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degrading some of the others. To evaluate compres- sion algorithms and also compare them pairwise, some measures were defined as briefly explained below.

Figure 1 degrading some of the others. To evaluate compres- sion algorithms and also compare them pairwise, some measures were defined as briefly explained below.

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Table 1 Comparison between Saupe’s method and entropy-based algorithm (DN denotes the size of the domain pool) As one can easily see, when the pool size has small values, PSNR, SSIM and compression ratio are very small, which are not desirable, but they grow rapidly when the pool size is increased. For the greater values of the pool size, the growth of the two measures becomes slower, and increasing the pool size only increases the encoding time. These results verify the validity of the domain pool reduction approach. Using these three figures, one can approximately adjust the performance attributes of the algorithm by adjusting the pool size.
Table 1 Comparison between Saupe’s method and entropy-based algorithm (DN denotes the size of the domain pool) As one can easily see, when the pool size has small values, PSNR, SSIM and compression ratio are very small, which are not desirable, but they grow rapidly when the pool size is increased. For the greater values of the pool size, the growth of the two measures becomes slower, and increasing the pool size only increases the encoding time. These results verify the validity of the domain pool reduction approach. Using these three figures, one can approximately adjust the performance attributes of the algorithm by adjusting the pool size.
The last row is cited from Ref. 16, and the two others are from our experiments. As shown above, the entropy-based method is superior to the Saupe’s method, so we can compare our algorithm to the entropy-based one. To understand the significance of the size of the domain pool, one can consider a 512 x 512 image, with domain block of size 16 x 16 with overlap of 4 pixels; in this case, there are 15 625 domain blocks that must be checked if they match to each range block. A huge number of computations in this case are obvious. By restricting the domain pool to a number of less than 500 members, for example, the large amount of computations given above will be decreased by about 30 times.
The last row is cited from Ref. 16, and the two others are from our experiments. As shown above, the entropy-based method is superior to the Saupe’s method, so we can compare our algorithm to the entropy-based one. To understand the significance of the size of the domain pool, one can consider a 512 x 512 image, with domain block of size 16 x 16 with overlap of 4 pixels; in this case, there are 15 625 domain blocks that must be checked if they match to each range block. A huge number of computations in this case are obvious. By restricting the domain pool to a number of less than 500 members, for example, the large amount of computations given above will be decreased by about 30 times.
number of these permutations, is given in equation (13). 3.2 The effect of contrast scaling factor S
number of these permutations, is given in equation (13). 3.2 The effect of contrast scaling factor S
values. Obviously, restricting the size of the search set of S to a two-member set will decrease the encoding time considerably. To find a realistic estimate for S, a large number of experiments with exhaustive search for S$ were performed. One can easily see that at Step 1, the optimal S$ has often lower value than 0.1, independently on the image, so for this step, we let S=0.1. At Step 2, the optimal value of S is less than 0.5, so here we can choose S from {0.2, 0.4}. At Step 3, S has approximately uniform distribution across [0, 1], so in order to determine distinct values in this phase, we chose S from {0.3, 0.8}. For Step 4, S gets higher values in [0, 1], so we can choose S from {0.5, 0.9}. In this step, the blocks’ sizes are 2 x 2, and therefore, they can be encoded very accurately. drastically decreased as the following quantitative comparison demonstrates
values. Obviously, restricting the size of the search set of S to a two-member set will decrease the encoding time considerably. To find a realistic estimate for S, a large number of experiments with exhaustive search for S$ were performed. One can easily see that at Step 1, the optimal S$ has often lower value than 0.1, independently on the image, so for this step, we let S=0.1. At Step 2, the optimal value of S is less than 0.5, so here we can choose S from {0.2, 0.4}. At Step 3, S has approximately uniform distribution across [0, 1], so in order to determine distinct values in this phase, we chose S from {0.3, 0.8}. For Step 4, S gets higher values in [0, 1], so we can choose S from {0.5, 0.9}. In this step, the blocks’ sizes are 2 x 2, and therefore, they can be encoded very accurately. drastically decreased as the following quantitative comparison demonstrates
rp 5 Histogram of S with pool size as parameter for (a) step 1 and (b) step 2
rp 5 Histogram of S with pool size as parameter for (a) step 1 and (b) step 2
approaches. Figure 7 shows the associated data of a range block stored as compressed data. The coordination of domain blocks is kept in a list, and the entries of the list are used as the address. It is clear t hat the addresses of the range blocks need not to be stored, since they follow the same regular order in the image and in the stored data. They are stored in order from left to right, and rows from up to down. The last field is S with 1-bit length for Steps 2-4, indica stored ing one of the two predefined values for S. The data frames do not contain this field if the step is 1, since in this case there is only one default value for S.
approaches. Figure 7 shows the associated data of a range block stored as compressed data. The coordination of domain blocks is kept in a list, and the entries of the list are used as the address. It is clear t hat the addresses of the range blocks need not to be stored, since they follow the same regular order in the image and in the stored data. They are stored in order from left to right, and rows from up to down. The last field is S with 1-bit length for Steps 2-4, indica stored ing one of the two predefined values for S. The data frames do not contain this field if the step is 1, since in this case there is only one default value for S.
Table 2 Entropy based algorithm
Table 2 Entropy based algorithm
Table 3. Proposed algorithm
Table 3. Proposed algorithm
Table 6 The comparison results for Boat
Table 6 The comparison results for Boat
Table 5 The comparison results for Baboon
Table 5 The comparison results for Baboon
Table 4 The comparison results for F16
Table 4 The comparison results for F16
To judge the performance of this algorithm by the human eye, the results of applying different techni- ques on three of the used images are shown in Fig. 10.
To judge the performance of this algorithm by the human eye, the results of applying different techni- ques on three of the used images are shown in Fig. 10.
Related topics:
Image ProcessingData CompressionVideo CodingImage and Video Compression
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