Fundamenta Informaticae 87 (2008) 313–329
313
IOS Press
New Bit Reduction of Vector Quantization Using Block Prediction and Relative Addressing Yu-Chen Hu∗ Department of Computer Science and Information Management Providence University, Taichung, 433, Taiwan
[email protected]
Piyu Tsai Department of Computer Science and Information Engineering National United University, Miaoli, 360, Taiwan
[email protected]
Chun-Chi Lo Department of Computer Science and Information Engineering Providence University, Taichung, 433, Taiwan
[email protected]
Abstract. A low bit rate image coding scheme based on vector quantization is proposed. In this scheme, the block prediction coding and the relative addressing techniques are employed to cut down the required bit rate of vector quantization. In block prediction coding, neighboring encoded blocks are taken to compress the current block if a high degree of similarity between them is existed. In the relative addressing technique, the redundancy among neighboring indices are exploited to reduce the bit rate. From the results, it is shown that the proposed scheme significantly reduces the bit rate of VQ while keeping good image quality of compressed images.
Keywords: Image Compression, Vector Quantization, Bit Rate Reduction, Block Prediction ∗
Address for correspondence: Department of Computer Science and Information Management, Providence University, Taichung, 433, Taiwan
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1. Introduction Vector quantization (VQ) [1, 2, 3] is a commonly used scheme for grayscale image compression. Basically, VQ has the advantages of requiring a low bit rate and having a simple image decoding structure. VQ is often used for image and speech compression. It is especially suitable for the multimedia applications that having a limited computation power. VQ had been also be used for data hiding and data mining. The basic concept of VQ is to generate a set of representative vectors, also called the codewords, to form the codebook. These codewords in the codebook are then used for image encoding and image decoding. In other words, VQ consists of three main procedures: codebook generation, image encoding, and image decoding. The goal of codebook generation procedure is to produce a set of representative codewords. In current literature, the LBG algorithm [1] is the commonly used algorithm to design the VQ codebooks. It is a clustering-based algorithm that is proofed to be sub-optimal. The performance of the LBG algorithm is highly affected by the codebook initialization. Once a codebook is designed, the image encoding/decoding procedures of VQ can then be triggered. In the image encoding procedure, each grayscale image to be compressed is first divided into a set of nonoverlapped image blocks of the size n × n pixels. Each image block can be viewed as a k-dimensional vector where k = n × n. Then, each image block is processed in the left-to-right and top-to-bottom order. Given one image block x and a codebook of N codewords, the closest codeword in the codebook is to be determined. Generally, the squared Euclidean distance (SED) is taken to measure the degree of similarity between two given vectors. To find out the closest codeword for x, the SED between each codeword and x is calculated. A total of N SEDs are calculated and the codeword corresponding to the least SED is selected. Finally, the index of the searched codeword is recorded and taken as the compressed code of x. After each image block is sequentially compressed, the compressed codes of one given image are the indices of the codewords in the codebook. In the image decoding procedure, the same codebook used in the image encoding procedure is required. To recover each compressed block x, the index of x is first extracted. Then, the corresponding codeword in the codebook is taken to rebuild the compressed block. By successively processing each extracted index, the whole compressed image of VQ can then be reconstructed. VQ has the advantage of requiring a low bit rate for image compression. The bit rate of VQ is lg2kN bpp. The bit rate of VQ is 0.5 bpp when the codebook size and the vector dimensions are 256 and 16, respectively. Another advantage of VQ is that it has a low-complexity image decoding procedure. By simply referencing the appropriate table, the image decoding procedure is executed. It is especially suitable for some multimedia applications that have limited computational power for image decoding. Generally, the reconstructed image quality of VQ highly depends on the codebook used. If a representative set of codewords is designed, a good reconstructed image quality of the compressed image is achieved. In the LBG algorithm, the codebook initialization plays an important role in the resultant codebook. Several initialization techniques [4, 5, 6] have been proposed to solve this problem. The codebook design procedure using the LBG algorithm usually consumes a great deal of computational cost. Several rounds are iterated in the LBG algorithm to design the VQ codebook. There is a higher computational cost when a large-sized codebook is to be designed. Several fast algorithms [7, 8, 9]have been proposed to cut down the computational cost of the LBG algorithm. Also, the image encoding procedure is time consuming because it needs to find the closest codewords for the image
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blocks. To accelerate the image encoding procedure without incurring any extra image distortion, some fast codebook search algorithms [10, 11, 12, 13] have been proposed. In the traditional VQ scheme, the bit rate is fixed because each index is stored in lg2 N bits. To cut down the bit rate of VQ, two main approaches are introduced. The first approach employs the postprocessing of the indices by combining the lossless coding. Some index compression techniques [14, 15, 16, 17] are introduced in the lossless compression of the indices. Note that additional computational cost is required for the post-processing work. Another approach for the bit rate reduction of VQ exploits the inter-block correlation among neighboring blocks. The side match vector quantization (SMVQ)[18] proposed by Kim in 1992 is a typical example of this approach. In SMVQ, the blocks either in the first column or the first row are processed using the traditional VQ scheme. The remaining blocks are sequentially processed by the SMVQ scheme. The encoded left and upper blocks of the current encoding block x are used to generate the state-codebook for SMVQ. Instead of all the codewords in the codebook, only portion of them are possibly similar to x and are taken to form the state-codebook. Since the size of the state-codebook is less than that of the original codebook, the required bit rate is thus reduced. However, SMVQ suffers from the image degradation problem and it consumes more computational cost than VQ in both the image encoding/decoding procedures. Some modified techniques of SMVQ have also been proposed [19, 20]. In addition, the quadtree segmentation vector quantization (QSVQ) [21] that exploits the spatial similarity among neighboring pixels by using the quadtree segmentation technique have been proposed. In this scheme, each input image is partitioned into various-sized blocks based on a three-level quadtree structure. The initial block size for quadtree segmentation is set to 16 × 16 and the smallest block size is 4 × 4 in this scheme. Each 16 × 16 or 8 × 8 block is first subsampled into one 4 × 4 block. The closest codeword in the codebook for the subsampled block is decided, and the index of the closest codeword is transmitted to the decoder. Each 4 × 4 block is compressed using the traditional VQ scheme. The compressed codes of one image using this scheme consist of the quadtree codes and the indices. In the decoding procedure, the quadtree codes are taken to construct the quadtree-segmented image. Then, the index that is corresponding to one 4 × 4 image block is directly used to recover the compressed image. The index that corresponds to one image block of 8 × 8 or 16 × 16 is taken to rebuild one image block of 4 × 4. Then, this block is up-sampled to a large block. In 2001, the subsampling vector quantization (SVQ) scheme was proposed [22]. Each image is first partitioned into a set of non-overlapped blocks the size of k pixels. If two adjacent blocks are quite similar in block activities, they are merged and subsampled to form a block of size k . Three block type classifiers are designed to decide the block activities of the image blocks. The inter-block correlation between each two adjacent blocks is exploited in this scheme. In 2002, Zhu proposed the subsampled-based predictive vector quantization[23]. In this scheme, the inter-block correlation and the intra-block correlation are exploited. Two codebooks including the traditional codebook and the small codebook for subsampled image blocks are used. Each image to be compressed is partitioned into a set of non-overlapped image blocks of 4 × 4 pixels. Then, each block x is down-sampled into a smaller block y of size 4 × 2 pixels. The closest codeword in the small codebook is searched for y. The closest searched codeword is then up-sampled into a block z of size 4 × 4 pixels and the squared Euclidean distance between x and z is calculated. If the calculated distance is less than or equal to the predefined threshold, x is compressed to the subsampled VQ with the small codebook. Otherwise, x is then compressed by VQ with the traditional codebook. This scheme works well for smooth image blocks and most of the image blocks tend to be
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Get each image block x ?X »X XXX »»» » XXX » » Is x in either first » X » XX »» XXX column row? »»» » XX or first XX»»»
Y
N
Y
? »X XX »»»
X » »» Is similar neighborXXXXX » » XXX »» XXX of x found ? »»»» XXX»»» N ?
Find the index of closest codeword of x ?
?
Encode its similar neighbor by the block prediction technique Figure 1.
Encode the index by the relative addressing technique
?
Encode x by the VQ scheme
Flowchart of the proposed encoding procedure
smooth in most digital images. That is why the bit rate of this scheme can be reduced compared to the VQ scheme. To further cut down the required storage cost for VQ compressed imaging, the block prediction technique and the relative addressing technique are employed in the proposed method. The rest of this paper is organized as follows. In Section 2, the proposed method based on VQ is introduced. In Section 3, the experimental results are shown. Finally, some conclusions are given in Section 4.
2. The Proposed Scheme The goal of the proposed scheme is to cut down the required bit rate of the traditional VQ scheme. One observation on digital images helps us to design the proposed scheme. We find that most adjacent image blocks tend to be similar. If these adjacent blocks are compressed by VQ using the same codebook, it is quite possible that they are encoded by the same or nearly the same codeword in the codebook. This assumption motivates us to design a codeword reordering process to deal with the VQ codebook. The block prediction technique and the relative addressing technique are then used to encode image blocks and similar indices in the proposed scheme.
2.1.
The Encoding Procedure
The flowchart of the proposed encoding procedure is depicted in Fig.1. To encode one grayscale image with the proposed scheme, the image is first partitioned into a set of non-overlapped image blocks of n × n pixels. Each image block can be viewed as a k-dimensional vector where k =n × n. Suppose
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U L
Figure 2.
x
Position diagram of the two adjacent neighbors for the currently encoded block x
the VQ codebook Y = {y1 , y2 , . . . , yN } of N codewords was previously generated by using the LBG algorithm. Before the encoding procedure is executed, the codeword reordering process is performed. In the codeword reordering process, the codewords in Y are sorted by their sum values in ascending order. By doing so, we hope that close codewords are located in the neighboring areas. But, it is not guaranteed that two codewords having the closest sum values are definitely similar. For most smooth codewords, the claim might be true. For complex codewords, it is possible that two codewords having close sum values but a large difference in variance values is found. In the traditional VQ scheme, image blocks are encoded in the order of left-to-right and top-tobottom. The same order is employed in the proposed image encoding procedure. To simplify the encoding procedure, each image block x that is either in the first column or the first block row of the image is compressed by the traditional VQ scheme. This is because these image blocks do not have enough neighbors for the block prediction technique. For each remaining image block x to be processed, we first check whether the block prediction technique can be employed. A predefined threshold θ is used to control the degree of similarity for two given image blocks. Two adjacent encoded neighbors of x as shown in Fig. 2 are examined to find whether a suitable one exists to represent it. Let L and U denote the two encoded blocks in the codebook, respectively. If L is not equal to U , two SED values are calculated. They can be computed as follows. k X d(x, L) = (xi , Li )2
(1)
i=1
d(x, U ) =
k X
(xi , Ui )2
(2)
i=1
Then, the smaller SED value among them is selected and stored in dmin . If dmin is less than or equal to θ, the block prediction technique is employed to encode x. Otherwise, the relative addressing technique is employed to process the index. If the encoded neighbors of x are the same, only one SED value is computed.
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Table 1.
Encoding rule for the close distance in the relative addressing technique
dra
Corresponding codes in decimal value
-(RT /2)
0
-(RT /2)+1
1
-(RT /2)+2
2
· · ·
· · ·
(RT /2))-1
RT -1
Table 2.
Storage cost of different encoding rules of the proposed scheme
Encoding Methods
Indicator Cost (bits)
Indicator Codes
Total Cost (bits)
Traditional VQ
NA
NA
lg2 N
Block Prediction (L = U )
1
(0)2
1
Block Prediction (L 6= U )
1+1
(00)2 or (01)2
2
Relative Addressing (within range)
2
(10)2
2+ lg2 RT
Relative Addressing (outside range)
2
(11)2
2+ lg2 N
If x is not encoded by using the block prediction technique, the traditional codebook search process is executed to find the closest codeword for x. Let I(x) denote the index of the searched closest codeword for x. The relative addressing technique is then employed to process I(x). Here, the predefined range threshold RT is used to control the allowable distance between two given indices. The referenced index for calculating the distance can be set to the left or upper index of x. Here, the upper index of x is taken as the referenced index in the relative technique. The distance between I(x) and I(U ) can be computed as follows. dra = I(x) − I(U ) (3) If the calculated distance dra ranges from -(RT /2) to (RT /2)-1, the two indices are assumed to be close to each other. The encoding rule to code the distance within the range of -(RT /2) to (RT /2)-1 is given in Table 1. If the calculated dra is within the allowable range from -(RT /2) to (RT /2)-1, then the 1-bit indicator valued at 0 along with the encoded displacement is transmitted to the receiver. Otherwise, the 1-bit indicator valued at 1 along with the original index value (lg2 N bits) is transmitted In the encoding procedure, each image block can be encoded either by the block prediction technique or the relative addressing technique. The storage cost for each possible encoding method is listed in Table 2. For each image block x that is either in the first column or the first block row of the image, it is compressed by the traditional VQ scheme. It means that the traditional VQ index of lg2 N bits is needed. When the one image block x is encoded by the block prediction technique, two possible cases can be encountered. First, the two encoded neighbors L and U are the same; which means, the indices of
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its adjacent encoded neighbors are the same. Only one bit is needed to represent this case. The other possibility is that the two encoded neighbors L and U are different; in which case, an additional bit records whether L or U is used to encode x. Therefore, a total of two bits are needed for the block prediction technique. In the relative addressing technique, two possible cases are found. First, if the current index is quite close to the referenced index, it is encoded by 2-bit indicators valued at (10)2 along with the encoded dra of lg2 RT bits. Otherwise, it is encoded by 2-bits indicators valued at (11)2 along with the original index of lg2 N bits.
2.2.
The Decoding Procedure
To decode the compressed image, the same codebook Y as used in the encoding procedure is stored and used here. Since the image blocks are encoded in the left-to-right and top-to-bottom order, the same order is used to decompress them. Three different approaches are used in the decoding procedure to rebuild each image block x. First, if x is either in the first row or the first column of the image, the index of size lg2 N bits is extracted. Then, the corresponding codeword in the codebook is taken to recover x. To continue the decoding procedure, the first bit of the compressed code is extracted. Let c denote the extracted data. If c is equal to (0)2 , it indicates that the current decoding block x was compressed by using the block prediction technique. Two different decoding rules are used here. When x is to be decompressed, its neighbors L and U (as shown in Fig. 2) have already been rebuilt. The indices of L and U , i.e. I(L) and I(U ), are taken to determine the decoding rules. If I(L) is equal to I(U ), it indicates that the encoded neighbor L, i.e. U , was used to represent x. Then, x is recovered by its decoded neighbor L. Otherwise, additional one bit d is extracted to determine which one of the two neighboring encoded blocks was used to compress x. Then, x is reconstructed by L and R when the d is equal to (0)2 and (1)2 , respectively. If c is equal to (1)2 , it indicates that x was processed by using the relative addressing technique. The additional one bit t is extracted to determine the decoding rules. If t is equal to (0)2 , it indicates that the current decoding index I(x) is quite close to the referenced index I(U ). By extracting the successive lg2 RT bits from the compressed codes, the encoded distance between I(x) and I(U ) can be obtained. The encoded distance is then decoded by using Table 1 to generate dra . Then, the current decoding index I(x) is computed as follows. I(x) = I(U ) + dra
(4)
Finally, the corresponding codeword in the codebook of I(x) is taken to recover x. If t is equal to (1)2 , it indicates that the current decoding index I(x) is far from the referenced index I(U ). Then, the successive lg2 N bits from the compressed codes are extracted to generate I(x). A simple table reference is executed by using I(x) to recover x.
3.
Experimental Results
To evaluate the performance of the newly proposed scheme, a variety of experiments have been performed. All the experiments were performed on the IBM compatible PC with a Pentium IV 3G Hz CPU and 1G RAM. To generate LBG codebooks, four grayscale images “Airplane”, “Boat”, “Goldhill” and
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Table 3.
Results of image quality of the VQ scheme
Images
32 (0.3125 bpp)
64 (0.375 bpp)
128 (0.4375 bpp)
256 (0.5 bpp)
512 (0.5625 bpp)
1024 (0.625 bpp)
Airplane
27.839
29.079
30.317
31.285
32.163
32.995
Girl
28.437
29.419
30.206
31.072
31.857
32.326
Goldhill
27.787
28.861
29.807
30.627
31.519
32.326
Lenna
28.105
29.077
30.179
30.978
31.784
32.440
Peppers
28.340
29.357
30.323
31.127
31.825
32.402
Toys
27.698
29.215
30.439
31.707
32.655
33.552
Average
28.034
29.168
30.212
31.133
31.967
32.712
“Toys” of 512 × 512 pixels were used as the training images. In the experiments, the LBG algorithm is employed to design codebooks of different sizes. The terminated threshold of the LBG algorithm is set to 0.001. For any M × N image of 8-bit resolution, the mean square error (M SE) between the original image and the encoded image is defined as M SE =
M X N X 1 (xij − eij )2 M ×N
(5)
i=1 j=1
Here xij and eij denote the original and encoded pixel elements, respectively. The quality of the reconstructed image is measured by means of the peak signal-to-noise-ratio (P SN R), which is defined as 2552 P SN R = 10 × lg10 (6) M SE Note that mean squared error is generally considered an indication of image quality rather than a definitive measurement; however, it is a commonly used measurement for evaluating the image quality. In the simulations, six test images “Airplane”, “Girl”, “Goldhill”, “Lenna”, “Peppers” and “Toys” of 512 × 512 pixels are taken to evaluate the average performance of comparative schemes. Here, three of them are within the training set for codebook design. These images are shown in Fig. 3. Results of the traditional VQ scheme are listed in Table 3. Image qualities of VQ using different codebook sizes are listed. The bit rates of VQ using different codebook sizes are also listed in Table 3. It is shown that the image quality increases as the codebook size increases in VQ. An average image quality of 30.212 dB is obtained in VQ when the bit rate is equal to 0.4375 bpp. In addition, the average image quality is 31.133 dB when a codebook of 256 codewords is used in VQ. Average image qualities and bit rates of the QSVQ scheme are listed in Tables 4 and 5, respectively. In QSVQ, each image block is encoded by using a three-level quadtree. The possible sizes of image blocks are 16 × 16, 8 × 8, and 4 × 4 pixels. To determine whether each large block is to be split, all pixels in this block are classified into two groups according to the block’s mean value. Then, the difference
Y.C. Hu et al. / New Bit Reduction of Vector Quantization Using Block Prediction and Relative Addressing
(a) Airplane
(b) Girl
(c) Goldhill
(d) Lenna
(e) Peppers
(f) Toys
Figure 3.
Test images of size 512 × 512 pixels
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Table 4.
Average image qualities of the QSVQ scheme [21]
Sizes
5
10
15
20
25
30
128
30.232
30.118
29.789
29.321
28.730
28.091
256
31.142
30.965
30.519
29.924
29.213
28.470
512
31.961
31.702
31.120
30.400
29.581
28.747
1024
32.684
32.328
31.613
30.779
29.864
28.957
Table 5.
Average bit rates of the QSVQ scheme [21]
Sizes
5
10
15
20
25
30
128
0.462
0.346
0.277
0.232
0.199
0.173
256
0.511
0.380
0.304
0.252
0.216
0.186
512
0.560
0.415
0.330
0.273
0.233
0.200
1024
0.609
0.449
0.356
0.293
0.249
0.214
between the two mean values is calculated. A predefined threshold value is set to control the activity of image blocks for the quadtree segmentation technique. From the results in Table 4, it is shown that the image quality and the required bit rate of QSVQ increases when a large codebook is used. In addition, the required bit rate decreases as the increment of the threshold value rises. But, the resultant image quality of QSVQ degrades as the bit rate decreases. It is shown that an average image quality of 30.519 dB is obtained at 0.304 bpp when a 256 codebook is used in QSVQ. In the proposed scheme, the block prediction coding technique plays an important role for the reduction of VQ bit rates. Analysis of block similarity in these test images is given in Fig. 4. Here, we assume two image blocks are similar if the calculated SED value between them is less than or equal to the given threshold value. Two SED values between each image block x and its left and upper blocks are computed by using Eqs. (1) and (2), respectively. It is shown that about 49.358% and 49.253% of image blocks have similar left hand and upper blocks, respectively when the similar threshold is set to 800. Meanwhile, about 37.776% of image blocks have similar left hand and upper blocks. The percentage of similar blocks increases when a large similar threshold value is used. The percentage of similar upper blocks for image blocks is slightly higher than that of similar left hand blocks. That is why we take the index of the upper block as the referenced index for the relative addressing technique. Average bit rates of the proposed scheme using codebooks of sizes 128, 256, 512, and 1024 are given in Tables 6 to 9, respectively. Different values of the controlling threshold θ and RT are set to verify the performance of the proposed scheme. Note that θ and RT are used in the block prediction technique and the relative addressing technique, respectively. From the results shown in Tables 6 to 9, we find that the selection of adequate RT value is very important because it affects the consumed bit rates. From the results in Table 6, it is shown that the
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323
Figure 4. Analysis of block similarity based on the squared Euclidean distance
Table 6.
Average bit rates (unit: bpp) of the proposed scheme with a codebook of 128 codewords
θ values
RT =4
RT =8
RT =16
RT =32
RT =64
200
0.343
0.333
0.326
0.340
0.372
400
0.307
0.295
0.285
0.292
0.315
600
0.284
0.273
0.262
0.266
0.285
800
0.267
0.257
0.247
0.248
0.265
1000
0.253
0.244
0.235
0.235
0.249
lowest bit rates are achieved in the proposed scheme with the use of a 128 codebook when RT is set to 16. In other words, RT is equal to N8 where the codebook size N is 128. By checking the results in Tables 7 to 9, we suggest that RT should be set to N8 for the relative addressing technique. Average image qualities of the proposed scheme using different sized codebooks are listed in Table 10. Most of these P SN R values are greater than or equal to 30 dB except for the one when θ and N are set to 1000 and 128, respectively. When a codebook of 256 codewords is used in the proposed scheme, average image qualities range from 30.714 dB to 31.108 dB. But the required bit rates with adequately selected RT values are less than 0.36 bpp. Besides, an average image quality of 31.880 dB is obtained at 0.305 bpp when a codebook of 1024 codewords is used. An average image quality of 32.639 dB is obtained at 0.441 bpp when a codebook of 1024 codewords is used. To understand the performance of the proposed scheme, average numbers of image blocks encoded by different ways of the proposed scheme are listed in Table 11. Here a VQ codebook of 256 codewords is used and RT is set to 32. There are 16384 image blocks in each 512 × 512 image when the block size is set to 16. From the results, it is shown that the number of blocks processed by the block prediction technique increases as the increment of θ value. The results shown in Table 11 can be used to explain the encoding rules of the proposed scheme as shown in Table 2. Comparing the results of VQ and QSVQ, the proposed scheme provides the best performance. A higher quality image can be achieved with the proposed scheme while keeping a low bit rate when adequate threshold values are set. This is because the block prediction technique exploits the inter-block
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Table 7.
Average bit rates (unit: bpp) of the proposed scheme with a codebook of 256 codewords
θ values
RT =4
RT =8
RT =16
RT =32
RT =64
RT =128
200
0.394
0.386
0.371
0.363
0.360
0.408
400
0.350
0.341
0.327
0.316
0.323
0.346
600
0.321
0.314
0.302
0.290
0.294
0.313
800
0.299
0.294
0.283
0.271
0.273
0.289
1000
0.282
0.278
0.269
0.257
0.258
0.272
Table 8.
Average bit rates (unit: bpp) of the proposed scheme with a codebook of 1024 codewords
θ values
RT =4
RT =8
RT =16
RT =32
RT =64
RT =128
RT =256
200
0.449
0.442
0.429
0.410
0.403
0.417
0.448
400
0.391
0.385
0.376
0.359
0.348
0.355
0.379
600
0.355
0.351
0.344
0.330
0.318
0.322
0.341
800
0.330
0.326
0.320
0.309
0.297
0.299
0.316
1000
0.311
0.308
0.303
0.294
0.281
0.282
0.297
Table 9.
Average bit rates (unit: bpp) of the proposed scheme with a codebook of 1024 codewords
θ values
RT =8
RT =16
RT =32
RT =64
RT =128
RT =256
RT =512
200
0.495
0.485
0.466
0.445
0.441
0.456
0.487
400
0.426
0.419
0.407
0.388
0.379
0.388
0.412
600
0.387
0.381
0.373
0.357
0.346
0.351
0.371
800
0.358
0.354
0.347
0.334
0.323
0.326
0.343
1000
0.337
0.334
0.328
0.318
0.305
0.307
0.322
Y.C. Hu et al. / New Bit Reduction of Vector Quantization Using Block Prediction and Relative Addressing
Table 10.
325
Average image qualities of the proposed scheme with different sizes of codebooks
θ values
128
256
512
1024
200
30.199
31.108
31.923
32.639
400
30.154
31.045
31.821
32.481
600
30.089
30.950
31.686
32.292
800
30.020
30.851
31.534
32.074
1000
29.993
30.714
31.360
31.880
Table 11. Average numbers of image blocks encoded by different ways of the proposed scheme with a 256 codebook
θ values
VQ
Block Prediction L=U L6= U
Relative Addressing Within range Outside range
200
255
2651.33
2768.50
7349.67
3359.50
400
255
3727.50
3844.50
5379.00
3178.00
600
255
4345.67
4395.33
4354.00
3034.00
800
255
4680.67
4875.50
3666.67
2906.17
1000
255
4945.33
5217.00
3147.67
2819.00
correlations among neighboring blocks. The redundancy among neighboring image blocks is removed. Another benefit with the relative addressing technique is a decrease in the required storage area for these compressed indices. That is why the required bit rates can be significantly reduced while keeping good image qualities of compressed images. To understand the visual qualities of these comparative schemes, compressed images of VQ, QSVQ and the proposed scheme using codebooks of 256 and 1024 codewords are listed in Figs.5 and 6, respectively. It is shown that the blocking artifact can be observed in these compressed images of QSVQ. This is because the up-sampling process is employed in QSVQ. The visual qualities of the compressed image using the proposed scheme are quite good.
4. Conclusions A low bit rate image compression scheme based on VQ is proposed in this paper. By exploiting the high correlation among neighboring blocks, the block prediction technique refers two neighboring encoded blocks. The encoding rules for the block prediction technique makes use of block similarity to cut down the bit rates of VQ. By using the codeword reordering process, the codewords in the codebook are reorganized so that similar codewords are arranged in the neighborhood.
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(a) VQ (31.285 dB at 0.5 bpp)
(c) QSVQ (31.065 dB at 0.314 bpp)
(e) Proposed (31.045 dB at 0.254 bpp) Figure 5.
(b) VQ (30.978 dB at 0.5 bpp)
(d) QSVQ (30.798 dB at 0.354 bpp)
(f) Proposed (30.806 dB at 0.280 bpp)
Compressed images of comparative schemes using a codebook of 256 codewords
Y.C. Hu et al. / New Bit Reduction of Vector Quantization Using Block Prediction and Relative Addressing
(a) VQ (32.995 dB at 0.625 bpp)
(b) VQ (32.440 dB at 0.5 bpp)
(c) QSVQ (32.402 dB at 0.349 bpp)
(d) QSVQ (32.026 dB at 0.417 bpp)
(e) Proposed (32.472 dB at 0.303 bpp)
(f) Proposed (32.039 dB at 0.334 bpp)
Figure 6.
Compressed images of comparative schemes using a codebook of 1024 codewords
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The relative addressing technique is then employed to cut down on storage costs of the indices by using the reordered codebook. From the results, it is suggested that the range threshold RT should be set to N8 for the relative addressing technique. According to the results, it is shown that the proposed scheme achieves good image quality while keeping a low bit rate.
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