77 CHAPTER 5 RATIO-MODIFIED BLOCK TRUNCATION CODING FOR REDUCED BITRATES 5.1 INTRODUCTION In this chapter, two algorithms for Modified Block Truncation Coding (MBTC) are proposed for reducing the bitrate below 2 bpp. The proposed algorithms are compared with MBTC and the algorithms obtained by combining JPEG standard (DCT and Huffman coding) with MBTC in terms of bitrate, PSNR and subjective quality. It is found that the reconstructed images obtained using the proposed algorithms yield better results. 5.2 MODIFIED BLOCK TRUNCATION CODING Block Truncation Coding (BTC) techniques are known for their speed and reduced computational complexity since complicated transforms are not used (Delp and Mitchell 1979, Udpikar and Raina 1987, Halverson et al 1984, Wu and Coll 1991, Ma and Huang 1997, Amarunnishad et al 2007). The principle used in BTC algorithm is to use two-level quantizer on each non-overlapping 4 4 blocks of the image. The quantizer adapts to local properties of the image while preserving the first- or first- and second-order statistical moments. The BTC technique of Delp (Delp and Mitchell 1979) preserves the first- and second-order moments. In the Modified BTC (MBTC) of Udpikar (Udpikar and Raina 1987), only the first-order moments are
78 preserved. The parameters transmitted or stored in the BTC based algorithms are the statistical moments and the bitplane. The BTC or MBTC techniques yield good quality images at a bitrate of 2 bpp or a CR of 4. In order to reduce the bitrate further, the moments and bitplane are coded in different ways. In the techniques of (Udpikar and Raina 1987, Wu and Coll 1991, Ma and Huang 1997), DCT and VQ techniques are used to achieve bitrates less than 1 bpp at the cost of image quality. Bitrate in MBTC algorithm can be further reduced by manipulating the moments and bitplane without causing too much degradation in the subjective quality of reconstructed images. 5.3 PROPOSED RATIO-MODIFIED BTC ALGORITHMS The following two algorithms for MBTC are proposed for reducing the bitrate below 2 bpp. 1. Ratio-MBTC (RMBTC) algorithm in which the block averages, ratio values are coded using the state-based dynamic multi-alphabet arithmetic coding proposed in the previous chapter and the bitplane is not coded. 2. RMBTC with Bit Plane Coding (RMBTC-BPC) in which the block averages, ratio values are coded using state-based dynamic multi-alphabet arithmetic coding proposed in the previous chapter and the bitplane is also coded. In the proposed algorithms, a ratio parameter and block average is computed for each non-overlapping 4 4 block. The ratio parameter is the ratio of average value of pixels that are less than or equal to the block average and the block average. The ratio values and block average values are entropy
79 coded using lossless state-based dynamic multi-alphabet arithmetic coding proposed in the previous chapter of this thesis. 5.3.1 RMBTC encoding algorithm The proposed RMBTC encoding algorithm is as follows: STEP 1: The image is divided into non-overlapping 4 4 blocks. STEP 2: The average value of each pixel block, called block average X avg is computed. STEP 3: A 16-bit bit plane is formed which contains 0s and 1s. A 0 in the bitplane represents a pixel with a value less than or equal to the block average where as 1 represents a pixel with a value greater than the block average. STEP 4: The average value of the pixels in a block that are less than or equal to the block average, called lower average X Lavg is computed. STEP 5: The ratio of X Lavg and X avg is computed. The ratio values lie between 0 and 1. STEP 6: The ratio obtained in Step 5 is rounded to the nearest integer between 0 and 15 (both numbers inclusive). STEP 7: The parameters X avg and ratio are entropy coded using the lossless state-based dynamic multi-alphabet arithmetic coding. STEP 8: The coded X avg and ratio values are then transmitted or stored along with the bitplane.
80 5.3.2 RMBTC decoding algorithm The proposed RMBTC decoding algorithm is as follows: STEP 1: The values of X avg and ratio values are decoded using the decoding algorithm described in the state-based dynamic multi-alphabet arithmetic coding. STEP 2: Using X avg and ratio, X Lavg is computed. STEP 3: The average value of the pixels that are greater than X avg, called higher average X Havg is computed using Equation (5.1). X Xavg - XLavg 16 Havg XLavg nones (5.1) where nones = number of 1s in 4 4 block in bitplane. STEP 4: The block is reconstructed by using the bit plane, X Havg and X Lavg values. For a 1 in the bit plane, X Havg value is substituted where as X Lavg value is substituted for a 0. 5.3.3 RMBTC-BPC encoding algorithm The steps in the proposed RMBTC-BPC algorithm are the same as the steps in RMBTC algorithm and in addition the bitplane is coded using the algorithm of Rao (Rao and Eswaran 1995). It considers only one-half of the bits in the original bitplane for transmission or storage. Figure 5.1 shows the bitplane for a 4 4 block. There is a high correlation between bits in the bitplane (Rao and Eswaran 1995). So only the alternate bits, viz. the circled bits are transmitted or stored.
81 Figure 5.1 Bitplane for a 4 4 block 5.3.4 RMBTC-BPC decoding algorithm The steps in the proposed RMBTC-BPC decoding algorithm are the same as in the RMBTC decoder algorithm. The bitplane in the RMBTC-BPC algorithm is reconstructed using the decision procedure of Rao (Rao and Eswaran 1995). The dependent bits, viz. the uncircled bits are then interpolated from the values of the surrounding circled bits. The interpolation to reconstruct pixels in position B, D, E, G, J, L, M and O of Figure 5.1 is performed according to the following rules: B = 1 iff A, C and F are equal to 1. D = C. E = 1 iff A, F and I are equal to 1. G = 1 iff C, F, H and K are equal to 1. J = 1 iff F, I, K and N are equal to 1. L = 1 iff H, K and P are equal to 1. M = N. O = 1 iff K, N and P are equal to 1.
82 5.4 RESULTS AND DISCUSSION For the purpose of evaluating the performance of proposed algorithms, four gray scale images, namely lena, barbara, mandrill and goldhill, each of size 512 512, are considered. The proposed RMBTC algorithm is compared with Algorithm 1 which is defined below: Algorithm 1: MBTC algorithm (Udpikar and Raina 1987) (with no bitplane coding) in which the block average values and lower average values are coded using the state-based dynamic multi-alphabet arithmetic coding. The proposed RMBTC-BPC algorithm is compared with two algorithms, namely Algorithm 2 and Algorithm 3 which are defined below: Algorithm 2: MBTC algorithm (Udpikar and Raina 1987) (with no bitplane coding) in which the lower average values and the differences of higher and lower averages are coded using JPEG standard. This is similar to the algorithms in (Udpikar and Raina 1987, Wu and Coll 1991, Ma and Huang 1997). Algorithm 3: RMBTC algorithm (with no bitplane coding) in which the block average values and ratio values are coded using JPEG standard. Table 5.1 shows the PSNR values and bitrates obtained using Algorithm 1 and the proposed RMBTC algorithm for the four test images. The reconstructed images are obtained using Algorithm 1 and the proposed RMBTC algorithm. Figures 5.2 and 5.3 show reconstructed lena images. Figures 5.4 and 5.5 show the reconstructed barbara images.
83 Figures 5.6 and 5.7 show the reconstructed mandrill images. Figures 5.8 to 5.9 show the reconstructed goldhill images. The subjective quality and PSNR in the reconstructed images obtained using Algorithm 1 and the proposed RMBTC algorithm for the four test images are almost the same. It can be seen from Table 5.1 that the proposed RMBTC algorithm yields a lower bitrate. Table 5.2 shows the PSNR values and bitrates obtained using Algorithm 2, Algorithm 3 and the proposed RMBTC-BPC algorithm for the four test images. The reconstructed images are obtained using Algorithm 2, Algorithm 3 and the proposed RMBTC-BPC algorithm for the bitrate that is obtained in the proposed RMBTC-BPC algorithm. Figures 5.10 to 5.12 show reconstructed lena images. Figures 5.13 and 5.15 show the reconstructed barbara images. Figures 5.16 and 5.18 show the reconstructed mandrill images. Figures 5.19 to 5.21 show the reconstructed goldhill images. The RMBTC BPC algorithm is found to yield bitrates close to 1 bpp. It can be seen from Figures 5.10 to 5.21 and Table 5.2 that the RMBTC-BPC algorithm yields better PSNR values and better subjective quality images than those obtained with Algorithm 2 and Algorithm 3 in which JPEG is used without bitplane coding.
84 Table 5.1 PSNR (db) vs bitrate (bpp) for the four test images using Algorithm 1 and RMBTC algorithm Image Algorithm 1 PSNR Bitrate (bpp) PSNR RMBTC Bitrate (bpp) lena 37.86 1.94 36.93 1.59 barbara 34.31 1.96 33.94 1.63 mandrill 33.35 1.91 32.96 1.60 goldhill 36.77 1.94 36.07 1.59 Table 5.2 PSNR (db) vs bitrate (bpp) for the four test images using Algorithm 2, Algorithm 3 and RMBTC-BPC algorithm Image Algorithm 2 Algorithm 3 RMBTC-BPC PSNR Bitrate (bpp) PSNR Bitrate (bpp) PSNR Bitrate (bpp) lena 33.02 1.09 33.32 1.09 35.04 1.09 barbara 31.87 1.13 32.10 1.13 32.47 1.13 mandrill 30.75 1.10 30.84 1.10 31.47 1.10 goldhill 32.47 1.09 32.38 1.09 33.68 1.09
85 Figure 5.2 Reconstructed lena 512 512 image using Algorithm 1 (PSNR = 37.86 db, bpp = 1.94) Figure 5.3 Reconstructed lena 512 512 image using proposed RMBTC algorithm (PSNR = 36.93 db, bpp = 1.59)
86 Figure 5.4 Reconstructed barbara 512 512 image using Algorithm 1 (PSNR = 34.31 db, bpp = 1.96) Figure 5.5 Reconstructed barbara 512 512 image using proposed RMBTC algorithm (PSNR = 33.94 db, bpp = 1.63)
87 Figure 5.6 Reconstructed mandrill 512 512 image using Algorithm 1 (PSNR = 33.35 db, bpp = 1.91) Figure 5.7 Reconstructed mandrill 512 512 image using proposed RMBTC algorithm (PSNR = 32.96 db, bpp = 1.60)
88 Figure 5.8 Reconstructed goldhill 512 512 image using Algorithm 1 (PSNR = 36.77 db, bpp = 1.94) Figure 5.9 Reconstructed goldhill 512 512 image using proposed RMBTC algorithm (PSNR = 36.07 db, bpp = 1.59)
89 Figure 5.10 Reconstructed lena 512 512 image using Algorithm 2 (PSNR = 33.02 db, bpp = 1.09) Figure 5.11 Reconstructed lena 512 512 image using Algorithm 3 (PSNR = 33.32 db, bpp = 1.09)
90 Figure 5.12 Reconstructed lena 512 512 image using proposed RMBTC-BPC algorithm (PSNR = 35.04 db, bpp = 1.09) Figure 5.13 Reconstructed barbara 512 512 image using Algorithm 2 (PSNR = 31.87 db, bpp = 1.13)
91 Figure 5.14 Reconstructed barbara 512 512 image using Algorithm 3 (PSNR = 32.10 db, bpp = 1.13) Figure 5.15 Reconstructed barbara 512 512 image using proposed RMBTC-BPC algorithm (PSNR = 32.47 db, bpp = 1.13)
92 Figure 5.16 Reconstructed mandrill 512 512 image using Algorithm 2 (PSNR = 30.75 db, bpp = 1.10) Figure 5.17 Reconstructed mandrill 512 512 image using Algorithm 3 (PSNR = 30.84 db, bpp = 1.10)
93 Figure 5.18 Reconstructed mandrill 512 512 image using proposed RMBTC-BPC algorithm (PSNR = 31.47 db, bpp = 1.10) Figure 5.19 Reconstructed goldhill 512 512 image using Algorithm 2 (PSNR = 32.47 db, bpp = 1.09)
94 Figure 5.20 Reconstructed goldhill 512 512 image using Algorithm 3 (PSNR = 32.38 db, bpp = 1.09) Figure 5.21 Reconstructed goldhill 512 512 image using proposed RMBTC-BPC algorithm (PSNR = 33.68 db, bpp = 1.09)
95 5.5 CONCLUSION In this chapter, two algorithms based on MBTC that provide bitrates below 2 bpp are proposed. In the first algorithm (RMBTC), the block average and a ratio parameter are entropy coded using the state-based arithmetic coding. The bitplane is not coded. In the second algorithm (RMBTC-BPC), the block average and a ratio parameter are entropy coded using the state-based arithmetic coding. The bitplane also is coded. It is found that the proposed RMBTC algorithm yields almost the same subjective quality as that of the original MBTC algorithm. The proposed RMBTC-BPC algorithm is found to yield better reconstructed images than those obtained with the MBTC based algorithms in which JPEG is used.