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3. MODIFIED BLOCK TRUNCATION CODING
3.1 MODIFIED BTC METHODS FOR IMPROVED CONTRAST
To improve the quality of the BTC images, several methods have
been proposed, such as vector quantization (VQ) which improves the
compression ratio [3], [13]. Vector quantization is the process of quantizing
the values of the pixels of the blocks of images. This is also called as block
quantization. The pixel values are encoded from a multidimensional vector
space (image pixels) into a finite set of values from a discrete subspace of
lower dimension (block pixels).
Using moment preservation and visual information to further
compress the image and to retain the image quality for real time processing
has been proposed [11]. A hybrid coding method by using look up tables
(LUT) and VQ to encode the bit map and low mean of the blocks is used for
compressing the images [14]; However these methods are usually
associated with high computational complexity.
Since the main aim of compression is to reduce the bit rate, the block
size is increased for higher compression ratio and lower bit rates. But the
annoying blocking artifacts and the blurred edges are prominently visible
when the Traditional BTC is applied for higher block sizes. This is evident in
the images shown in Figure 2.4, 2.5, 2.6 and 2.7 respectively in chapter 2.
To overcome this problem, a heuristic method has been designed which
gives the modified ‘low mean’ intensity value ‘a’ and ‘high mean’ intensity
value ‘b’ for each block, resulting in image reconstruction with improved
contrast. Two such modified BTC methods are presented in this chapter.
Both the methods are based on using modified low mean ‘a’ and high
mean ‘b’ values. Four number of sample images are subjected to BTC,
BTC1 and BTC2. The resulting RMSE, PSNR and Contrast parameters are
estimated for various block sizes of the images, and compared. The results
are tabulated in various Tables and also graphically displayed in various
Figures.
3.2 LOW MEAN AND HIGH MEAN VALUES FOR BTC1.
The low mean ‘a’ and high mean ‘b’ of BTC, specified in Eqns. (2.3.1)
and (2.3.2) are reproduced below.
(3.2.1)
(3.2.2)
We heuristically modify them and label them as ‘a1’ and ‘b1’.
(3.2.3)
(3.2.4)
where ‘ ’ is the block size ( 4/8/16/32).
3.3 LOW MEAN AND HIGH MEAN VALUES FOR BTC2.
The ‘a’ and ‘b’ values are modified as ‘a2’ and ‘b2’ in BTC2, as
shown in (3.3.1) and (3.3.2).
(3.3.1)
(3.3.2)
mk
qxa
+
−= σ1
q
mkxb
++= σ
1
2/)(2
Maxvaluexb +=
qm
qxa
−
−= σ
q
qmxb
−+= σ
2/)(2
Minvaluexa +=
where denotes the minimum value of the pixel intensity in
the block and denotes the maximum value of the pixel intensity
in the block. This second modification has lesser computational complexity
compared to the traditional method of BTC as shown in Table 3.1.
Table 3.1:Comparison of computational complexities between the
Traditional BTC, BTC1 and BTC2.
BTC
Techniques
No. of additions/
subtractions
No. of Divisions/
Multiplications
Square root
operations
Traditional BTC [2(k x k] + 3 [k x k ] +9 2
BTC1 [2(k x k] + 3 [k x k ] +9 2
BTC2 [k x k] + 2 [k x k] + 2 0
Four sample images are taken and the modified methods of BTC are
processed on all the images for various block sizes and the results are
compared with the Traditional BTC method.
Also, the processing time of the CPU and elapsed time of the
algorithm is also measured and compared with the Traditional BTC method.
3.4 NUMERICAL ANALYSIS BASED ON SIMULATION RESULTS
FOR SAMPLE IMAGES
Four sample images, namely ,’copya.jpg’, ‘city.jpg’, ‘hurricane.jpg’,
‘boat.jpg’, are taken and processed with BTC ,BTC1 and BTC2 techniques
for various block sizes and the results are compared.
Also, the processing time of the CPU and elapsed time of the
algorithm are measured and compared.
3.4.1 SIMULATION RESULTS FOR ‘COPYA.JPG’ IMAGE.
The original ‘copya.jpg’ image and the 4x4, 8x8, 16x16, 32x32 and
64x64 block based processed images using the BTC, BTC1 and BTC2
techniques are shown in Figure 3.1.
(a) Original Image ‘copya.jpg’.
(b) 4x4 BTC (c) 4x4 BTC1 (d) 4x4 BTC2
(e) 8x8 BTC (f) 8x8 BTC1 (g) 8x8 BTC2
(h) 16x16 BTC (i) 16x16 BTC1 (j) 16x16 BTC2
(k) 32x32 BTC (l) 32x32 BTC1 (m) 32x32 BTC2
(n) 64x64 BTC (o) 64x64 BTC1 (p) 64x64 BTC2
Figure 3.1: (a) Original Image ‘copya.jpg’; [(b), (e), (h), (k), (n)] BTC images;
[(c), (f), (i), (l), (o)] BTC1images and [(d), (g), (j), (m), (p)] BTC2 images, for
block sizes of 4x4, 8x8, 16x16, 32x32 and 64x64 respectively.
The following Table 3.2 shows the comparison of MSE, PSNR and contrast
values between BTC, BTC1 and BTC2 techniques for original image
‘copya.jpg’.
Table 3.2: RMSE, PSNR and contrast values of BTC, BTC1 and BTC2 for
original image ‘copya.jpg’.
Block Size Technique RMSE
PSNR Contrast
BTC 1.4936
45.24 78.8770
BTC 1 1.4806
47.83 80.2447 4x4
BTC 2 1.4164
47.99 82.2195
BTC 1.4114
45.85 79.5046
BTC 1 1.4071
48.56 80.4273 8x8
BTC 2 1.4065
48.78 82.5615
BTC 1.2784
46.21 79.6656
BTC 1 1.2414
48.82 80.5774 16x16
BTC 2 1.2248
48.96 82.9433
BTC 1.1014
46.44 80.7490
BTC 1 1.0588
48.99 80.9915 32x32
BTC 2 1.0555
49.00 83.3243
BTC 1.0007
46.98 80.9710
BTC1 1.0003
49.01 81.1503 64x64
BTC 2 1.0000
49.03 83.7737
The contents of Table 3.2 are graphically shown in Figure 3.2 and 3.3. It is
clear that the RMSE decreases and contrast increases with the increase in
block size of the image ‘copya.jpg’, compared to the traditional BTC.
Figure 3.2: Graph showing the comparison of RMSE values between BTC,
BTC1 and BTC2 techniques for ‘copya.jpg’.
Figure 3.3: Graph showing the comparison of Contrast values between
BTC, BTC1 and BTC2 techniques for ‘copya.jpg’.
3.4.2 SIMULATION RESULTS FOR ‘CITY.JPG’ IMAGE.
The original ‘city.jpg’ image and the 4x4, 8x8, 16x16, 32x32 and
64x64 block based images produced using BTC, BTC1 and BTC2
techniques are shown in Figure 3.4 .
(a) Original image ‘city.jpg’
(b) 4x4 BTC (c) 4x4 BTC1 (d) 4x4 BTC2
(e) 8x8 BTC (f) 8x8 BTC1 (g) 8x8 BTC2
(h) 16x16 BTC (i) 16x16 BTC1 (j) 16x16 BTC2
(k) 32x32 BTC (l) 32x32 BTC1 (m) 32x32 BTC2
n) 64x64 BTC (o) 64x64 BTC1 (p) 64x64 BTC2
Figure 3.4: (a) Original Image ‘city.jpg’; [(b), (e), (h), (k), (n)] BTC images;
[(c), (f), (i), (l), (o)] BTC1 images and [(d), (g), (j), (m), (p)] BTC2 images, for
block sizes of 4x4, 8x8, 16x16, 32x32 and 64x64 respectively.
The following Table 3.3 shows the comparison of RMSE, PSNR and
contrast values of BTC, BTC1 and BTC2 techniques for the image ‘city.jpg’.
Table 3.3: RMSE, PSNR and contrast values of BTC, BTC1 and BTC2
techniques for the image ‘city.jpg.’
Block Size Technique RMSE PSNR Contrast
BTC 1.4884 45.25 69.0979
BTC 1 1.4609 45.56 74.4971 4x4
BTC 2 1.4557 45.67 75.3629
BTC 1.4107 45.90 70.4971
BTC 1 1.4095 45.98 74.9919 8x8
BTC 2 1.4016 45.99 75.7854
BTC 1.2056 46.68 72.3398
BTC 1 1.1639 46.75 75.1763 16x16
BTC 2 1.1145 46.80 77.3704
BTC 1.0640 46.87 72.5891
BTC 1 1.0578 46.93 75.2245 32x32
BTC 2 1.0456 46.97 84.4975
BTC 1.0006 46.99 73.0150
BTC1 1.0002 47.03 75.3372 64x64
BTC 2 1.0001 47.06 100.3550
The contents of Table 3.3 are graphically shown in Figure 3.5 and 3.6. It is
clear that the RMSE decreases and contrast increases with the increase in
block size of the image ‘city.jpg’, compared to the traditional BTC.
Figure 3.5: Graph showing the comparison of RMSE values of BTC, BTC1
and BTC2 techniques for the image ‘city.jpg’.
Figure 3.6: Graph showing the comparison of Contrast values of BTC,
BTC1 and BTC2 techniques for the image ‘city.jpg’.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
4x4 8x8 16x16 32x32 64x64
RM
SE
Block Size
RMSE for
Traditional
BTC
RMSE for
BTC 1
RMSE for
BTC2
60
65
70
75
80
85
90
95
100
4x4 8x8 16x16 32x32 64x64
Co
ntr
ast
Block Size
Contrast for
Traditional
BTC
Contrast for
BTC 1
Contrast for
BTC 2
3.4.3 SIMULATION RESULTS FOR ‘HURRICANE.JPG’ IMAGE.
The Figure 3.7 shows the image ‘hurricane.jpg’ and its BTC, BTC1 and
BTC2 images for various block sizes.
(a) Original image ‘hurricane.jpg'.
(b) 4x4 BTC (c) 4x4 BTC1 (d) 4x4 BTC2
(e) 8x8 BTC (f) 8x8 BTC1 (g) 8x8 BTC2
(h) 16x16 BTC (i) 16x16 BTC1 (j) 16x16 BTC2
(k) 32x32 BTC (l) 32x32 BTC1 (m) 32x32 BTC2
(n) 64x64 BTC (o) 64x64 BTC1 (p) 64x64 BTC2
Figure 3.7: (a) Original Image hurricane.jpg, [(b), (e), (h), (k), (n)] BTC
images;
[(c), (f), (i), (l), (o)] BTC1 images and [(d), (g), (j), (m), (p)] BTC2 images for
block sizes of 4x4, 8x8, 16x16, 32x32 and 64x64 respectively.
The following Table 3.4 shows the comparison of RMSE, PSNR
and contrast values of BTC, BTC1 and BTC2 techniques for the image
‘hurricane.jpg’.
Table 3.4: RMSE, PSNR and contrast values of BTC, BTC1 and BTC2
techniques for the image ‘hurricane.jpg’.
Block Size Technique RMSE PSNR Contrast
BTC 1.4954 45.27 88.7278
BTC 1 1.4685 45.54 90.3342 4x4
BTC 2 1.4462 45.78 91.5343
BTC 1.4106 45.86 88.8158
BTC 1 1.4101 45.92 91.2428 8x8
BTC 2 1.4040 45.97 91.7896
BTC 1.2526 46.65 88.7278
BTC 1 1.1628 46.72 91.3247 16x16
BTC 2 1.1402 46.81 94.9780
BTC 1.1152 46.83 88.9196
BTC 1 1.0604 46.92 91.5248 32x32
BTC 2 1.0567 46.99 101.5987
BTC 1.0061 46.97 89.2277
BTC1 1.0017 47.04 91.7761 64x64
BTC 2 1.0004 47.11 108.8039
The contents of Table 3.4 are graphically shown in Figure 3.8 and 3.9. It is
clear that the RMSE decreases and contrast increases with the increase in
block size of the image ‘hurricane.jpg’, compared to the traditional BTC.
1.2
1.4
1.6
RMSE for Traditional BTC
RMSE for BTC1
RMSE for BTC2
Figure 3.8: Graph showing the comparison of RMSE values for BTC, BTC1
and BTC2 techniques for the image
‘hurricane.jpg’.
Figure 3.9: Graph showing the comparison of Contrast values of BTC,
BTC1 and BTC2 techniques for the image ‘hurricane.jpg’.
3.4.4 SIMULATION RESULTS FOR ‘BOAT.JPG’ IMAGE.
The Figure 3.10 shows the image ‘boat.jpg’ and its BTC, BTC1 and BTC2
images for various block sizes.
(a) Original image ‘boat.jpg’
(b) 4x4 BTC (c) 4x4 BTC1 (d) 4x4 BTC2
(e) 8x8 BTC (f) 8x8 BTC1 (g) 8x8 BTC2
(h) 16x16 BTC (i) 16x16 BTC1 (j) 16x16 BTC2
(k) 32x32 BTC (l) 32x32 BTC1 (m) 32x32 BTC2
(n) 64x64 BTC (o) 64x64 BTC1 (p) 64x64 BTC2
Figure 3.10: (a) Original Image ‘boat.jpg’, [ (b),(e), (h), (k) , (n)] BTC
images;
[(c), (f), (i), (l), (o)] BTC1 images and [(d), (g), (j), (m), (p)] BTC2 images for
block sizes of 4x4, 8x8, 16x16, 32x32 and 64x64 respectively.
The following Table 3.5 shows the comparison of RMSE, PSNR and
contrast values of BTC, BTC1 and BTC2 techniques for the image
‘boat.jpg.
Table 3.5: RMSE, PSNR and Contrast values of BTC, BTC1 and BTC2
techniques for the image ‘boat.jpg’.
Block Size Technique RMSE PSNR Contrast
BTC 1.4887 45.29 66.5552
BTC 1 1.4655 45.51 69.8724 4x4
BTC 2 1.4177 45.72 72.6433
BTC 1.4130 45.83 67.6581
BTC 1 1.4091 45.91 70.7878 8x8
BTC 2 1.4059 45.98 73.2778
BTC 1.2423 46.64 69.5588
BTC 1 1.1741 46.76 71.0560 16x16
BTC 2 1.1415 46.94 73.6965
BTC 1.1064 46.88 69.5962
BTC 1 1.0946 46.96 71.3211 32x32
BTC 2 1.0536 46.99 78.3487
BTC 1.0078 47.01 69.6929
BTC1 1.0014 47.06 72.0257 64x64
BTC 2 1.0007 48.21 87.2638
The contents of Table 3.5 are graphically shown in Figure 3.11 and 3.12. It
is observed that the RMSE decreases and contrast increases with the
increase in block size of the image ‘boat.jpg’, compared to the traditional
BTC.
Figure 3.11: Graph showing the comparison of RMSE values for of BTC,
BTC1 and BTC2 techniques for the image ‘boat.jpg’.
Figure 3.12: Graph showing the comparison of Contrast values of BTC,
BTC1 and BTC2 techniques for the image ‘boat.jpg’.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
4x4 8x8 16x16 32x32 64x64
RM
SE
Block Size
RMSE for
Trditional BTC
RMSE for BTC 1
RMSE for BTC 2
60
65
70
75
80
85
90
4x4 8x8 16x16 32x32 64x64
Co
ntr
ast
Block size
Contrast for
Trditional BTC
Contrast for
BTC 1
Contrast for
BTC 2
3.4.5 COMPARISION OF COMPUTATIONALTIME FOR BTC, BTC1 AND
BTC2.
In Section 2.7, the computational time for BTC images of various
block sizes are listed. In this Section, the computational time ( Elapsed Time
and CPU Time) for BTC1 and BTC 2 are compared with traditional BTC, in
respect of the images ‘copya.jpg’, ‘city.jpg’, ’hurricane.jpg’ and ‘boat.jpg’.
The results are listed in separate Tables and also illustrated graphically in
separate Figures.
Table 3.6: Elapsed time and CPU time for BTC, BTC1 and BTC2
techniques for image ‘copya.jpg’.
Block Size Technique Elapsed time
In seconds
CPU time
In seconds
BTC 7.4964 4.0716
BTC 1 4.5328 3.2349 4x4
BTC 2 3.6531 1.4820
BTC 3.9663 1.1076
BTC 1 3.7115 0.9861 8x8
BTC 2 3.4313 0.5748
BTC 2.9917 0.7020
BTC 1 2.9690 0.6724 16x16
BTC 2 2.9320 0.3276
BTC 2.8148 0.6396
BTC 1 2.7523 0.5814 32x32
BTC 2 2.7378 0.2496
BTC 2.6026 0.5421
BTC1 2.5663 0.4219 64x64
BTC 2 2.5446 0.1872
Figure 3.13: Graph showing Elapsed time for BTC, BTC1 and BTC2
techniques and block sizes for image ‘copya.jpg’.
In figure 3.13, the elapsed time for BTC2 < BTC1 < BTC.
Figure 3.14: Graph showing CPU time for BTC, BTC1 and BTC2 techniques
and block sizes for image ‘copya.jpg’.
In figure 3.14, the CPU time for BTC2 < BTC1 < BTC.
Table 3.7: Elapsed time and CPU time of BTC, BTC1 and BTC2 techniques
for image ‘city.jpg’.
2
3
4
5
6
7
8
4x4 8x8 16x16 32x32 64x64
Ela
pse
d T
ime
in
Se
con
ds
Block Size
Traditional BTC
BTC 1
BTC 2
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
4x4 8x8 16x16 32x32 64x64
CP
U T
ime
(in
Se
con
ds)
Block Size
Traditional BTC
BTC 1
BTC 2
Block Size Technique Elapsed time
In seconds
CPU time
In seconds
BTC 7.7197 3.4476
BTC 1 6.0120 3.0888 4x4
BTC 2 4.2625 1.5756
BTC 5.0510 1.1700
BTC 1 4.8926 1.1544 8x8
BTC 2 4.3002 0.6708
BTC 4.5638 0.5772
BTC 1 3.7930 0.6281 16x16
BTC 2 3. 5721 0.4912
BTC 4.0711 0.6084
BTC 1 3.4917 0.4524 32x32
BTC 2 3.2096 0.2964
BTC 3.8789 0.4197
BTC1 3.1327 0.4056 64x64
BTC 2 3.0026 0.1092
4
5
6
7
8
9
d t
ime
(in
Se
con
ds)
Traditional BTC
BTC 1
Figure 3.15: Graph showing Elapsed time for BTC, BTC1 and BTC2
techniques and block sizes for image ‘city.jpg’.
In figure 3.15, the elapsed time for BTC2 < BTC1 < BTC.
Figure 3.16: Graph showing CPU time for BTC, BTC1 and BTC2 techniques
and block sizes for image ‘city.jpg’.
In figure 3.16 , the CPU time for BTC2 < BTC1 < BTC.
Table 3.8: Elapsed time and CPU time of BTC, BTC1 and BTC2 techniques
for image ‘‘hurricane.jpg’.
0
0.5
1
1.5
2
2.5
3
3.5
4
4x4 8x8 16x16 32x32 64x64
Traditional BTC
BTC 1
BTC 2
Block Size Technique Elapsed time
In seconds
CPU time
In seconds
BTC 7.1648 3.4593
BTC 1 5.9649 3.1898 4x4
BTC 2 3.9714 1.5288
BTC 5.0324 1.1604
BTC 1 4.0308 1.1974 8x8
BTC 2 3.6239 0.5148
BTC 4.0001 0.5072
BTC 1 3.6242 0.5066 16x16
BTC 2 3.4812 0.3120
BTC 3.5744 0.4656
BTC 1 3.4013 0.4533 32x32
BTC 2 3.2911 0.2184
BTC 3.1979 0.4385
BTC1 3.1033 0.4122 64x64
BTC 2 3.0719 0.1872
2
3
4
5
6
7
8
Ela
pse
d T
ime
in
Se
con
ds Traditional BTC
BTC 1
BTC 2
Figure 3.17: Graph showing Elapsed time of BTC, BTC1 and BTC2
techniques for image ‘hurricane.jpg’.
In figure 3.17 , the elapsed time for BTC2 < BTC1 < BTC.
Figure 3.18: Graph showing CPU time of BTC, BTC1 and BTC2 techniques
for image ‘hurricane.jpg’.
In figure 3.18 , the CPU time for BTC2 < BTC1 < BTC.
Table 3.9: Elapsed time and CPU time of BTC, BTC1 and BTC2 techniques
for image ‘boat.jpg’.
Block Size Technique Elapsed time CPU time
0
0.5
1
1.5
2
2.5
3
3.5
4
4x4 8x8 16x16 32x32 64x64
Traditional BTC
BTC 1
BTC 2
In seconds In seconds
BTC 6.1134 3.2760
BTC 1 5.6977 3.0108 4x4
BTC 2 4.1575 1.4820
BTC 4.1570 1.2792
BTC 1 3.5513 0.9828 8x8
BTC 2 2.5408 0.4212
BTC 3.5266 0.6864
BTC 1 3.4396 0.6084 16x16
BTC 2 2.7437 0.2964
BTC 3.1266 0.4836
BTC 1 2.7744 0.4680 32x32
BTC 2 2.5200 0.1872
BTC 3.0701 0.4801
BTC1 2.7690 0.4368 64x64
BTC 2 2.4988 0.1716
1
2
3
4
5
6
7
Ela
pse
d T
ime
in
Se
con
ds
Traditional BTC
BTC 1
BTC 2
Figure 3.19: Graph showing Elapsed time of BTC, BTC1 and BTC2
techniques for image ‘boat.jpg’.
In figure 3.19 , the elapsed time for BTC2 < BTC1 < BTC.
Figure 3.20: Graph showing CPU time of BTC, BTC1 and BTC2 techniques
for image ‘boat.jpg’.
In figure 3.20 , the CPU time for BTC2 < BTC1 < BTC.
0
0.5
1
1.5
2
2.5
3
3.5
4x4 8x8 16x16 32x32 64x64
CP
U T
ime
in
Se
con
ds
Block Size
Traditional BTC
BTC 1
BTC 2