Image Quality Prediction

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International Journal of Computer Applications (0975 8887)Volume 7No.5, September 2010

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Image Quality Prediction by Minimum Entropy Calculationfor Various Filter Banks

Sarita Kumari

Department of Physics, BanasthaliUniversity, India

Vijander Singh Meel

Department of computer Science,Jaipur National University, Jaipur

Ritu Vijay

Department of Electronics,Banasthali University, India

ABSTRACTWe implement image compression using various wavelet filterbanks and measure performance with rate distortioncharacterizations. Various separable filter banks are chosen andcompared. Coefficients in the subbands obtained by waveletdecomposition are quantized. The image is then reconstructedfrom the quantized coefficients, and distortion is measured. Threedistortion measures are used: Entropy of reconstructed image,

energy retained (ER) and redundancy.

Key wordsImage compression, wavelets, entropy, energy retained, andredundancy

1. INTRODUTIONCompression methods are being rapidly developed to compresslarge data files such as images, where data compression inmultimedia applications has lately become more vital [1]. With

the increasing growth of technology and the entrance into thedigital age, a vast amount of image data must be handled to bestored in a proper way using efficient methods usually succeed incompressing images, while retaining high image quality andmarginal reduction in image size [2].

Recently, discrete wavelet transform (DWT) has emerged as apopular technique for image coding applications [3,4]. In waveletbased image coding, the coding performance depends on thechoice of wavelets. Several wavelets which provide suboptimalcoding performance have been proposed in the literature [5].Recently, a few approaches for selecting the optimal filterbank inan image coder have beenproposed in the literature. Generally, awavelet providing optimal performance for the whole image isselected. Finding the optimal wavelet for a particular image is acomputationally intensive task. In the proposed work optimalbasis is provided on the basis of entropy calculation and it hasbeen concluded that biorthogonal wavelets perform better as

compare to orthogonal ones. The viability of symmetric extensionwith biorthogonal wavelets is the primary reason cited for theirsuperior performance.

2. DISTORTION CHARACTERIZATIONS

2.1EntropyThe image entropy can be estimated as [6]:

255

0

logi

ii ppXH

.(1)

N

Np i

i ..(2)

where the number of pixels with grey level is iN ; the total

number of pixels in the image is N; ip is the probability of

occurrence of one gray level intensity , and

,1255

0

i

i

p .10 ip ..(3)

The entropy of a given source is affected by the number ofelements in X. Thus a normalized measure, redundancy, is better

for comparing multiple sources.

2.2Energy RetainedWhen compressing with orthogonal wavelets the energy retainedis :

2

2

))2,_(

))2,____((100

signaloriginalnormvector

iondecompositcurrenttheofcoeffsnormvector

.(4)

2.3RedundancyThe common characteristics of most of the images is that, theneighbouring pixels are correlated, and image contains redundant

information [7]. Therefore the most important task in imagecompression is to find a less correlated representation of theimage. The fundamental component of image compression isreduction of redundancy and irrelevancy. Redundancy reductionaims at removing duplication from image, and irrelevancyreduction omits parts of the signal that will not be noticed byHuman Visual System (HVS). The redundancies in an image can


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be identified as spatial redundancy, spectral redundancy andtemporal redundancy. Image compression research aims atreducing the number of bits needed to represent an image byremoving the spatial and spectral redundancies as much aspossible. Since the focus is only on still natural image

compression, the temporal redundancy is not considered as it isused in motion picture [7]. Information redundancy, r, is

r = b He ..(5)

where b is the smallest number of bits for which the imagequantization levels can be represented.

3. ENTROPY AND HISTOGRAM

Figure 1: Lena ImageFigure 2: Histogram of lena

image

Figure 3: CameramanImage

Figure 4: Histogram ofcameraman image

From Equation (1), a histogram of an image is measured using256 bins, which correspond to the 256 quantize levels, and the

count of each level is divided byN to give the probability ip . The

maximum entropy value is achieved when the gray level valuesare distributed uniformly, and the minimum entropy value isachieved when the image consists of only one gray level value

and the histogram shows one bin. Therefore, the entropy of a grayscale image changes with the distribution of the histogram of theimage. When an image is natural image [8], the histogramtypically consists of combinational Gaussian distributions in therange (0, 255). In image compression, low image entropy suggeststhat a high compression ratio can be achieved using efficientcoding. The image with lower entropy implies lower imagequality for lower information content. In Figure 3 and 4,

histograms of test images lena and cameraman are shown. Thenormalized histogram of Lena has more rise and fall; it has a moreuniform distribution with more consistent numbers in each bin.Thus, the entropy of Lena image is higher than the entropy of thecameraman image.

Effect of threshold value on Energy retained

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

20 40 60 80 100

Threshold value

Entropy

Haar

Db2

Db6

Db10

Db20

Db30

db40

Effect of threshold value on Redundancy

0.5

0.550.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

20 40 60 80 100

Threshold

Redundancy

Haar

db2

db6

db10

db20

db30

db40

Effect of level of deomposition on Redundancy values

0.989

0.9892

0.9894

0.9896

0.9898

0.99

0.9902

2 3 4

level of decomposition

Redundancy

Haar

Db2

Db6

Db10

Db20

Db30

Db40

Figure 5: Experimental results of Daubechies wavelet family

4. MATERIALS AND METHODSThe following tasks are identified to accomplish efficient imagecompression.

1. A bitmap image (raw image) of varying sizes 256X256 and512X512 are taken.

2. Compression is performed by apply 2D DWT over the wholeimage.

3. Image data entropy is estimated from the gray levelhistogram.

4. The pseudo program for the ER and redundancy is alsodepicted.

5. Experimental ResultsThe proposed algorithm is used to measure objective quality ofcompressed images. The quality parameters are energy retained,entropy and redundancy. Importance of these parameters has been


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stated earlier. The algorithm is applied on images, Lena,Cameraman, Papper, Wbarb, and Mandrill using wavelet toolbox.However, experimental results for Lena image are shown here.

Effect of thres hold value on Entropy

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.951

20 40 60 80 100

Threshol d value

Entropy

Coif1

Coif2

Coif3

Coif4

Coif5

Effect of threshold value on Energy Retained

99.4

99.5

99.6

99.7

99.8

99.9

20 40 60 80 100

Thresh old value

EnergyRetained Coif1

Coif2

Coif3

Coif4

Coif5


0.9899

0.98991

0.98992

0.98993

0.98994

0.98995

0.98996

0.98997

0.98998

0.98999

0.99

2 3 4


Redundancy Coif1

Coif2

Coif3

Coif4

Coif5

Figure 6: Experimental results of Coiflet wavelet family

6. RESULTS AND DISCUSSIONSHere analysis of results for image compression for differentwavelet families is presented. Results are represented for energy

retained, average entropy and redundancy. The average entropy ofany source symbols decides the maximum codeword length. It

means if the entropy of the compressed image is larger, more noof bits are required to present it. All the wavelets do not have thesame properties so the compression for different wavelets willhave to be different.

Effect of thre shol d value on Entropy

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

20 40 60 80 100

Thres hold value

Entropy

Sym2

Sym5

Sym12

Sym20

Effect of threshol d value on Energy Retaine d

99.2

99.3

99.4

99.5

99.6

99.7

99.8

99.9

20 40 60 80 100

Thresh old value

EnergyRetained

Sym2

Sym5

Sym12

Sym20

Effect of level of deompositi on on Redundancy value s

0.9899

0.98991

0.98992

0.98993

0.98994

0.98995

0.98996

0.98997

0.98998

0.98999

0.99

2 3 4


Redundancy

Sym2

Sym5

Sym12

Sm20

Figure 7: Experimental results of Symlet wavelet family

On the basis of above tables it is clear that average entropy isminimum for Biorthogonal wavelets for all the test images used.Results indicate that maximum energy in the compressed image isretained in Sym 20 at level of decomposition4 whereas theaverage entropy found minimum for Biorto 2.6. Also, theprobability of occurrence of events can be used to calculate thecoding redundancy. For reducing the redundancy the 2D pixelarray that is normally used for human viewing and interpretationmust be transformed into a more efficient format. Thistransformation is called reversible if the original image elementscan be reconstructed from the transformed image. Thus the visualredundancies can be reduced using the fact that the human eyedoes not respond with equal sensitivity to all visual information.Using this fact redundancy calculations have been made andcoding redundancy is found minimum for Biortho 2.6 wavelet.

This shows that the objective quality of the compressed image isbetter for Biortogonal wavelet family. Reason behind thisperformance is that Biorthogonal wavelets can use filters withsimilar or dissimilar order for decomposition (Nd) andreconstruction (Nr). Therefore Biorthogonal wavelet is


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parameterized by two numbers and filter length is {max (2Nd,2Nr) +2}. Higher filter orders give higher degree of smoothness.Wavelet based image compression prefers smooth functions ofrelatively short support and so the Biorthogonal wavelets performbetter.

Effect of threshold value on Entropy

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

20 40 60 80 100

Threshold value

Entropy

Biortho1.3

Biortho 1.5

Biortho2.2

Biortho2.4

Biortho2.6

Effect of threshold value on Energy Retained

99.3

99.4

99.5

99.6

99.7

99.8

99.9

20 40 60 80 100

Threshold value

EnergyRetained Biortho1.3

Biortho1.5

Biortho2.2

Biortho2.4

Biortho2.6


0.4

0.5

0.6

0.7

0.8

0.9

2 3 4


Redundancy

Biortho1.3

Biortho1.5

Biortho2.2

Biortho2.4

Biortho2.6

Figure 8: Experimental results of Biorthogonal wavelet family

7. REFERENCES[1] Nadenau M. J., Reichel J., and Kunt M., 2003, Wavelet

Based Color Image Compression: Exploiting the ContrastSensitivity Function, IEEE Transactions Image Processing,vol. 12, no.1, pp. 58-70.

[2] Jain Y. K., Jain S., 2007, Performance Analysis andComparision of wavelet families Using for ImageCompression, International Journal of Soft Computing, 2(1),161-171.

[3] Talukder K. H. and Harada K., Haar, 2007, WaveletBased Approach for Image Compression and QualityAssessment of Compressed Image, IAENG InternationalJournal of Applied Mathematics.

[4] Z. Ye, Mohamadian H. and Y.Ye, 2007, InformationMeasures for Biometric Identification via 2D DiscreteWavelet Transform, Proceedings of the 3rd Annual IEEEConference on Automation Science and Engineering,CASE2007, pp. 835-840.

[5] Salomon.D.: Data compression (Springer, 2nd edn.2000).

[6] Misiti, M. Misiti, Y. Oppenheim, G. Poggi, J-M., 2000,Wavelet Toolbox Users Guide, Version 2.1, TheMathworks, Inc.

[7] Subhasia Saha, 2000, Image Compressionfrom DCT toWavelets: A review, ACM Cross words studentsmagazine,Vol.6, No.3, Springer.

[8] Sukanesh R. et al, 2007, Analysis of ImageCompression by Minimum Relative Entropy (MRE) andRestoration through Weighted Region Growing Techniquesfor Medical Images, Engineering Letters, 14:1.

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Image Quality Prediction