCS-based
method, closed convex constraint sets are first defined that
represent all of the available data on the original uncoded
image. Then, alternating projections onto these convex sets
are iteratively computed to recover the original image from
the coded image. POCS is effective in eliminating blocking
artifacts but less practical for real time applications, since the
iterative procedure adopted increases the computation com-
plexity. In [18] and [21], the constrained least-square method is
proposed, which aims to reconstruct the image by minimizing
an objective function reflecting a smoothness property.
Very few approaches in the literature have tackled the
problem of blocking artifact reduction in the transform domain
[33], [34]. In the JPEG standard [1], a method for suppressing
the block to block discontinuities in smooth areas of the image
is introduced. It uses dc values from current and neighboring

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TRIANTAFYLLIDIS et al.: BLOCKING ARTIFACT DETECTION AND REDUCTION IN COMPRESSED DATA879
blocks for interpolating the first few ac coefficients into the
current block. In [33], Minami and Zakhor present a new
approach for reducing the blocking effect. A new criterion,
the mean squared difference of slope (MSDS)—a measure of
the impact of blocking effects—is introduced. It is shown that
the expected value of the MSDS increases after quantizing the
DCT coefficients. This approach removes the blocking effect
by minimizing the MSDS, while imposing linear constraints
corresponding to quantization bounds. To minimize the MSDS,
a quadratic programming (QP) problem is formulated and
solved using a gradient projection method. The solution is
obtained in the form of the optimized value of the three lowest
DCT coefficients. The blocking effect due to the quantization
of low frequency coefficients is reduced if the quantized DCT is
replaced by the optimized values during the decoding phase. To
remove the high-frequency blocking effect, low-pass filtering
of the decoded image is proposed. In [34], Lakhani and Zhong
follow the approach proposed in [33] for reducing blocking
effects using, however, a different solution of the optimization
problem, minimizing the MSDS globally and predicting the
four lowest DCT coefficients.
Our proposed method for the reduction of blocking artifacts
also adopts thecriterion of MSDS. However,the form of MSDS
which is now used has been enhanced by also involving the
diagonal neighboring pixels. Furthermore, the optimization is
performed in the subband-like domain for each frequency sep-
arately using the Laplacian corrected DCT coefficients. Before
applying the blockiness reduction algorithm, a method is used
for the detection of the most disturbing blocking artifacts in
the reconstructed image. This method of blockiness detection
is elaborated in the next section.
III. DETECTION OF BLOCKING ARTIFACTS USING THE DCT
LAPLACIAN MODEL IN THE SUBBAND-LIKE DOMAIN
In the classical B-DCT formulation, the input image is first
divided into 8
8 blocks, and the 2-D DCT of each block is
determined. The 2-D DCT can be obtained by performing a 1-D
DCT on the columns and a 1-D DCT on the rows. The DCT
coefficients of the spatial block
following formula:
are then determined by the
(1)
where
are the DCT coefficients of the
istheluminancevalueofthepixel
are the dimensions of the image, and
block,
ofthe
block,
if
if.
(2)
The transformed output from the 2-D DCT is ordered so that
the dc coefficient
is in the upper-left corner and the
Fig. 1.Subband-like domain of DCT coefficients.
higher frequency coefficients follow, depending on their dis-
tance from the dc coefficient. The higher vertical frequencies
arerepresentedbyhigherrownumbersandthehigherhorizontal
frequencies are represented by higher column numbers.
A typicalquantization-reconstruction process of the DCT co-
efficients as described in JPEG [1] is given by
(3)
(4)
where
coefficient,
efficient
structed quantized coefficient. Then, the reconstructed pixel in-
tensity is obtained from the inverse DCT.
DCT coefficients with the same frequency index
all DCT transformed blocks can be scanned and grouped to-
gether, starting from the dc coefficients (
transforming an image with an 8
producehierarchicaldataequivalenttothoseproducedbyasub-
band transform of 64 frequency bands. Fig. 1 shows the scheme
ofthesubband-liketransformdomainandFig.2showstheDCT
coefficients reallocated to form a subband-like transform of the
image “Lena.”
We shall assume that for typical input image statistics, the
DCT coefficients may be reasonably modeled by a Laplacian
pdf as [35]
indicatesthequantizationwidthbinforthegiven
indicates the bin index in which the co-
falls, andrepresents the recon-
from
). Thus,
8 2-D DCT can be seen to
(5)
which is a zero-mean pdf with variance
(6)
If the Laplacian-modeled variable is quantized using uniform
step sizes, the only information available to the receiver is that
the original DCT coefficient is in the interval
whereand
(7)

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880IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 12, NO. 10, OCTOBER 2002
Fig. 2.Subband-like domain of DCT coefficients of “Lena” image.
ThetrivialsolutionsuggestedinJPEGistoreconstructthecoef-
ficientin thecenterof theintervalas
plifies implementation. The optimal reconstruction (minimum
mean squared error) lies in the centroid of the distribution for
the interval
, thus, under the assumption of Lapla-
cian statistics [36], we have the following:
,which sim-
(8)
Note that this implies a bias
toward the origin
(9)
For different coefficients, we have different step sizes and vari-
ances [37]. Therefore, considering the DCT coefficient of block
atfrequency,wehavequantizationstepsize
and variance. Then, the bias
be found from (9) and (7)
toward the origin can
(10)
Given the coefficient variances, we can estimate the
eters using (6), thus
can be easily estimated by
estimation is only used for the calculation of
the reconstructed DCT coefficients in place of the original DCT
coefficients, since only the former coefficients are available.
Alternatively,wemayestimate
in [40], which estimates the variances of the DCT coefficients
from the variances of the pixel values using the form
param-
. The variances
[38]. This
and employs
inthewayproposed
(11)
Experimentshaveshownthattheresultsareverysimilartothose
of the adopted method, described earlier. However, we did not
choose to employ the method in [40] because it is more compu-
tationally inefficient.
Therefore, we can use (9) to precalculate all
tain the optimal estimation
coefficient (Laplacian corrected DCT coefficients)
so as to ob-
of the reconstructed DCT
(12)
where the
positive and negative values and
The above concepts are now extended and applied to define
a method for blockiness detection. First, we define the newly
introduced relative theoretical quantization error
cient
by
function is appropriately used to handle both
.
for coeffi-
(13)
We nextfocusonthedifference
blocks. Occurrences of large values of this difference indi-
cate that very different levels were used to quantize the
blocks, producing a blocking artifact between these blocks.
Thus, we shall infer the presence of an artifact between blocks
andif
betweentheand
and
(14)
where
is an adaptive threshold defined by
(15)
For a given compressed image, the detection criterion is
applied on each coefficient in all of the 64 bands of the DCT
subband-like domain, in order to locate the most disturbing
blocking artifacts. More specifically, for each band in the
subband-like domain, we scan the coefficients vertically,
horizontally and diagonally, and apply criterion (14). We
assume that a blocking artifact between the
neighboring
block is disturbing when (14) is satisfied for
more than two frequencies in the subband-like domain, e.g.,
andfrequencies. Thus, we introduce the following
criterion:
Artifact between neighboring blocks
iffrequencies
block and the
and
that
and
(16)
This criterion was tested in a large number of pictures and
was found to be very efficient in detecting the most disturbing
blocking artifacts.
IV. REDUCTION OF BLOCKING ARTIFACT IN THE
FREQUENCY DOMAIN
As noted, blocking effects result in discontinuities across
block boundaries. Based on this observation, a metric called

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TRIANTAFYLLIDIS et al.: BLOCKING ARTIFACT DETECTION AND REDUCTION IN COMPRESSED DATA881
MSDS was introduced in [33], involving the intensity gradient
(slope) of the pixels close to the boundary of two blocks.
Specifically, it is based on the empirical observation that
quantization of the DCT coefficients of two neighboring blocks
increases the MSDS between the neighboring pixels on their
boundaries.
To better understand this metric, consider an 8
the input image and a block
horizontally adjacent to . If the
coefficients of the adjacent blocks are coarsely quantized, a dif-
ferenceintheintensitygradientacrosstheblockboundaryisex-
pected.Thisabruptchangeinintensitygradientacrosstheblock
boundaries of the original unquantized image is rather unlikely,
because most parts of most natural images can be considered to
be smoothly varying and their edges are unlikely to line up with
block boundaries. From the above, it is clear that a reasonable
method for the removal of the blocking effects is to minimize
the MSDS, which is defined by
8 blockof
(17)
where
the
is the intensity slope across the boundary between
blocks, defined byand
(18)
and
is the average between the intensity slope of
blocks close to their boundaries, defined by
and
(19)
The ideas in the above discussion are applicable to both hori-
zontal and vertical neighboring blocks. Specifically, if blocks
, denote the blocks horizontally adjacent to , and blocks ,
present the blocks vertically adjacent to
which involves both horizontal and vertical adjacent blocks
(hereafter, MSDS ) is given by
, then, the MSDS
MSDS
(20)
where
We now extend the definition of MSDS by involving the four
diagonally adjacent blocks. If
to
, then we define
, andare defined similarly to (17)–(19).
is a block diagonally adjacent
(21)
where
and
(22)
If
to
(hereafter, MSDS ) is
,,, and are the four blocks diagonally adjacent
; the MSDS involving only the diagonally adjacent blocks
MSDS
(23)
where
and (22). Thus, the total MSDS (hereafter, MSDS ) considered
,, andare defined in a manner similar to (21)
Fig. 3.Vertical and horizontal slope (MSDS ) and diagonal slope (MSDS ).
in this paper, involving the intensity slopes of all the adjacent
blocks is
MSDS
MSDSMSDS(24)
Fig. 3 shows the pixels involved in the calculation of MSDS
and MSDS .
The form of MSDS used in the proposed methods of [33] and
[34] is MSDS which, as mentioned above, involves only the
horizontal and vertical adjacent blocks for its computation and
thusdoesnotusetheintensityslopesofthefourdiagonallyadja-
cent blocks. This implies that their methods cannot remove the
specific type of blocking artifact called “corner outlier” [26],
which may appear in a corner point of the 8
over, even if we ignore the reduction of the corner outliers, the
introduction of the MSDS yields better results than the simple
form of MSDS , since more neighboring pixels (i.e., the neigh-
boring diagonal pixels) are used, providing a better estimation
for the DCT recalculation.
In [34], a global minimization of the MSDS is proposed
for the reduction of blocking effects. However, since B-DCT
schemes (such as JPEG) use scalar quantization (i.e., quanti-
zation of individual samples) for each frequency separately, a
separate minimization of the contribution of the quantization
of each particular coefficient to the blocking artifact is more
appropriate than a global minimization. Global minimization
would be more suitable if vector quantization (i.e., quantiza-
tion of groups of samples or vectors) of the DCT coefficients
were used, which is, however, not the case in B-DCT coding
schemes. Consider also that, since the DCT transform is very
close to the KL transform, the DCT coefficients are almost un-
correlated [41]. Thus, the modification of each DCT coefficient
based on the minimization of MSDS which includes values of
the low-, middle-, and high-pass frequency coefficients is obvi-
ously not the best solution, and the minimization of MSDS for
each frequency separately is the appropriate procedure.
The new enhanced form of the MSDS
eight neighboring blocks is used in this paper, and its local
constrained minimization for each frequency, produces a
closed-form representation for the correction of the DCT
coefficients in the subband-like domain of the DCT transform.
To achieve this, the form of MSDS in the frequency domain
is obtained, and all other frequencies apart from the one
under consideration are set to zero. It was observed that only
8 block. More-
involving all