Conference PaperPDF Available

SSIM image quality metric for denoised images

November 2010

Conference: Proceedings of the 3rd WSEAS international conference on Visualization, imaging and simulation

Authors:

Peter Ndajah

University of the Commonwealth Caribbean, Kingston, Jamaica

Hisakazu Kikuchi

Niigata University

Hidenori Watanabe

Niigata University

Show all 5 authorsHide

The mean square error (MSE) and its related metrics such as peak signal to noise ratio (PSNR), root mean square error (RMSE), mean absolute error (MAE), and signal to noise ratio (SNR) have been the basis for mathematically defined image quality measurement for a long time. These methods are all based on the MSE. Denoisng quality has also been traditionally measured in terms of the MSE or its derivatives. But none of these metrics takes the structural fidelity of the image into account. Here, we investigate the structural changes that occur during the denoising process. In particular, we ascertain the structural fidelity of TV-denoised images.

Images with different structural distortions but the same MSE values

…

Figures - uploaded by Hisakazu Kikuchi

Content may be subject to copyright.

Content uploaded by Hisakazu Kikuchi

Content may be subject to copyright.

SSIM Image Quality Metric for Denoised Images

PETER NDAJAH, HISAKAZU KIKUCHI, MASAHIRO YUKAWA,

HIDENORI WATANABE and SHOGO MURAMATSU

Department of Electrical and Electronics Engineering,

Niigata University,

JAPAN

email: ndajah@telecom0.eng.niigata-u.ac.jp

September 3, 2010

Abstract

The mean square error (MSE) and its related metrics such as peak

signal to noise ratio (PSNR), root mean square error (RMSE), mean

absolute error (MAE), and signal to noise ratio (SNR) have been the

basis for mathematically deﬁned image quality measurement for a long

time. These methods are all based on the MSE. Denoisng quality has

also been traditionally measured in terms of the MSE or its derivatives.

But none of these metrics takes the structural ﬁdelity of the image into

account. Here, we investigate the structural changes that occur during

the denoising process. In particular, we ascertain the structural ﬁdelity

of TV-denoised images.

Keywords: SSIM, MSE, TV, PSNR, NOISE, DENOISE, METRIC

1MSE-based Im-

age Quality Mea-

sure

The MSE has been the basis for

image quality measure. Usu-

ally, one of the images (the orig-

inal) is assumed to contain no

distortions while the other im-

age is contaminated by noise or

some other kind of error. Sup-

pose x={xi|i=1,2, ..., N }and

y={yi|i=1,2, ..., N }where xi

and yiare the ith samples in x

and yand Nis the number of

signal samples. Then the MSE

between the signals is

MSE(x,y)= 1



i=1

(xi−yi)2

ei=(xi−yi) is referred to as error

signal. An image is a two dimen-

sional signal so the MSE is given

d(x,y)=N



i=1

|ei|2

Generally, in image processing,

the MSE is often used in the form

of the peak signal to noise ra-

tio(PSNR) measure

PSNR =10log

MSE

ADVANCES in VISUALIZATION, IMAGING and SIMULATION

ISSN: 1792-6130

ISBN: 978-960-474-246-2

The PSNR is more useful than the

MSE only when images of diﬀer-

ent dynamic ranges are being com-

pared otherwise it is equivalent to

the MSE [7].

2Drawbacks of

MSE-based Im-

age Quality Mea-

sure

In imaging, the true aim of any

denoising method is to improve

the visual quality and ﬁdelity of a

noisy image but the MSE does not

take into account image depen-

dencies such as textures, order-

ings, patterns, etc. all of which af-

fect image perception quality. Im-

age pixel order transmit vital in-

formation about the structure of

a visual scene. Unfortunately the

MSE does not measure this. The

correlation between the error sig-

nal and the underlying image sig-

niﬁcantly aﬀects perceptual image

distortion but this is also ignored

by the MSE. The MSE does not

take into account the signs of the

error (since its square is used) sig-

nal added to an image. However,

the visual ﬁdelity of the resulting

image has been proved to be dras-

tically diﬀerent. Since all images

are treated equally in the formu-

lation of the MSE, image content-

dependent variations in image ﬁ-

delity cannot be accouted for.

3 Structural Simi-

larity (SSIM)

The SSIM is a recently proposed

image ﬁdelity measure which has

proved highly eﬀective in mea-

suring the ﬁdelity of signals. The

SSIM approach was originally mo-

tivated by the observation that

natural images have highly struc-

tured signals with strong neigh-

borhood dependencies. These de-

pendencies carry useful informa-

tion about the structures of the

objects in the visual scene.

The human visual system is highly

adapted to extract structural in-

formation from visual scenes. For

this reason, image ﬁdelity mea-

surement should retain the signal

structure as an important content.

A distinction has to be made be-

tween non-structural distortions

such as variations in luminance,

contrast, Gamma distortions, and

spatial shift(these do not change

the structure of the image in any

way) and the structural distor-

tions such as additive Gaussian

noise, blur and lossy compres-

sion(e.g. JPEG). These distort

the structure of the image signiﬁ-

cantly.

The human visual system is highly

sensitive to structural distortions

and easily compensates for non-

structural distortions. The main

function of the SSIM is to simu-

late this functionality.

Let x={xi|i=1,2, ..., N}and

y={yi|i=1,2, ..., N }be the

original and the test image signals

respectively. Then, the SSIM

Q=4σxy ¯x¯y

(σ2

x+σ2

y)[(¯x)2+(¯y)2](1)

The above equation can be

rewritten as

Q=σxy

σxσy

·2¯x¯y

(¯x)2+(¯y)2·2σxσy

σ2

x+σ2

(2)

The SSIM measures distor-

tionsasacombinationofthree

ADVANCES in VISUALIZATION, IMAGING and SIMULATION

ISSN: 1792-6130

ISBN: 978-960-474-246-2

factors: loss of correlation, lumi-

nance distortion and contrast dis-

tortion. The ﬁrst component in

(2) is the correlation coeﬃcient

between xand y.Itmeasures

the degree of correlation between

xand y. Its dynamic range is

[−1,1] and the best value 1 is ob-

tained when yiis linear with re-

spect to xifor all i=1,2, ..., N i.e.

yi=axi+b. The second compo-

nent has a value range of [0,1]. It

measures the mean luminance be-

tween x. It equals 1 if and only if

¯x=¯y. The third compnent meau-

res the similarity of the contrast

between xand y. Its range is also

[0,1], where the best value is 1.

This occurs only when σx=σy.

4 A Comparison of the MSE and the SSIM

Reference Image

MSE = 0, SSIM =1 Contrast Stretch

MSE = 255, SSIM = 0.9172 Negative Image

MSE = 255, SSIM = −0.1632

Gaussian White Noise

MSE = 255, SSIM = 0.5927 Lossy compression

MSE = 255, SSIM = 0.6947 Blurred Image

MSE = 255, SSIM = 0.7722

Figure 1: Images with diﬀerent structural distortions but the same MSE

values

Figure 1 illustrates the shortcom-

ings of the MSE. In all the images

shown, the MSE = 255 even when

the visual structures are greatly

distorted. The SSIM on the other

hand seems to reﬂects the struc-

tural changes in the images more

faithfully. This is the advantage of

the SSIM over the MSE. The hu-

man visual system (HVS) is very

sensitive to structural changes,

therefore any metric that will be

well correlated to the HVS must

take into account the structural

dependencies of the signal samples

in order to provide eﬀective pre-

ADVANCES in VISUALIZATION, IMAGING and SIMULATION

ISSN: 1792-6130

ISBN: 978-960-474-246-2

Reference Image: MSE = 255, SSIM = 1

(a) Denoised Image: λ = 60,τ = 0.01,

MSE = 255, SSIM = 0.653430

(b)

Denoised Image: λ = 12, τ = 0.01,

MSE = 255, SSIM = 0.892388

(c)

Denoised Image: λ = 2, τ = 0.01,

MSE = 255, SSIM = 0.748494

(d)

Denoised Image: λ = 1, τ = 0.01,

MSE = 255, SSIM = 0.712412

(e)

Denoised Image: λ = 0.5, τ = 0.01,

MSE = 255, SSIM = 0.685501

(f)

Figure 2: Denoised images showing values MSE values and SSIM index

values

dictions of image quality. As of-

ten happens during denoising of

images, structural changes such

as blurring can happen. Most

denoising algorithms do not ac-

tually ’remove’ the noise. It is

more a process of noise minimiza-

tion rather than removal. The

amount of noise still left in the im-

age sample after the denoising op-

eration depends on the amount of

noise originally in the image be-

fore the denoising operation. But

the MSE-based metrics may not

be able to capture this reality be-

cause they are not designed to to

measure the structural distortions

that may occur.

5 Denoised Image

Structural Fi-

delity

So why use the SSIM index to

measure the quality of denoised

images? Because the MSE-based

metrics do not tell the whole story.

The ultimate objective of denois-

ing is to produce an image that

is judged to be a good representa-

tion of the reference image (known

or unknown). The HVS is the ul-

timate judge of what a good qual-

ity image is. This means that the

structural ﬁdelity of the denoised

image is of utmost importance be-

cause the HVS uses the structural

ﬁdelity to measure the quality of

an image. The MSE-based met-

rics fail to measure the structural

improvement or degradation in an

image after denoising. This is be-

ADVANCES in VISUALIZATION, IMAGING and SIMULATION

ISSN: 1792-6130

ISBN: 978-960-474-246-2

cause in the MSE-based metrics,

the signal samples are considered

to be independent of each other.

As we can see in Figure 2, the de-

noised images have diﬀerent SSIM

values (as judged by the HVS) but

they have practically the same

MSE values.

The total variation denoising al-

gorithm was used to denoise the

images because of its eﬀectiveness

and also because it has tunable

parameters λand τthat control

the eﬀectiveness of the denoising

process. We have varied the val-

ues of λand kept τconstant in the

experiments.

6Conclusion

We used the lena image as the test

image in our experiments. As Fig-

ure 2 shows, the changes in struc-

tural similarity indices of the im-

ages correlate somewhat with hu-

man visual system. For example,

when λ≤2, ((d)-(f)), the algo-

rithm causes blurring in the im-

ages. The SSIM index reﬂects this

fact as the SSIM values become

progressively smaller with reduc-

ing visual quality of the images,

However, the MSE remained the

same throughout our experiments.

for this reason, it may be use-

ful to use the SSIM as an alter-

native metric of denoised image

quality since it is a good measure

of the structural degradation or

improvement in a denoised image.

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ISSN: 1792-6130

ISBN: 978-960-474-246-2

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