Image Compression Comparative Analysis of Basic Algorithms

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```					    Image Compression:
Comparative Analysis of Basic
Algorithms

Yevgeniya Sulema (Ukraine)
Samira Ebrahimi Kahou (Iran)

National Technical University of Ukraine
“Kyiv Polytechnic Institute”
sulema@scs.ntu-kpi.kiev.ua
samira_ebrahimi@hotmail.com
Outline

 Existing compression methods and classification
 Criteria
 How to choose image set for testing
 Realizing algorithms
 Getting numerical values on chosen criteria
 Verifying results obtained from test
 Analysis and conclusion
Compression algorithms-Classification

5 Main Classification Types chosen.

By data type :

 General algorithms
 Algorithms for audio-compression
 Algorithms for image-compression
 Algorithms for video-compression
Compression algorithms-Classification (..2)

By data source :

 Dynamic
 Static

By redundancy type :

 Statistical redundancy reduction
 Spatial redundancy reduction
Compression algorithms-Classification (..3)
By restoring the original dataset:

 Lossless
 Lossy

By computational approach :

 Statistical
 Dictionary
 Transformation based
 Hybrid
Classes of Images

 Business graphics (schemes, diagrams, charts)
 Pictures created in graphic editors (photoshop)
 Photorealistic images (photos, textures)

Coefficient of correlation can be used
between an analyzed (test) image and an etalon
image to classify images :

cov  I A , I E   
 
D(I A )  D(I E )
Sample images

   Image with two monochrome areas
   Image with large monochrome fields
   Image with small monochrome fields
Correlation coefficients
(Sample images)

0.5    0.437366167

0.4

0.3                   0.239146336

0.2
0.062622429
0.1

0

-0.1

-0.2

-0.3
-0.300682476
-0.4
image 1        image 2       image 3       image 4
Criteria
1.   Compression ratio
2.   Time of compression
3.   Time of decompression
4.   Peak signal-to-noise ratio (PSNR)

 max ( I ) 
  20  log 10            
     
           
MSE : Mean Squared Error
n   m
1

2
                      p i , j  p i, j
nm
i 1 j 1

5.   Coefficient of correlation between original
and decompressed image
Matlab image processing Toolbox
Why Matlab?

 It provides a comprehensive set of reference-
standard algorithms.
 The software is a collection of functions that
extend the capability of the MATLAB.
 The toolbox supports a wide range of image
processing operations.
 Most toolbox functions are written in the open
MATLAB language, giving us the ability to
inspect the algorithms, modify the source code.
Algorithms:

Lossless :             Lossy :
   LZW                   JPEG
(Coarse and Fine)
   LZ77
   Wavelet
   Huffman                (Daubechies, Coiflets, Symlets,
   Adaptive Huffman       Discrete Meyer wavelet,
Biorthogonal, Reverse
   Shannon-Fano           Biorthogonal)
   Arithmetic            SPIHT
   Fractal
Lossless
Time of compression
102.6
100                                                                                                91.8
87.0
78.8
80
63.2
59.6
60

40
25.7

20           12.2                                                                           11.8
4.8                          5.8                         6.6
1.9       3.7
0.7                                                        0.9

0
Image 1                       Image 2                      Image 3                    Image 4

LZ77     Huffman           ShannonFano         Arithmetic
Lossless
Time of decompression
113.8

100

80
63.8

60                                                               51.6

40
20.2
15.9
20                                            10.8
0.8 0.6 1.1 2.2       1.9 2.6                   0.8 2.8                 3.5 4.0

0
Image 1             Image 2                   Image 3                 Image 4

LZ77    Huffman    ShannonFano      Arithmetic
Lossless
Compression ratio
10
9.0
9
8.0 8.0
8      7.3                                              7.1

7

6
5
4

3

2                                 1.4 1.5 1.4 1.5
1.1 1.1 1.2         1.0 1.0 1.0
0.7
1

0
Image 1                  Image 2                 Image 3             Image 4

LZ77     Huffman        ShannonFano   Arithmetic
Lossless Algorithm Observation
Dictionary Based Algorithms most Effective

   LZ77 – prime example from our research

 Minimal Time for Compression
 Minimal Time for Decompression
 High Compression Ratio
Lossy
Time of compression
157.0                  154.4                      153.6                 154.0

140

120

100

80

60

40

20
0.1 0.1 0.7            0.1 0.2 0.9                0.1 0.1 0.7           0.1 0.4 1.1
0
Test1                  Test2                      Test3                 Test4

JPEG Coarse      JPEG Fine   SPIHT        Fractal
Lossy
Time of decompression
1
0.9
0.9
0.8

0.7                                     0.6
0.6         0.6                                                                          0.6
0.5               0.5                        0.6               0.5
0.6
0.5                                                    0.5 0.5               0.5
0.5

0.4                                           0.3
0.3
0.3
0.2
0.2

0.1
0
Test1                     Test2                       Test3                  Test4

JPEG Coarse         JPEG Fine     SPIHT        Fractal
Lossy
Compression ratio
19.2                                                  18.8
20
17.6
18
16

14                               12.3
11.9
12

10

8

6                                                                                     4.8
4.0 4.0                 4.0 4.0                       4.0 4.0               4.0 4.0
3.5
4
1.2
2

0
Test1                   Test2                         Test3                 Test4

JPEG Coarse          JPEG Fine     SPIHT           Fractal
Lossy
Correlation coefficient
1.0 1.0 1.0 1.0      0.9         1.0 1.0        1.0 1.0 1.0 1.0                     1.0
1

0.9
0.8
0.7
0.7
0.6
0.6
0.5
0.5

0.4

0.3
0.2
0.1
0.0
0
Test1                 Test2                     Test3              Test4

JPEG Coarse    JPEG Fine     SPIHT      Fractal
Lossy
PSNR
99.2
100

90
80

70
60                                                                         53.5
48.1                                                        48.1
50                                                      41.1
37.7          38.1                                   37.8
35.8
40      32.7                         31.0 29.8
27.6 26.2 27.7
30                                                                                                               21.7

20

10

0
Test1                      Test2                            Test3                     Test4

JPEG Coarse             JPEG Fine   SPIHT           Fractal
Lossy Algorithm Observations
   Fractal Algorithm not practical.

   All remaining algorithms are Hybrid

   Combination of procedures can result in
increased quality.
Conclusion
Our research allows us to draw 3 main conclusions:

   The selection of the proper compression
algorithm for each image class should be made

   Hybrid algorithms, JPEG, can be modified in
order to achieve better result

   Combination of a dictionary and transforms
most promising.
Thank YOU!

   Questions…???

samira_ebrahimi@hotmail.com

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