3. MODIFIED BLOCK TRUNCATION CODING 3.1 MODIFIED BTC METHODS FOR IMPROVED CONTRAST

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1 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

2 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) a = x σ q m q (3.2.2) b = x + σ m q q We heuristically modify them and label them as a 1 and b 1. a 1 = x σ q k + m (3.2.3) (3.2.4) b 1 = x + σ k + m q 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 a 2 and b 2 in BTC2, as shown in (3.3.1) and (3.3.2). (3.3.1) a 2 = ( x + Minvalue) / 2 b 2 = ( x + Maxvalue) / 2 (3.3.2)

3 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 No. of additions/ No. of Divisions/ Square root Techniques subtractions Multiplications 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] 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.

4 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

5 (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

6 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 4x4 8x8 16x16 32x32 64x64 BTC BTC BTC BTC BTC BTC

7 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.

8 Figure 3.3: Graph showing the comparison of Contrast values between BTC, BTC1 and BTC2 techniques for copya.jpg 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

9 (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;

10 [(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 4x4 8x8 16x16 32x32 64x BTC 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.

11 RMSE RMSE for Traditional BTC RMSE for RMSE for BTC2 0 4x4 8x8 16x16 32x32 64x64 Block Size Figure 3.5: Graph showing the comparison of RMSE values of BTC, BTC1 and BTC2 techniques for the image city.jpg. 100 Contrast Contrast for Traditional BTC Contrast for Contrast for 60 4x4 8x8 16x16 32x32 64x64 Block Size Figure 3.6: Graph showing the comparison of Contrast values of BTC, BTC1 and BTC2 techniques for the image city.jpg.

12 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

13 (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.

14 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 4x4 8x8 16x16 32x x64 BTC 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 RMSE for Traditional BTC RMSE for BTC1 RMSE for BTC2

15 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.

16 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

17 (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.

18 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 4x4 8x8 16x16 32x32 64x BTC The contents of Table 3.5 are graphically shown in Figure 3.11 and 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.

19 1.6 RMSE RMSE for Trditional BTC RMSE for RMSE for 0 4x4 8x8 16x16 32x32 64x64 Block Size Figure 3.11: Graph showing the comparison of RMSE values for of BTC, BTC1 and BTC2 techniques for the image boat.jpg Contrast Contrast for Trditional BTC Contrast for x4 8x8 16x16 32x32 64x64 Block size Contrast for Figure 3.12: Graph showing the comparison of Contrast values of BTC, BTC1 and BTC2 techniques for the image boat.jpg.

20 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 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 x BTC x x16 32x32 64x BTC

21 Elapsed Time in Seconds Traditional BTC 2 4x4 8x8 16x16 32x32 64x64 Block Size 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. CPU Time (in Seconds) x4 8x8 16x16 32x32 64x64 Block Size Traditional 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.

22 Block Size Technique Elapsed time In seconds CPU time In seconds BTC x BTC x x16 32x32 64x BTC BTC BTC BTC time (in Seconds) Traditional BTC

23 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 Traditional BTC x4 8x8 16x16 32x32 64x64 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.

24 Block Size Technique Elapsed time In seconds CPU time In seconds BTC x BTC x x16 32x32 64x BTC BTC BTC BTC Elapsed Time in Seconds Traditional BTC

25 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 Traditional BTC x4 8x8 16x16 32x32 64x64 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

26 4x4 8x8 16x16 32x32 64x64 In seconds In seconds BTC BTC BTC BTC BTC BTC Elapsed Time in Seconds Traditional BTC

27 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 CPU Time in Seconds Traditional BTC 0 4x4 8x8 16x16 32x32 64x64 Block Size 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.