Determination of the cause and amount of image

degradation using a reduced reference approach

Ankan Bhattacharya and Sarbani Palit

Indian Statistical Institute, Kolkata, INDIA

E-mail: ankan.bhattacharya@gmail.com, sarbanip@isical.ac.in

Abstract—Multimedia data transmission, particularly

sending images, is an important feature of modern com-

munication systems. These activities usually occur on a

very large scale and hence, reduction of the data volume

and storage requirements become crucial. Reduction is

achieved through compression, typically JPEG2000. Since

this is a lossy compression technique, the image quality

is degraded, the extent depending on the amount of

compression. The transmission channel is another source

of quality loss of images. At the receiving end, the absence

of a clean reference image makes the task of quality

assessment difficult. Since image quality assessment is

required for different applications, various reduced and no

reference approaches have evolved to meet the demand.

The job of restoring the image quality is facilitated by

the knowledge of the exact source of degradation. There

has been however, little work in this area. This article

proposes a reduced reference approach, which, starting

with a received degraded image, is able to distinguish

between two different types of degradation – Gaussian

noise (commonly arising from transmission channels) and

compression due to JPEG2000. The approach can, not only

correctly determine the cause of the degradation but also

the amount of it, with only minimal information regarding

the original image. This is the most significant contribution

of this article. The performance of the proposed approach

is established through extensive simulations using images

from well-known databases.

Keywords—Multiresolution, Discrete Wavelet Transform,

noise, compression, image quality.

I. INTRODUCTION

An important application of image quality assessment

[1], [2], [3], [4] is in the evaluation of transmitted

images, over the Internet or otherwise. Objective image

quality assessment models typically require the access

to a reference image that is assumed to have perfect

quality. In practice, such full-reference methods [5] may

not be applicable because the reference image is often

not available. Reduced reference approaches have been

reported in [6], [7], [8], [9], [10] while some no reference

techniques can be found in [11], [12], [13].

The two major degrading factors in a transmission

channel are compression and noise. In certain applica-

tions involving the cleaning or restoration of the trans-

mitted and received images, it would be very helpful

to correctly determine the cause of the degradation. For

this purpose, distinguishing between the effects of noise

and compression becomes crucial. However, none of

the existing techniques address this challenging problem.

The salient feature of the present article is the extraction

of an useful feature from the image. This feature, apart

from acting as an indicator of the image quality, is also

able to correctly distinguish between noise and com-

pression. The multiresolution property of the Discrete

Wavelet Transform (DWT) [14], [15] is employed for

the construction of the feature. Section II describes the

procedure and provides a justification for the method.

The performance of the proposed approach for compres-

sion and noise are presented in Section III. Simulations

have been conducted using images in [16]. The effect

of channel noise has been simulated by the addition

of white Gaussian noise to the test images, (AWGN),

a commonly used model for channel disturbances. The

effect of compression has been simulated by subjecting

the test images to JPEG2000 compression. The met-

ric Structural Similarity Index Measure (SSIM) [17],

[18] has been used for evaluation of performance. Also

outlined in Section III is a modification for extending

the reduced reference approach so that it becomes a

truly no reference one. Appropriate justification has been

included. Section IV concludes the article.

II. THE BASIC PRINCIPLE

The construction of a feature with the twin objective

of acting as a degradation assesser and also having the

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capability to detect its type, is developed here. The DWT,

its multiresolution decomposition of a matrix and its

behaviour upon compression of or addition of noise to

the matrix will be utilized.

Two-level DWT, using the Haar wavelet, is used to

transform the image of size M × N into its horizontal,

vertical and diagonal components. Let ch1, cv1 and

cd1 be the first-level horizontal, vertical and diagonal

detail component matrices, each of size M/2 × N/2and ch2, cv2 and cd2 each of size M/4 × N/4 be the

corresponding quantities at the second level. DWT is now

applied to ch1 and cv1 , using the Haar wavelet, yielding

the respective approximation matrices hca and vca, each

of size M/4×N/4.

Now divide ch2 into non overlapping blocks of size

16× 16, equalling M/64×N/64 = N1, say, in number.

For a matrix A, let abs(A) denote a matrix whose

elements are the absolute values of A. Let the pth block

be denoted as ch2p and the mean and standard deviation

of its absolute values i.e. abs(ch2p) be µp and σp,

p = 1, · · · ,N1. Consider an array A1 of the same size

as that of ch2, i.e. M/4 × N/4, divided into N1 non

overlapping blocks of size 16 × 16, in the same fashion

as ch2. Corresponding to the (i, j)th entry of the pth

block of ch2 represented as ch2pi,j , the (i, j)th entry of

the pth block of A1, denoted as A1pi,j is calculated as

follows:

A1pi,j =

1 if abs(ch2pi,j) > µp + σp or

abs(ch2pi,j) < µp − σp

0 otherwise

The binary matrices A2, A3 and A4 are similarly con-

structed from cv2, hca and vca respectively. The binary

XOR operation is performed between A1 and A3 to

obtain A13, while XOR operation between A2 and A4yields A24. Let CT1 be the total number of ones in

A13 and CT2 be the total number of ones in A24.

The average mismatch MIS is given by CT1+CT22 . The

Normalized Hamming distance, (NHD) is then calculated

as NHD = MIS(M/4×N/4)

Two important observations about the NHD are:

1) As the image is degraded, the value of NHDchanges in a fairly uniform manner. Hence it

may be considered as a candidate for providing

an estimate of the amount of degradation, in the

absence of a reference image. In order to verify

this observation, ISSIM has been modelled as

a cubic function of the NHD, of the form

ISSIM = a(NHD)3+b(NHD)2+c(NHD)+d

for all the test images. The coefficients a, b, cand d have been obtained from a curve fitting

exercise. Separate sets of simulations for AWGN

and JPEG2000 compression have been run for

each image, at different levels of noise and

compression. The results have been presented

in Tables 1 and 2. The mean values of the

coefficients have been computed in Table 3.

It may be observed that both the coefficients aand b have negligible magnitude (a is mostly

zero), in comparison with that of c and d for both

noise and compression. An affine relationship

between NHD and ISSIM implies that the

normalized Hamming distance between the ma-

trices A24 and A13, derived from the degraded

image, may be used as an indicator of the image

degradation.

2) The behaviour of NHD in the presence of noise

is just the opposite of its behaviour in the pres-

ence of compression. While NHD increases as

the magnitude of noise increases, increasing the

level of compression causes the value of NHDto decrease. This property is investigated by

running a large number of simulations, results

of which are reported in Section III.

Justification for this behaviour of the NHD can be

made by considering the structure of the matrices ch2and hca and the expression for the DWT using the Haar

wavelet. Without loss of generality, consider an image of

size 8× 8, with its pixels denoted as aij , i, j = 1, · · · 8.

Let

X1 =∑4

j=1 a1j , X2 =∑4

j=1 a2j ,

X3 =∑4

j=1 a3j , X4 =∑4

j=1 a4j ,

X5 =∑4

j=1 a5j , X6 =∑4

j=1 a6j ,

X7 =∑4

j=1 a7j , X8 =∑4

j=1 a8j ,

X9 =∑8

j=5 a1j , X10 =∑8

j=5 a2j ,

X11 =∑8

j=5 a3j , X12 =∑8

j=5 a4j ,

X13 =∑8

j=5 a5j , X14 =∑8

j=5 a6j ,

X15 =∑8

j=5 a7j , X16 =∑8

j=5 a8j .

Then, ch2 is computed to be,

1

2

X1 +X2 −X3 −X4 X9 +X10 −X11 −X12

X5 +X6 −X7 −X8 X13 +X14 −X15 −X16

2013 28th International Conference on Image and Vision Computing New Zealand

419

and, hca is computed to be

1

2

X1 −X2 +X3 −X4 X9 −X10 +X11 −X12

X5 −X6 +X7 −X8 X13 −X14 +X15 −X16

Note that (X2 −X3), (X6 −X7), (X10 −X11) and

(X14−X15) are the differences between the correspond-

ing pixel values of consecutive rows of the image matrix.

It is known that JPEG2000 achieves image compres-

sion by eliminating the differences of relatively smaller

magnitude, the extent of elimination depending on the

amount of compression. On the other hand, Gaussian

random noise, being random in nature tends to increase

the differences. Comparing the corresponding entries of

ch2 and hca, it may be observed that the values will,

in accordance with the explanation given, come closer

to each other with increasing compression but move

further apart when subjected to AWGN. The change in

the amount of mismatch between cv2 and vca may be

explained along similar lines. Hence, CT1 and CT2and consequently NHD would decrease with increasing

compression, while an increase would be observed for

AWGN.

TABLE I. COEFFICIENTS OF CUBIC POLYNOMIAL FOR AWGN

Image a b c dLena 0.0000 -0.0001 0.0028 0.9854

Boat -0.0000 0.0003 -0.0050 1.0464

Stream bridge -0.0003 0.0244 -0.7367 8.5006

Acropolis -0.0001 0.0047 -0.1325 2.3047

Building 0.0000 0.0020 -0.0519 1.4683

Man 0.0000 0.0009 -0.0204 1.1610

Cameraman -0.0036 0.2124 -4.2802 29.7864

Canal -0.0001 0.0050 -0.1372 2.3178

City 0.0000 -0.0010 0.0281 0.7790

Couple 0.0000 -0.0004 -0.0142 1.1254

Crossing 0.0000 0.0000 -0.0081 1.0927

Mandrill 0.0001 -0.0083 0.2691 -1.7143

Golden gate 0.0000 -0.0003 0.0118 0.9041

House car 0.0000 -0.0013 0.0272 0.8533

Monarch 0.0000 0.0004 -0.0072 1.0647

Peppers 0.0000 0.0003 -0.0090 1.1127

Plane -0.0001 0.0049 -0.0915 1.5971

Seagull 0.0000 -0.0002 0.0170 0.8385

TABLE II. COEFFICIENTS OF CUBIC POLYNOMIAL FOR

JPEG2000 COMPRESSION

Image a b c dLena 0.0002 -0.0070 0.0797 0.6853

Boat -0.0003 0.0106 -0.0909 1.1044

Stream bridge 0.0001 -0.0034 0.0767 0.2810

Acropolis -0.0002 0.0095 -0.1318 1.4043

Building 0.0001 -0.0035 0.0570 0.6023

Man 0.0000 -0.0024 0.0396 0.7777

Cameraman -0.0004 0.0149 -0.1400 1.1295

Canal 0.0000 0.0010 0.0098 0.6851

City 0.0000 -0.0050 0.0891 0.4323

Couple 0.0001 -0.0034 0.0538 0.6534

Crossing 0.0000 -0.0013 0.0557 0.5897

Mandrill 0.0000 -0.0004 0.0352 0.3238

Golden gate -0.0039 0.1446 -1.7151 7.5569

House car 0.0000 -0.0007 0.0252 0.7154

Monarch 0.0005 -0.0190 0.2480 -0.0748

Peppers 0.0003 -0.0093 0.0942 0.6451

Plane -0.0006 0.0175 -0.1286 1.1372

Seagull 0.0002 -0.0086 0.1109 0.5185

TABLE III. MEAN VALUES OF COEFFICIENTS OF CUBIC

POLYNOMIAL

Degradation a b c dAWGN -2.28×10−4 0.0135 -0.2854 3.0680

JPEG2000 -2.17×10−4 0.0075 -0.0684 1.0648

III. RESULTS:PERFORMANCE OF THE

APPROACH

A. PERFORMANCE FOR NOISE

In order to verify the performance of the approach

in noise, simulations are carried out by adding white

Gaussian noise, of increasing magnitude, to each image

and observing the values of image SSIM and NHD as

explained in Section II. Figures 1-3 show these plots.

0.75 0.8 0.85 0.9 0.95 110

15

20

25

30

35

40

Image SSIM (ISSIM)

No

rmalized

Ham

min

g D

ista

nce(%

)

Lena

Streambridge

Boat

Mandrill

Peppers

Man

Fig. 1. NHD vs. Image SSIM for AWGN.

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420

0.65 0.7 0.75 0.8 0.85 0.9 0.95 110

15

20

25

30

35

40

Image SSIM (ISSIM)

No

rmalized

Ham

min

g D

ista

nce(%

)

Cameraman

Couple

Seagull

Acropolis

Building

Canal

Fig. 2. NHD vs. Image SSIM for AWGN.

0.75 0.8 0.85 0.9 0.95 110

15

20

25

30

35

40

Image SSIM (ISSIM)

No

rmalized

Ham

min

g D

ista

nce(%

)

City

Crossing

Golden Gate

House car

Monarch

Plane

Fig. 3. NHD vs. Image SSIM for AWGN.

In each case, the curve has an overall negative slope,

i.e. in general, an increase in the noise level or decrease

in image SSIM causes an increase in NHD.

B. PERFORMANCE FOR COMPRESSION

The test images are subjected to JPEG2000 com-

pression for a range of compression ratios varying from

5 (low compression) to 100 (high compression), on a

scale of 0–100. As for noise, the image SSIM and the

normalized Hamming distance NHD is calculated in

each case. Figures 4-6 show the corresponding plots. In

each case, the curve has an overall positive slope, i.e.

in general, an increase in the noise level or decrease in

image SSIM causes a decrease in NHD.

0.75 0.8 0.85 0.9 0.95 10

5

10

15

20

25

30

Image SSIM (ISSIM)

No

rmalized

Ham

min

g D

ista

nce(%

)

Lena

Streambridge

Boat

Mandrill

Peppers

Man

Fig. 4. NHD vs. Image SSIM for JPEG2000 compression.

0.75 0.8 0.85 0.9 0.95 10

5

10

15

20

25

Image SSIM (ISSIM)

No

rmalized

Ham

min

g D

ista

nce(%

)

Cameraman

Couple

Seagull

Acropolis

Building

Canal

Fig. 5. NHD vs. Image SSIM for JPEG2000 compression.

0.75 0.8 0.85 0.9 0.95 12

4

6

8

10

12

14

16

18

20

22

Image SSIM (ISSIM)

No

rmalized

Ham

min

g D

ista

nce(%

)

City

Crossing

Golden Gate

House car

Monarch

Plane

Fig. 6. NHD vs. Image SSIM for JPEG2000 compression.

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421

C. REDUCED REFERENCE TO NO REFERENCE

It may be noted that for each image, the quantity

NHD has a particular value for the undegraded image.

This may be treated as a reference value since compres-

sion causes this value to decrease while noise causes it

to increase. For example, the reference value of NHDis 14.459 for Lena, 27.002 for Streambridge, 15.790 for

Boat, etc. It is crucial, therefore, for the receiver to have

prior knowledge of this value in order to determine the

type of the degradation from a degraded image. This

value may be sent to the receiver through an ancillary

secure channel.

The proposed approach may become a truly no refer-

ence one if the reference value of NHD can be obtained

directly from the degraded image. To this end, the nor-

malized Hamming distance between the corresponding

detail images after performing 4th level DWT, have been

examined for both noise and compression. Figures 7-8

show boxplots of the values for noise and compression,

respectively, for each image. Results for only 6 images

have been shown, for brevity.

Lena Streambridge Boat Mandrill Peppers Man

8

10

12

14

16

18

20

22

24

26

Valu

es

Fig. 7. NHD at 4th level of DWT vs. Image SSIM for AWGN.

It may be observed for each image that the variation

in this value for different noise levels is very small,

indicated by the small height of the box. For example,

the value varies from 8.59 to 9.17 for Lena, from 21.87

to 22.36 for Streambridge etc. Hence, this value may

be used directly as a reference for noise while a scaled

value may be used as a reference for compression, where

the scaling factor may be determined empirically. The

approach then becomes a completely no reference one.

Lena Streambridge Boat Mandrill Peppers Man

8

10

12

14

16

18

20

22

24

26

Valu

es

Fig. 8. NHD at 4th level of DWT vs. Image SSIM for compression.

IV. COMPARISON OF PERFORMANCE

A partial comparison has been performed with the

Blind Image Quality Index (BIQI) [12], a no-reference

approach. Though BIQI has been found to change fairly

uniformly in response to degradation due to AWGN, its

performance for compression is not as smooth, as is ev-

ident from Figure 9. More importantly, it increases with

increasing noise as well as compression, thus making it

impossible to distinguish between the two.

0.75 0.8 0.85 0.9 0.95 120

30

40

50

60

70

80

Image SSIM (ISSIM)

BIQ

I

Lena

Streambridge

Boat

Mandrill

Peppers

Man

Fig. 9. BIQI vs. Image SSIM for JPEG2000 compression.

V. CONCLUSIONS & SCOPE FOR FUTURE

WORK

A novel reduced reference approach for image quality

assessment has been proposed. Its viability and efficiency

has been established through simulations using a large

2013 28th International Conference on Image and Vision Computing New Zealand

422

number of test images. An extension of the approach to

handle no reference assessment has also been suggested

and partly established. Further investigation is being

conducted so that the approach may be suitably modified

to become a fully no reference one. Extension of the

approach to handle situations where the image may be

subjected to both compression and noise is also being

studied.

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