A Novel PSNR-B Approach for Evaluating the Quality of De-blocked Images

IOSR Journal of Computer Engineering (IOSRJCE)
ISSN: 2278-0661 Volume 4, Issue 5 (Sep.-Oct. 2012), PP 40-49
www.iosrjournals.org
www.iosrjournals.org 40 | Page
A Novel PSNR-B Approach for Evaluating the Quality of
De-blocked Images
Trinadh Tadala1
, Sri E.Venkata Narayana2
1,2
Dept. Of Electronics and communication engineering, University College of Engineering, JNTUK, Kakinada,
East Godavari Dist, Andhra Pradesh, India.
Abstract: JPEG Compression is the most prevalent technique or method for images codecs. But it suffers from
blocking artifacts. In this paper a comparison of the perceptual quality of deblocked images based on various
quality assessments metric is done. A proposed PSNR including blocking effect factor was used instead of
PSNR. Another quality assessment metric SSIM was used which produces results largely in accordance with
PSNR-B. We show the simulation results, which prove PSNR-B produces objective judgments. The efficiency of
deblocking algorithms was studied.
Keywords: Deblocked images, blocking artifacts, quality assessment, quality metric
I. INTRODUCTION
Many practical and commercial systems use digital image compression when it is required to transmit
or store the image over limited resources. JPEG compression is the most popular image compression standard
among all the members of lossy compression standards family. JPEG image coding is based on block based
discrete cosine transform. BDCT coding has been successfully used in image and video compression
applications due to its energy compacting property and relative ease of implementation. After segmenting an
image in to blocks of size N×N, the blocks are independently DCT transformed, quantized, coded and
transmitted. One of the most noticeable degradation of the block transform coding is the “blocking artifact”.
These artifacts appear as a regular pattern of visible block boundaries. This degradation is the result of course
quantization of the coefficients and of the independent processing of the blocks which does not take in to
account the existing correlations among adjacent block pixels [12]. In order to achieve high compression rates
using BTC with visually acceptable results, a procedure known as deblocking is done in order to eliminate
blocking artifacts.
In this paper a research has done on quality assessment of deblocked images by estimating various
quality metrics and the effect of quantization step of the measured quality of deblocked image is studied.
Simulations are done using quality metrics such as peak signal-to-noise ratio (PSNR), structural similarity index
(SSIM) and PSNR-B. PSNR-B is a new quality metric which includes PSNR by a blocking factor. By going
through simulation results, it is shown that PSNR-B correlates well with the SSIM index and subjective quality
and its performance is much better than the PSNR.
II. QUALITY ASSESSMENT & DEBLOCKING
To remove blocking effect, several deblocking techniques have been proposed in the literature as post
process mechanisms after JPEG compression, depending on the angle from which the blocking problem is
tackled. If deblocking is viewed as an estimation problem, the simplest solution is probably just to low pass the
blocky JPEG compressed image. More sophisticated methods involve iterative methods such as projection on
convex sets [3, 4] and constrained least squares [4, 5] In this paper we use deblocking algorithms including
lowpass filtering and projection on to convex sets. The efficiency of these algorithms can be analyzed by
introducing a proposed method in the following section.
In this project We consider the two reference models class of quality assessment (QA) methods that are
full-reference (FR) QA, which compares the test (distorted) image with a reference (original) image., the
distorted images will ostensibly suffer from blocking artifacts or from the residual artifacts.
III. PROPOSED METHOD
Deblocking operation is performed in order to reduce blocking artifacts. Deblocking operation can be
achieved by using various deblocking algorithms, employing deblocking filters. The effects of deblocking
filters can be analyzed by introducing a change in distortion concept.
The deblocking operation results in the enhancement of image quality in some areas, while degrading in other
areas.

A Novel PSNR-B Approach For Evaluating The Quality Of De-blocked Images
Fig 1 Block diagram showing JPEG compression
Let X be the reference image and Y be the test image (decoded image) distorted by quantization errors
and Y ̃ be the deblocked image as shown in figure1. Let f represent the
Deblocking operation and is given by Y ̃ =f(Y). Let the quality metric between X and Y be M(X,Y). For the
given image Y, the main aim of deblocking operation f is to maximize M(X,f(Y)).
IV. ESTIMATION OF QUALITY METRICS
To Measure the quality degradation of an available distorted image with reference to the original
image, a class of quality assessment metrics called full reference (FR) are considered. Full reference metrics
perform distortion measures having full access to the original image. The quality assessment metrics are
estimated as follows
A. Peak signal to noise ratio
The simplest and most widely used FR QA metrics are the peak signal-to-noise ratio (PSNR) and the
mean-squared error (MSE) [1], [3].
It is most easily defined via the mean squared error (MSE) which for two m×n monochrome images I and K
where one of the images is considered a noisy approximation of the other is defined as
Let x and y represent the vectors of reference and test image signals, respectively. Let e be the vector of error
signal between x and y. If the number of pixels in an image is N
𝐌𝐒𝐄 𝐱, 𝐲 =
𝟏
𝐍
𝐞𝐢
𝟐
=
𝟏
𝐍
𝐱𝐢 − 𝐲𝐢
𝟐
𝐍
𝐢=𝟏
𝐍
𝐢=𝟏
𝟏
The PSNR is defined as:
𝐏𝐒𝐍𝐑 𝐱, 𝐲 = 𝟏𝟎𝐥𝐨𝐠 𝟏𝟎
𝟐𝟓𝟓 𝟐
𝐌𝐒𝐄 𝐱, 𝐲
𝟐
B. Structural similarity index metrics
A product of three aspects of similarity is measured: luminance, contrast, and structure. The structural
similarity (SSIM) metric aims to measure quality by capturing the similarity of images. The luminance
comparison function L(x, y) for reference image x and test image y is defined as
𝐥 𝐱, 𝐲 =
𝟐𝛍 𝐱 𝛍 𝐲 + 𝐂 𝟏
𝛍 𝐱
𝟐 + 𝛍 𝐲
𝟐 + 𝐂 𝟏
(𝟑)
Where 𝜇 𝑥 and 𝜇 𝑦 are the mean values of x and y , respectively ,and C1 is a stabilizing constant.
The contrast comparison function C(x, y) is defined similarly as
𝐂 𝐱, 𝐲 =
𝟐𝛔 𝐱 𝛔 𝐲 + 𝐂 𝟐
𝛔 𝐱
𝟐 + 𝛔 𝐲
𝟐 + 𝐂 𝟐
(𝟒)
Where 𝜎𝑥and𝜎𝑦 are the standard deviation of x and y , respectively, and C2 is a stabilizing constant.
The structure comparison functions S(x, y) is defined as
𝐒 𝐱, 𝐲 =
𝛔 𝐱𝐲 + 𝐂 𝟑
𝛔 𝐱 𝛔 𝐲 + 𝐂 𝟑
(𝟓)
Where 𝜎𝑥𝑦 is the correlation between x and y and C3 is also a constant that provides stability.
The SSIM index is obtained by combining the three comparison functions
𝐒𝐒𝐈𝐌 𝐱, 𝐲 = [𝐥 𝐱, 𝐲 ] 𝛂
∙ [𝐂 𝐱, 𝐲 ] 𝛃
∙ [𝐒 𝐱, 𝐲 ] 𝛄
(𝟔)
The parameters are set as
𝛂 = 𝛃 = 𝛄 = 𝟏 And C3=C2/2
𝐒𝐒𝐈𝐌 𝐱, 𝐲 =
𝟐𝛍 𝐱 𝛍 𝐲 + 𝐂 𝟏 (𝟐𝛔 𝐱𝐲 + 𝐂 𝟐)
𝛍 𝐱
𝟐 + 𝛍 𝐲
𝟐 + 𝐂 𝟏 (𝛍 𝐱
𝟐 + 𝛍 𝐲
𝟐 + 𝐂 𝟐)
(𝟕)
Local SSIM statistics are estimated using a symmetric Gaussian weighting function. The mean SSIM
index pools the spatial SSIM values to evaluate the overall image quality.
𝐒𝐒𝐈𝐌 𝐱, 𝐲 =
𝟏
𝐌
𝐒𝐒𝐈𝐌(𝐱𝐣. 𝐲𝐣)
𝐌
𝐣=𝟏
(𝟖)
Where M is the number of local windows over the image, and 𝑥𝑗 and 𝑦𝑗 are image patches covered by the jth
window.
Encoder Decoder deblocking
operation
x
Channel
y ỹ

V. EFFECT OF QUANTIZATION STEP SIZE.
The amount of compression and the quality can be controlled by the quantization step. Quantization is
a key element of lossy compression, but information is lost. There are tradeoffs between compression ratio and
reconstructed image/video quality. As the quantization step is increased, the compression ratio becomes larger,
and the quality generally worsens. However, there has not been a study made of how perceptual quality suffers
as a function of step size or the degree to which deblocking augments perceptual quality. The emergence of new
and powerful IQA indices suggests this possibility.
In block transform coding, the input image is divided into LxL blocks, and each block is transformed
independently into transform coefficients. An input image block is transformed into a DCT coefficient block
𝐁 = 𝐓𝐁𝐓 𝐭
(𝟗)
Where T is the transform matrix and 𝑇 𝑡
is the transpose matrix of T. The transform coefficients are quantized
using a scalar quantizer Q
𝑩 = 𝑸 𝑩 = 𝑸 𝑻𝒃𝑻𝒕
(𝟏𝟎)
The quantization operator in (10) is nonlinear, and is a many-to-one mapping from 𝐑 𝐋 𝟐
to 𝐑 𝐋 𝟐
.In the decoder,
only quantized transform coefficients 𝐵 are available.
The output of the decoder is
𝐛 = 𝐓 𝐭
𝐁 𝐓 = 𝐓 𝐭
𝐐 𝐓𝐛𝐓 𝐭
𝐓 (𝟏𝟏)
Let represent the quantization step. It is well known that the PSNR is a monotonically decreasing function
of ∆. The SSIM index captures the similarity of reference and test images. As the quantization step size
becomes larger, the structural differences between reference and test image will generally increase, and in
particular the structure term S(X,f) in (5) will become smaller. Hence, the SSIM index would be a
monotonically decreasing function of the quantization step size.
VI. DEBLOCKING FILTER AND DISTORTION CHANGE
As before, x is the reference (original) image and y is the decoded image that has been distorted by
quantization errors. Let 𝑦 represent the de blocked image and f represent the deblocking operation: 𝐲 = 𝐟(𝐲) .
Fig. 1 shows a block diagram depicting the flow of reference, decoded, and deblocked images.
Let M(x, y) be the quality metric between and. The goal of the deblocking operation y is to maximize
M(x, f(y)), given image. Deblocking is a local operation. The de blocking operation may improve the
appearance of the image in some regions, while degrading the quality elsewhere.
Let 𝐝(𝐱𝐢, 𝐲𝐢) be the distortion between the ith pixels of and, expressed as squared Euclidean distance
𝐝 𝐱𝐢, 𝐲𝐢 = 𝐱𝐢 − 𝐲𝐢
𝟐
(𝟏𝟐)
Next, we define the distortion decrease region (DDR) to be composed of those pixels where the distortion is
decreased by the deblocking operation
𝐢 ∈ 𝐀, 𝐢𝐟 𝐝 𝐱𝐢, 𝐲𝐢 < 𝒅(𝐱𝐢, 𝐲𝐢)
The amount of distortion decrease for the ith pixel 𝛼𝑖 in the DDRA is
𝛂𝐢 = 𝐝 𝐱𝐢. 𝐲𝐢 − 𝐝 𝐱𝐢, 𝐲𝐢 (𝟏𝟑)
The distortion may also increase at other pixels by application of the deblocking filter. We similarly define the
distortion increase region (DIR) B
𝐢 ∈ 𝐁, 𝐢𝐟 𝐝 𝐱𝐢, 𝐲𝐢 < 𝒅 𝐱𝐢, 𝐲𝐢
The amount of distortion increase for the ith pixel 𝛽𝑖 in the DIRB is
𝛃𝐢 = 𝐝 𝐱𝐢. 𝐲𝐢 − 𝐝 𝐱𝐢, 𝐲𝐢 (𝟏𝟒)
We define the mean distortion decrease (MDD)
𝛂 =
𝟏
𝐍
(𝐝 𝐱𝐢, 𝐲𝐢 − 𝐝(𝐱𝐢, 𝐲𝐢)
𝐢∈𝐀
(𝟏𝟓)
Where N is the number of pixels in the image. Similarly the mean distortion increase (MDI) is
𝛃 =
𝟏
𝐍
(𝐝
𝐢∈𝐁
𝐱𝐢, 𝐲𝐢 − 𝐝 𝐱𝐢, 𝐲𝐢 (𝟏𝟔)
A reasonable approach for designing a deblocking filter would be to seek to maximize the MDD 𝛼 and
minimize the MDI 𝛽 . This is generally a very difficult task and of course, may not result in optimized
improvement in perceptual quality. Lastly, let be the mean distortion change (MDC), defined as the difference
between MDD and MDI
𝛄 = 𝛂 − 𝛃 (𝟏𝟕)
If𝛾 < 0, then the deblocking operation is likely unsuccessful since the mean distortion increase is larger than
the mean distortion decrease. We would expect a successful deblocking operation to yield𝛾 > 0. Nevertheless,
these conditions are not equated with levels of perceptual improvement or loss. Deblocking can be considered
as an image restoration problem. Let represent the deblocking operation function and 𝑁(𝑥𝑖) represent a

neighbourhood of pixel𝑥𝑖 . A lowpass filter is a simple deblocking filter. An LxL low pass filter can be
represented as
𝐠 𝐍 𝐱𝐢 = 𝐡 𝐤 ∙ 𝐱𝐢,𝐊
𝐋 𝟐
𝐤=𝟏
… … (𝟏𝟖)
Where ℎ 𝑘 is the kernel for the LxL filter and is the th pixel in the neighbourhood of pixel 𝑥𝑖 . While lowpass
filtering does reduce blocking artifacts, critical high frequency information is also lost and the image is blurred.
While the distortion will certainly decrease for some pixels that define the DDR, the distortion will likely
increase for a significant number of pixels in DIR. Indeed, it is quite possible that 𝛾 < 0 could result. Moreover,
blur is perceptually annoying. A variety of nonlinear methods have been proposed to reduce the blocking
artifacts, while minimizing the loss of original information. For example, deblocking algorithms based upon
projection onto convex sets (POCS) have demonstrated good performance for reducing blocking artifacts and
have proved popular.
In POCS, a low pass filtering operation is performed in the spatial domain, while a projection
operation is performed in the DCT domain. Typically, the projection operation is a clipping operation on the
filtered coefficients, confining these to fall within a certain range defined by the quantization step size. Since
the low pass filtering and the projection operations are performed in different domains, forward DCT and
inverse DCT (IDCT) operations are required. The low pass filtering, DCT, projection, IDCT operations
compose one iteration, and multiple iterations are required to achieve convergence. It is argued that under
certain conditions, POCS filtered images converge to an image that does not exhibit blocking artifacts.
VII. PSNR INCLUDING BLOCKING EFFECTS
In the following, we propose a new block-sensitive image quality metric which we term peak signal-to-
noise ratio including blocking effects (PSNR-B). As the quantization step size increases, blocking artifacts
generally become more conspicuous. Blocking artifacts are gray level discontinuities at block boundaries,
which are ordinarily oriented horizontally and vertically. They arise from poor representation of the block
luminance levels near the block boundaries. The following definitions are relative to an assumed block-based
compression tiling, e.g., 8x8 blocks as in JPEG compression. For simplicity, assume that an integer number of
blocks comprise the image, viz., that horizontal and vertical dimensions are divisible by the block dimension.
The definitions apply whether the image is compressed, not-compressed, or deblocked following
decompression.
We, therefore, consider blocking artifacts that occur along the horizontal and vertical orientations. Let
𝑵 𝑯 and 𝑵 𝒗 be the horizontal and vertical dimensions of the 𝑵 𝑯 𝑿𝑵 𝒗 image I. Let be the set of horizontal
neighbouring pixel pairs in I. Let 𝓗 𝑩 ⊂ 𝓗 be the set of horizontal neighbouring pixel pairs that lie across a
block boundary. Let 𝓗 𝑩
𝑪
be the set of horizontal
neighbouring pixel pairs, not lying across a block
boundary,
i.e. 𝓗 𝑩
𝑪
= 𝓗 − 𝓗 𝑩, . Similarly, let 𝜈 be the set of
vertical neighbouring pixel pairs, and 𝝂 𝑩 be the set
of vertical neighbouring pixel pairs lying across
block boundaries. Let 𝝂 𝑩
𝑪
be the set of vertical
neighbouring pixel pairs not lying across block
boundaries i.e.𝝂 𝑩
𝑪
= 𝝂 − 𝝂 𝑩.
Let 𝑵 𝑯 𝑩
, 𝑵 𝑯 𝑩
𝑪 , 𝑵 𝑽 𝑩
, 𝑵 𝑽 𝑩
𝑪 be the number of pixel
pairs in 𝓗 𝑩, 𝓗 𝑩
𝑪
, 𝝂 𝑩 and 𝝂 𝑩
𝑪
respectively .If B is
the block size then
𝐍𝐇 𝐁 = 𝐍 𝐕
𝐍 𝐇
𝐁
− 𝟏
𝐍 𝐇 𝐁
𝐂 = 𝐍 𝐕 𝐍 𝐇 − 𝟏 − 𝐍 𝐇 𝐁
𝐍 𝐕 𝐁
= 𝐍 𝐇
𝐍 𝐕
𝐁
− 𝟏
𝐍 𝐕 𝐁
𝐂 = 𝐍 𝐇 𝐍 𝐕 − 𝟏 − 𝐍 𝐕 𝐁
Fig. 2(a) example for illustration of (8x8) pixel blocks
y1 y2 y3 y4 y5 y6 y7 y8
y9 y10 y11 y12 y13 y14 y15 y16
y17 y18 y19 y20 y21 y22 y23 y24
y25 y26 y27 y28 y29 y30 y31 y32
y33 y34 y35 y36 y37 y38 y39 y40
y41 y42 y43 y44 y45 y46 y47 y48
y49 y50 y51 y52 y53 y54 y55 y56
y57 y58 y59 y60 y61 y62 y63 y64

Fig. 2(b) example for illustration of (16x16) pixel blocks
Fig. 2 shows a simple example for illustration of pixel blocks with𝐍 𝐇 = 𝟖, 𝐍 𝐕 = 𝟖 , and B=4 .
The thick lines represent the block boundaries. In this example 𝐍 𝐇 𝐁
= 𝟖 , 𝐍 𝐇 𝐁
𝐂 = 𝟒 , 𝐍 𝐕 𝐁
= 𝟖, and 𝐍 𝐕 𝐁
𝐂 = 𝟒𝟖.
y
1
y
2
y
3
y
4
y
5
y
6
y
7
y
8
y
9
y
1
0
y
1
1
y
1
2
y
1
3
y
1
4
y
1
5
y
1
6
y
1
7
y
1
8
y
1
9
y
2
0
y
2
1
y
2
2
y
2
3
y
2
4
y
2
5
y
2
6
y
2
7
y
2
8
y
2
9
y
3
0
y
3
1
y
3
2
y
3
3
y
3
4
y
3
5
y
3
6
y
3
7
y
3
8
y
3
9
y
4
0
y
4
1
y
4
2
y
4
3
y
4
4
y
4
5
y
4
6
y
4
7
y
4
8
y
4
9
y
5
0
y
5
1
y
5
2
y
5
3
y
5
4
y
5
5
y
5
6
y
5
7
y
5
8
y
5
9
y
6
0
y
6
1
y
6
2
y
6
3
y
6
4
y
6
5
y
6
6
y
6
7
y
6
8
y
6
9
y
7
0
y
7
1
y
7
2
y
7
3
y
7
4
y
7
5
y
7
6
y
7
7
y
7
8
y
7
9
y
8
0
y
8
1
y
8
2
y
8
3
y
8
4
y
8
5
y
8
6
y
8
7
y
8
8
y
8
9
y
9
0
y
9
1
y
9
2
y
9
3
y
9
4
y
9
5
y
9
6
y
9
7
y
9
8
y
9
9
y
1
0
0
y
1
0
1
y
1
0
2
y
1
0
3
y
1
0
4
y
1
0
5
y
1
0
6
y
1
0
7
y
1
0
8
y
1
0
9
y
1
1
0
y
1
1
1
y
1
1
2
y
1
1
3
y
1
1
4
y
1
1
5
y
1
1
6
y
1
1
7
y
1
1
8
y
1
1
9
y
1
2
0
y
1
2
1
y
1
2
2
y
1
2
3
y
1
2
4
y
1
2
5
y
1
2
6
y
1
2
7
y
1
2
8
y
1
2
9
y
1
3
0
y
1
3
1
y
1
3
2
y
1
3
3
y
1
3
4
y
1
3
5
y
1
3
6
y
1
3
7
y
1
3
8
y
1
3
9
y
1
4
0
y
1
4
1
y
1
4
2
y
1
4
3
y
1
4
4
y
1
4
5
y
1
4
6
y
1
4
7
y
1
4
8
y
1
4
9
y
1
5
0
y
1
5
1
y
1
5
2
y
1
5
3
y
1
5
4
y
1
5
5
y
1
5
6
y
1
5
7
y
1
5
8
y
1
5
9
y
1
6
0
y
1
6
1
y
1
6
2
y
1
6
3
y
1
6
4
y
1
6
5
y
1
6
6
y
1
6
7
y
1
6
8
y
1
6
9
y
1
7
0
y
1
7
1
y
1
7
2
y
1
7
3
y
1
7
4
y
1
7
5
y
1
7
6
y
1
7
7
y
1
7
8
y
1
7
9
y
1
8
0
y
1
8
1
y
1
8
2
y
1
8
3
y
1
8
4
y
1
8
5
y
1
8
6
y
1
8
7
y
1
8
8
y
1
8
9
y
1
9
0
y
1
9
1
y
1
9
2
y
1
9
3
y
1
9
4
y
1
9
5
y
1
9
6
y
1
9
7
y
1
9
8
y
1
9
9
y
2
0
0
y
2
0
1
y
2
0
2
y
2
0
3
y
2
0
4
y
2
0
5
y
2
0
6
y
2
0
7
y
2
0
8
y
2
0
9
y
2
1
0
y
2
1
1
y
2
1
2
y
2
1
3
y
2
1
4
y
2
1
5
y
2
1
6
y
2
1
7
y
2
1
8
y
2
1
9
y
2
2
0
y
2
2
1
y
2
2
2
y
2
2
3
y
2
2
4
y
2
2
5
y
2
2
6
y
2
2
7
y
2
2
8
y
2
2
9
y
2
3
0
y
2
3
1
y
2
3
2
y
2
3
3
y
2
3
4
y
2
3
5
y
2
3
6
y
2
3
7
y
2
3
8
y
2
3
9
y
2
4
0
y
2
4
1
y
2
4
2
y
2
4
3
y
2
4
4
y
2
4
5
y
2
4
6
y
2
4
7
y
2
4
8
y
2
4
9
y
2
5
0
y
2
5
1
y
2
5
2
y
2
5
3
y
2
5
4
y
2
5
5
y
2
5
6

The sets of pixel pairs in this example are
𝓗 𝑩 = 𝒚𝟒, 𝒚𝟓, 𝒚𝟏𝟐, 𝒚𝟏𝟑 , … … 𝒚𝟔𝟎, 𝒚𝟔𝟏
𝓗 𝑩
𝑪
= 𝒚𝟏, 𝒚𝟐 , 𝒚𝟐, 𝒚𝟑 , … . . (𝒚𝟔𝟑, 𝒚𝟔𝟒)
𝝂 𝑩 = { 𝒚𝟐𝟓, 𝒚𝟑𝟑 , 𝒚𝟐𝟔, 𝒚𝟑𝟒 , … … (𝒚𝟑𝟐, 𝒚𝟒𝟎)}
𝝂 𝑩
𝑪
= { 𝒚𝟏, 𝒚𝟗 , 𝒚𝟗, 𝒚𝟏𝟕 , 𝒚𝟏𝟕, 𝒚𝟐𝟓 , 𝒚𝟑𝟑, 𝒚𝟒𝟏 , … … (𝒚𝟓𝟔, 𝒚𝟔𝟒)}
Then we define the mean boundary pixel squared difference (𝐷 𝐵) and the mean non boundary pixel squared
difference (𝐷 𝐵 𝐶
)for image y to be
𝐃 𝐁 𝐲 =
(𝐲𝐢 − 𝐲𝐣) 𝟐
+ (𝐲𝐢 − 𝐲𝐣) 𝟐
(𝐲 𝐢,𝐲𝐣)∈𝐕 𝐁(𝐲 𝐢,𝐲𝐣)∈𝐇 𝐁
𝐍 𝐇 𝐁
+ 𝐍 𝐕 𝐁
(𝟏𝟗)
𝐃 𝐁
𝐂
𝐲 =
(𝐲𝐢 − 𝐲𝐣) 𝟐
+ (𝐲𝐢 − 𝐲𝐣) 𝟐
(𝐲 𝐢,𝐲𝐣)∈𝐕 𝐁(𝐲 𝐢,𝐲𝐣)∈𝐇 𝐁
𝐍 𝐇 𝐁
𝐂 + 𝐍 𝐕 𝐁
𝐂
(𝟐𝟎)
Generally, as the quantization step size increases, 𝐷 𝐵 will increase relative to𝐷 𝐵 𝐶
), and blocking artifacts will
become more visible. Of course, this does not establish any level of correlation between (19), (20) and
perceptual annoyance.
Also define the blocking effect factor
𝐁𝐄𝐅 𝐲 =  ∙ 𝐃 𝐁 𝐲 − 𝐃 𝐁
𝐂
𝐲 (𝟐𝟏)
Where
 =
𝒍𝒐𝒈 𝟐 𝑩
𝒍𝒐𝒈 𝟐 𝐦𝐢𝐧 𝑵 𝑯,𝑵 𝑽
𝟎
𝒊𝒇𝑫 𝑩 𝒀 >𝑫 𝑩
𝑪
(𝒚)
𝒐𝒕𝒉𝒆𝒓 𝒘𝒊𝒔𝒆
(𝟐𝟐)
emphasizes the BEF as a function of block size. The assumption here is that the visibility of blocking effects
increases with block size.
Of course, there can be multiple block sizes in a particular decoded image/video. For example, there
can be 16X16 macro blocks and 4X4 transform blocks, both contributing to blocking effects.
Let 𝑫 𝑩 𝒌
, 𝑫 𝑩 𝒌
𝑪
,𝑩𝑬𝑭 𝒌 ,and 𝜂 𝑘 modify (19)–(22) for block size . Then
𝐁𝐄𝐅𝐤 𝐲 = 
𝐤
∙ [𝐃 𝐁 𝐊 𝐲 − 𝐃 𝐁 𝐊
𝐂
𝐲 (𝟐𝟑)
The BEF over all block sizes is defined as
𝐁𝐄𝐅 𝐓𝐨𝐭 𝐲 = 𝐁𝐄𝐅𝐤(𝐲)𝐊
𝐤=𝟏 (𝟐𝟒)
The mean-squared error including blocking effects (MSE-B) for reference image x and test image y is then
defined as the sum of the MSE(x, y) in (1) and BEFtot (y) in (24)
𝐌𝐒𝐄 − 𝐁 𝐱, 𝐲 = 𝐌𝐒𝐄 𝐗, 𝐘 + 𝐁𝐄𝐅 𝐓𝐨𝐭 𝐲 (𝟐𝟓)
Finally, we propose the PSNR-B as
𝐏𝐒𝐍𝐑 − 𝐁 𝐱, 𝐲 = 𝟏𝟎𝐥𝐨𝐠 𝟏𝟎
𝟐𝟓𝟓 𝟐
𝐌𝐒𝐄−𝐁(𝐱,𝐲)
(𝟐𝟔)
The MSE term in (25) measures the distortion between the reference image and the test image, while
the BEF term in (25) specifically measures the amount of blocking artifacts just using the test image. The BEF
itself can be used as a no-reference quality index, these no-reference quality indices claim to be efficient for
measuring the amount of blockiness, but may not be efficient for measuring image quality relative to full-
reference quality assessment. On the other hand, the MSE is not specific to blocking effects, which can
substantially affect subjective quality. We argue that the combination of MSE and BEF is an effective
measurement for quality assessment considering both the distortions from the original image and the blocking
effects in the test image. The associated quality index PSNR-B is obtained from the MSE-B by a logarithmic
function, as is the PSNR from the MSE. The PSNR- B is attractive since it is specific for assessing image
quality, specifically the severity of blocking artifacts.
VIII. ALGORITHM FOR IMPLEMENTATION
Step 1: start
Step2: read the input image (jpg, png, tif, bmp), name as I
Step 3: resize the image of dimension of 256*256 in image I
Step 4: Construct the Compression for input image I using the DCT block coding and save the image as I2 as
compressed image and display the original image and compressed image
Step 5: compute the MSE, PSNR by using the equations (1)-(2) and calculate the MSE and PSNR values for
Compressed Image I2 and display the values

Step6: By using the Gaussian noise using k value compute the ssim_index by the equations (3)-(8) and display
the values of mean and ssim for I2
Step 6: Compute the PSNR-B by using the equations (19)-(26) the PSNR-B is calculated for the image I2 and
display the values
Step 7: Computing the MSE, PSNR, SSIM, PSNR-B are the quality metrics of the calculating image x
De-blocked images:
Step 8: using low pass filter compute the image g and display the image of the image I2 named as g. and
calculating the quality metrics for the image g and display the values
Pocs:
Step 9: By initialize the factor value =1 and delta_est = [1:2] compute the pocs named the image as y, resize the
result image to 256*256 and calculating the quality metrics for the image y and display the values of y
Step10: Compute the median filter (3*3) and (7*7) for the image I2 and display the results of I2
Difference Images:
Step11: By using the equations (12)-(14) the difference images for I2 , reshape and display the image d
step12: repeat the step11 for d1, d2 and display the images d1, d2.
Step13: compute the performance analysis and plot the graphs
Step 14: stop.
IX. SIMULATION RESULTS ON DEBLOCKED IMAGES
This section presents simulation results on quality assessment of deblocked images. Images are
compressed using DCT block coding as JPEG. In JPEG, quantization is applied using a different quantization
step size for each DCT coefficient, as defined by a quantization table. Here, we apply the same quantization
step size for all DCT coefficients, to more directly investigate the effects of quantization step size on image
quality. Quantization step sizes of 5, 10, 20, 40, 80, 120, and 160 were used in the simulations to investigate the
effects of quantization step size. Deblocking was applied on the decoded images for comparison
C. PSNR Analysis:
Figure 3 shows that when the quantization step size was large (Δ≥ 80), the 3×3 filter, 7×7filter and
POCS methods resulted in higher PSNR than the no filter case on both the images. All the deblocking methods
produced lower PSNR when the quantization step size was small (Δ≤ 30)
(a) Lena (b) Dewdrop
(c) Peppers (d) Barbara
Fig 3. PSNR comparison of images (a) Lena. (b) Dewdrop, (c) Peppers. (d) Barbara
D. SSIM Analysis:
Figure 4 show that when the quantization step was large (Δ≥80), on the two images, all the filtered
methods resulted in larger SSIM values. The 3×3 and 7×7 low pass filters resulted in lower SSIM values than
the low filter case when the quantization step size was small (Δ≤30).

(a) Lena (b) Dewdrop
Fig 4. SSIM comparison of images (a) Lena. (b) Dewdrop, (c) Peppers. (d) Barbara
E. PSNR-B Analysis:
For large quantization steps, the PSNR-B values improved for the two images by employing low pass
filtering methods. The POCS resulted in improved PSNR-B values compared to the no filtered case, even at
small quantization step size.
(a) Lena
(b) Dewdrop
Fig 5. PSNR-B comparison of images (a) Lena. (b) Dewdrop, (c) Peppers. (d) Barbara

(a) no filter image (b) POCS de blocking filter
Fig6. Reconstructed images of Lena with quantization step 80
(a) Quality metrics for no filter image: (Mean Square Error =0.0780, Peak Signal to Noise Ratio = 29.6041
ssim_index=0.0099, PSNR_B=53.6695), (b) quality metrics for POCS de blocked filter image: (Mean Square
Error = 0.0781, Peak Signal to Noise Ratio =29.6029, ssim_index=0.0108, PSNR_B=53.6683).
Fig.6 shows Lena reconstructed from compression, also using quantization step 80. When no filter is applied as
in Fig. 6(a), blocking artifacts are clearly visible, especially on the Lena. When the POCS deblocking filter was
applied as in Fig. 6(b), the blocking effects were mostly removed, resulting in better subjective quality. The
PSNR-B and SSIM quality indices produced larger values on the POCS filtered image, in agreement with
observation.
(a) no filter image (b) POCS de blocking filter
Fig 7. Reconstructed images of Dewdrop with quantization step 80
(a) Quality metrics for no filter image: (Mean Square Error =0.1600, Peak Signal to Noise Ratio = 28.0454
ssim_index=0.0069, PSNR_B=52.0070), (b) quality metrics for POCS de blocked filter image: (Mean Square
Error =0.1599, Peak Signal to Noise Ratio = 28.0459 ssim_index=0.0069, PSNR_B=52.1113)
Fig. 7 shows Dewdrop reconstructed from compression, also using quantization step 80. When no filter is
applied as in Fig. 7(a), blocking artifacts are clearly visible, especially on the leaves. When the POCS
deblocking filter was applied as in Fig. 7(b), the blocking effects were mostly removed, resulting in better
subjective quality. The PSNR-B and SSIM quality indices produced larger values on the POCS filtered image,
in agreement with observation
(a) no filter image (b) LPF de blocking filter
Fig 8. Reconstructed images of Cameraman with quantization step 80
(a) Quality metrics for no filter image: (Mean Square Error =0.1933, Peak Signal to Noise Ratio =27.6343
ssim_index=0.0120, PSNR_B=51.4032), (b) quality metrics for POCS de blocked filter image: (Mean
Square Error =0.1933, Peak Signal to Noise Ratio =27.6346, ssim_index=0.0120, PSNR_B=51.4340).

Fig. 8 shows Cameraman reconstructed from compression, also using quantization step 80. When no filter is
applied as in Fig. 8(a), blocking artifacts are clearly visible, especially on the Cameraman. When the LPF
deblocking filter was applied as in Fig. 8(b), the blocking effects were greatly removed, resulting in better
subjective quality. The PSNR-B and SSIM quality indices produced larger values on the POCS filtered image,
in agreement with observation.
X. CONCLUSION
We have tested our algorithm on few natural images. Those sample images are shown in above figure.
We have found that the better quality metric is obtained at quality factor 70 for JPEG compression. This
Analysis will brings out a new trend in the quality metrics of the image and proves to be efficient than the
conversional metrics.
References
[1] S.S Channappayya, A.C.Bovik, and R.W.Heath, Jr, “Design of linear equalizers optimized for the structural similarity index,”
IEEE Trans. Image Process., vol.17, no.6, pp.857-872, Jun.2008.
[2] Z.Wang, A.C.Bovik, H.R.Sheikh, and E.P.Simoncelli, “Image quality assessment: From error visibility to structural similarity,”
IEEE Trans. Image Process., vol.13, no.4, pp.600-612, Apr.2004.
[3] A.Zakhor , “Iterative procedure for reduction of blocking effects in transform image coding,” IEEE Trans. Circuits Syst. Video
Technol., vol.2,no.1 , pp.91-95,Mar.1992.
[4] .Yang, N.P.Galatsanos, and A.K.Katsaggelos, “Projection-based spatially adaptive reconstruction of block- transform compressed
images,” IEEE Trans. Image Process., vol.4, no.7, pp.896-908, Jul.1995.
[5] Y.Yang, N.P.Galatsanos, and A.K.Katsaggelos, “Regularized reconstruction to reduce blocking artifacts of block discrete cosine
transform compressed images,” IEEE Trans. Circuits Syst. Video Technol., vol.3, no.6, pp.421-432, Dec.1993.
[6] H.Paek, R.C.Kim, and S.U.Lee, “On the POCS-based post processing technique to reduce the blocking artifacts in transform coded
images,” IEEE Trans. Circuits Syst. Video Technol., vol.8, no.3, pp.358-367,Jun.1998.
[7] S.H.Park, and D.S.Kim, “Theory of projection onto narrow quantization constraint set and its applications,” IEEE Trans. Image
Process., vol.8, no.10, pp.1361-1373, Oct.1999.
[8] Z.Wang, A.C.Bovik, and E.P.Simoncelli, “Multi-scale structural similarity for image quality assessment,” in Proc. IEEE Asilomar
Conf.Signal Syst. Comput.,No v.2003.
[9] A.C.Bovik, and H.R.Sheikh,”Image information and visual quality,” IEEE Trans. Image Process., vol.15, no.2, pp.430-444,
Feb.2006.
[10] A.C.Bovik, and H.R.Sheikh, “A statistical evaluation of recent full reference image quality assessment algorithms,” IEEE Trans.
Image Process., vol.15, no.11, pp.3441-3452, Nov.2006.
[11] Z.Wang, and A.C.Bovik, “A Universal image quality Index,” IEEE Trans. Signal Process.Lett., vol.9, no.3, pp.81-84, Mar.2002.
[12] S.Liu, and A.C.Bovik, “Efficient DCT-domain blind measurement and reduction of blocking artifacts,” IEEE Trans. Circuits Syst.
Video Technol., vol.12, no.12, pp.1139-1149, Dec.2002.
[13] B.Girod, “What’s wrong with mean-squared error,” in Digital images and human vision, A.B.Watson, ED. Cambridge, MA: MIT
Press, 1993, pp.207-220.
[14] Z.Wang, and A.C.Bovik,” Blind measurement of blocking artifacts in images,” in Proc.IEEE Int.Conf.Image Process., Vancouver,
Canada, Oct.2000.pp.981-984.
[15] Y.Jeong, I.Kim, and H.Kang,” Practical projection based postprocessing of block coded images with fast convergence rate,” IEEE
Trans. Circuits Syt. Video Technol., vol.10, no.4, pp.617-623, Jun.2000.
XI. ABOUT AUTHORS PROFILE
Trinadh Tadala graduated from Lenora college of Engineering,
Rampachodavaram in Electronics And Communication Engineering (ECE)
Stream From JNTUK, Now pursuing Masters in Computers And
Communication (C&C) Stream from University college of Engineering,
JNTUK, Kakinada, Andhra Pradesh, India.
Sri E.Venkata Narayana completed B.E and M.E in first class from Andhra
University, Visakhapatnam. He has been in teaching since 1985. Presently he is
working as Asst. Professor in Dept. of ECE, JNTU college of Engineering
Kakinada. He published more than 45 papers in national and international
conferences and journals.
.

A Novel PSNR-B Approach for Evaluating the Quality of De-blocked Images

Recommended

Recommended

More Related Content

What's hot

What's hot (18)

Viewers also liked

Viewers also liked (20)

Similar to A Novel PSNR-B Approach for Evaluating the Quality of De-blocked Images

Similar to A Novel PSNR-B Approach for Evaluating the Quality of De-blocked Images (20)

More from IOSR Journals

More from IOSR Journals (20)

Recently uploaded

Recently uploaded (20)

A Novel PSNR-B Approach for Evaluating the Quality of De-blocked Images