3.1 MODIFIED BTC METHODS FOR IMPROVED CONTRASTshodhganga.inflibnet.ac.in/bitstream/10603/33680/4/chapter 3.pdf · BTC1 and BTC2. The resulting RMSE, PSNR and Contrast parameters are

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’





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


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



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'.






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


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’.


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



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’.


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’






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


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’.


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’.


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


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.


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


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’.



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’.


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

Documents

3.1 MODIFIED BTC METHODS FOR IMPROVED CONTRASTshodhganga.inflibnet.ac.in/bitstream/10603/33680/4/chapter 3.pdf · BTC1 and BTC2. The resulting RMSE, PSNR and Contrast parameters are