# A Novel Psychovisual Threshold on Large DCT for Image Compression

Authors: Nur Azman Abu; Ferda Ernawan
Journal: The Scientific World Journal
 (2015)

---

## Abstract

A psychovisual experiment prescribes the quantization values in image compression. The quantization process is used as a threshold of the human visual system tolerance to reduce the amount of encoded transform coefficients. It is very challenging to generate an optimal quantization value based on the contribution of the transform coefficient at each frequency order. The psychovisual threshold represents the sensitivity of the human visual perception at each frequency order to the image reconstruction. An ideal contribution of the transform at each frequency order will be the primitive of the psychovisual threshold in image compression. This research study proposes a psychovisual threshold on the large discrete cosine transform (DCT) image block which will be used to automatically generate the much needed quantization tables. The proposed psychovisual threshold will be used to prescribe the quantization values at each frequency order. The psychovisual threshold on the large image block provides significant improvement in the quality of output images. The experimental results on large quantization tables from psychovisual threshold produce largely free artifacts in the visual output image. Besides, the experimental results show that the concept of psychovisual threshold produces better quality image at the higher compression rate than JPEG image compression.


---

## Body

## 1. Introduction

Most digital cameras implement a popular block transform in image coding [1]. The sequential block-based coding is a popular technique since it is compact and easy to implement. In standard JPEG image compression, an image is compressed by one block of 8
×
8 pixels at a time. The block-based DCT coding has prevailed at reducing interpixel statistical redundancy [2]. However, in order to achieve high compression ratio, 8
×
8 image block size with default JPEG quantization tables produces discontinuity of intensities among adjacent image blocks. These discontinuities of the intensity image between two adjacent image blocks cause a visual artifact due to interblock correlations [3] in image reconstruction. Block transform coding always results in blocking artifact at low bit rate. Blocking artifact is one of the most annoying problems [4].The blocking effect becomes visible within smooth regions where adjacent block is highly correlated with an input image. Since the8
×
8 blocks of image pixels are coded separately, the correlation among spatially adjacent blocks provides boundary blocks when the image is reconstructed [5]. The artifact images in the compressed output are introduced by two factors. First, the transform coefficients coming out of the quantization process are rounded and then inadequately dequantized. Second, the blocking artifacts appear by the pixel intensity value discontinuities which occur along block boundaries [6]. These blocking artifacts are often visually observable.This research pays a serious attention to the role of block size in transform image coding. Referring to JPEG image compression, the block of8
×
8 image pixels based line coding has provided a low computational complexity. Previously, a compression scheme on 16
×
16 block has been investigated by Pennebaker and Mitchell [7] for image compression. This scheme does not provide an improvement on the image compression due to lack of progress on the central processing unit in terms of its computing power at the time. The larger 16
×
16 block requires an extra image buffering and a higher precision in internal calculations. Nowadays, the technology of the central processing unit grows rapidly in terms of its computing power. Therefore, two-dimensional image transform on larger blocks is now practically efficient to operate on image compression.In the previous research, the psychovisual threshold has been investigated on8
×
8 image block size [8–15]. This paper proposes psychovisual threshold on the large image block of 256
×
256 DCT in order to reduce significant blocking effect within the boundary of small image block. This paper also discusses the process and apparatus to generate 256
×
256 quantization tables via a psychovisual threshold.The organization of this paper is as follows. The next section provides a brief overview on a psychoacoustic model. Section3 discusses a brief description of the 256
×
256 discrete cosine transform. Section 4 explains the development of psychovisual threshold on the large discrete cosine transform in image compression. Section 5 discusses a quality measurement on compressed output images. Section 6 shows the experimental results of 256
×
256 quantization tables from psychovisual threshold in image compression. Lastly, Section 7 concludes this paper.


## 2. The Principle of Psychoacoustic Model

Psychoacoustics is the study on how humans perceive sound or human hearing. Psychoacoustic studies show that the sound can only be heard at certain or higher sound pressure levels (SPL) across frequency order [16]. The psychoacoustics indicates that human hearing sensation has a selective sensitivity to different frequencies [17]. In the noise-free environment, the human ear audibility requires different loudness across various frequency orders. The sound loudness that the human audibility can hear is called the absolute hearing threshold [18] as depicted in Figure 1.Figure 1
The absolute threshold of hearing under quiet condition.The principle of the psychoacoustic model by incrementing the sound pressure level one bark at a time has been used to detect audibility of human hearing threshold. The same principle of the psychoacoustic technique has been used to measure the psychovisual threshold in image compression by incrementing image frequency signal one-unit scale at a time. A block of image signals as represented by a transform coefficient at a given frequency is incremented one at a time on each frequency order. A psychovisual threshold has been conducted for image compression by calculating the just noticeable difference (JND) of the compressed image from the original image. This research will investigate the contribution of the transformed coefficient on each frequency order to the compressed output image. The average reconstruction error from the contribution of the DCT coefficients in image reconstruction will be the primitive of psychovisual threshold in image compression. This quantitative experiment has been conducted on256
×
256 image blocks.


## 3. Discrete Cosine Transform

The two-dimensional discrete cosine transform [19] has been widely used in image processing applications. The DCT is used to transform the pixel values to the spatial frequencies. These spatial frequencies represent the detailed level of image information. The standard JPEG compression uses 8
×
8 DCT as shown in Figure 2 in image compression.Figure 2
The first four8
×
8 DCT of set C
n
(
x
) for n
=
0
,
1
,
2
,
3.This paper proposes a large image block ofN
×
N DCT set C
n
(
x
) of size N
=
256 which can be generated iteratively as follows: (1)
C
0
(
x
)
=
1
N
,
C
1
x
=
2
N
cos
⁡
2
x
+
1
1
π
2
N
,
C
2
x
=
2
N
cos
⁡
2
x
+
1
2
π
2
N
,
C
3
x
=
2
N
cos
⁡
2
x
+
1
3
π
2
N
,for x
=
0
,
1
,
2
,
…
,
N
-
1. The first four one-dimensional 256
×
256 DCT above are depicted in Figure 3 for visual purposes.Figure 3
The first four256
×
256 DCT of set C
n
(
x
) for n
=
0
,
1
,
2
,
3.The kernel for the DCT is derived from the following definition [20]:(2)
g
=
λ
(
u
)
cos
⁡
(
2
x
+
1
)
u
π
2
N
,where(3)
λ
(
u
)
=
1
N
,
u
=
0
2
N
,
u
>
0
,for x
=
0
,
1
,
2
,
…
,
N
-
1 and u
=
0
,
1
,
2
,
…
,
N
-
1. The definition of the two-dimensional DCT of an input image A and output image B is given as follows [19]:(4)
B
p
q
=
α
p
β
q
∑
m
=
0
M
-
1
‍
∑
n
=
0
N
-
1
A
m
n
cos
⁡
π
(
2
m
+
1
)
p
2
M
cos
⁡
π
(
2
n
+
1
)
q
2
N
,for p
=
0
,
1
,
2
,
…
,
M
-
1 and q
=
0
,
1
,
2
,
…
,
N
-
1 where (5)
α
p
=
1
M
,
p
=
0
2
M
,
p
>
0
,
β
q
=
1
N
,
q
=
0
2
N
,
q
>
0
.The inverse of two-dimensional DCT is given as follows:(6)
A
p
q
=
∑
m
=
0
M
-
1
‍
∑
n
=
0
N
-
1
α
p
β
q
B
m
n
cos
⁡
π
(
2
m
+
1
)
p
2
M
cos
⁡
π
(
2
n
+
1
)
q
2
N
,for p
=
0
,
1
,
2
,
…
,
M
-
1 and q
=
0
,
1
,
2
,
…
,
N
-
1. The image input is subdivided into M
×
N blocks of image pixels. The DCT is used to transform each pixel in the 256
×
256 image block pixel into the frequency transform domain. The outputs of transforming 256
×
256 image blocks of frequency signals are 65536 DCT coefficients. The first coefficient in the upper left corner of the array basis function is called the direct current (DC) coefficient and the rest of the coefficients are called the alternating current (AC) coefficients. DC coefficient provides an average value over the 256
×
256 block domain.


## 4. Psychovisual Threshold on Large Discrete Cosine Transform

In this quantitative experiment, the DCT coefficients on each frequency order are incremented concurrently one at a time from 1 to 255. The impact of incrementing DCT coefficients one at a time is measured by average absolute reconstruction error (ARE). The contribution of DCT coefficients to the quality image reconstruction and compression rate is analyzed on each frequency order. In order to develop psychovisual threshold on256
×
256 DCT, ARE on each frequency order is set as a smooth curve reconstruction error. An ideal average reconstruction error score of an incrementing DCT coefficient on each frequency order on luminance and chrominance for 40 real images is shown in Figure 4.Figure 4
Average absolute reconstruction error of incrementing DCT coefficients on256
×
256 DCT luminance and chrominance for 40 real images.An ideal finer curve of ARE on a given order from zero to the maximum frequency order 510 for luminance and chrominance channels is presented by the red curve and blue curve, respectively. These finer curves of absolute reconstruction error are set as the psychovisual threshold on256
×
256 DCT. The contribution of an ideal error reconstruction for each frequency order is determined by two factors, its contribution to the quality on image reconstruction and the bit rates on image compression. The smooth curve of ARE is interpolated by a polynomial that represents the psychovisual error threshold on 256
×
256 DCT in image compression. With reference to Figure 4, this paper proposes the new psychovisual thresholds on 256
×
256 DCT basis function for luminance f
V
L and chrominance f
V
R which are simplified as follows:(7)
f
V
L
x
=
-
0.0000000000001435
x
5
+
0.000000000011
x
4
+
0.000000046
x
3
-
0.000009
x
2
+
0.00088
x
+
0.2352
,
f
V
R
x
=
-
0.000000000000457
x
5
+
0.000000000156
x
4
+
0.00000006
x
3
-
0.0000128
x
2
+
0.0012
x
+
0.2309
,for x
=
0
,
1
,
2
,
…
,
510, where x is a frequency order on 256
×
256 image block. Further, these thresholds are used to generate smoother 256
×
256 quantization values for image compression. The 256
×
256 quantization table has 511 frequency orders from order 0 until order 510. The order 0 resides in the top left most corner of the quantization matrix index of Q(0,0). The first order represents the quantization value of Q(1,0) and Q(0,1). The second order represents Q(2,0), Q(1,1), and Q(0,2). For each frequency order, the same quantization value is assigned to them.Due to the large size of these new256
×
256 quantization values, it is not possible to present the whole quantization matrix within a limited space in this paper. Therefore, the 256
×
256 quantization values are presented by traversing the quantization table on each frequency order in zigzag pattern as shown in Table 1. Table 1 presents one-dimensional index of quantization table on each frequency order. Each index represents the quantization value at those frequency orders. The new finer quantization tables from psychovisual threshold on 256
×
256 DCT for luminance and chrominance are shown in Tables 2 and 3, respectively. The visualization of the whole quantization values on each frequency order from the psychovisual threshold for luminance and chrominance channels is depicted in Figure 5.Table 1
The index of quantization value on each frequency order.
0
1
5
6
14
15
27
28
44
45
65
66
90
91
119
120
152
153
189
190
230
231
275
2
4
7
13
16
26
29
43
46
64
67
89
92
118
121
151
154
188
191
229
232
274
276
3
8
12
17
25
30
42
47
63
68
88
93
117
122
150
155
187
192
228
233
273
277
318
9
11
18
24
31
41
48
62
69
87
94
116
123
149
156
186
193
227
234
272
278
317
319
10
19
23
32
40
49
61
70
86
95
115
124
148
157
185
194
226
235
271
279
316
320
357
20
22
33
39
50
60
71
85
96
114
125
147
158
184
195
225
236
270
280
315
321
356
358
21
34
38
51
59
72
84
97
113
126
146
159
183
196
224
237
269
281
314
322
355
359
392
35
37
52
58
73
83
98
112
127
145
160
182
197
223
238
268
282
313
323
354
360
391
393
36
53
57
74
82
99
111
128
144
161
181
198
222
239
267
283
312
324
353
361
390
394
423
54
56
75
81
100
110
129
143
162
180
199
221
240
266
284
311
325
352
362
389
395
422
424
55
76
80
101
109
130
142
163
179
200
220
241
265
285
310
326
351
363
388
396
421
425
450
77
79
102
108
131
141
164
178
201
219
242
264
286
309
327
350
364
387
397
420
426
449
451
78
103
107
132
140
165
177
202
218
243
263
287
308
328
349
365
386
398
419
427
448
452
473
104
106
133
139
166
176
203
217
244
262
288
307
329
348
366
385
399
418
428
447
453
472
474
105
134
138
167
175
204
216
245
261
289
306
330
347
367
384
400
417
429
446
454
471
475
492
135
137
168
174
205
215
246
260
290
305
331
346
368
383
401
416
430
445
455
470
476
491
493
136
169
173
206
214
247
259
291
304
332
345
369
382
402
415
431
444
456
469
477
490
494
507
170
172
207
213
248
258
292
303
333
344
370
381
403
414
432
443
457
468
478
489
495
506
508
171
208
212
249
257
293
302
334
343
371
380
404
413
433
442
458
467
479
488
496
505
509
209
211
250
256
294
301
335
342
372
379
405
412
434
441
459
466
480
487
497
504
510
210
251
255
295
300
336
341
373
378
406
411
435
440
460
465
481
486
498
503
252
254
296
299
337
340
374
377
407
410
436
439
461
464
482
485
499
502
253
297
298
338
339
375
376
408
409
437
438
462
463
483
484
500
501Table 2
The quantization value on each frequency order for luminance.
16
12
9
9
7
7
7
7
7
7
7
7
8
8
9
9
11
11
16
16
23
23
34
11
9
8
8
7
7
7
7
7
7
7
8
8
9
9
11
11
16
16
23
23
34
34
10
8
8
7
7
7
7
7
7
7
8
8
9
9
11
11
15
16
23
24
34
35
47
8
8
7
7
7
7
7
7
7
8
8
9
9
11
12
15
16
22
24
33
35
46
47
8
7
7
7
7
7
7
7
7
8
8
9
11
12
15
16
22
24
33
35
46
47
58
7
7
7
7
7
7
7
7
8
8
9
11
12
15
17
22
24
33
35
46
48
58
58
7
7
7
7
7
7
7
8
8
9
11
12
15
17
22
25
33
36
45
48
58
59
66
7
7
7
7
7
7
8
8
9
11
12
15
17
22
25
32
36
45
48
57
59
66
66
7
7
7
7
7
8
8
9
10
12
15
17
21
25
32
36
45
48
57
59
66
66
68
7
7
7
7
8
8
9
10
12
15
17
21
25
32
37
45
49
57
59
65
66
68
68
7
7
7
8
8
9
10
12
14
17
21
26
32
37
44
49
57
60
65
66
68
69
65
7
7
8
8
9
10
13
14
18
21
26
32
37
44
49
56
60
65
67
68
69
66
65
7
8
8
10
10
13
14
18
21
26
31
37
44
50
56
60
65
67
68
69
66
65
56
8
8
10
10
13
14
18
20
26
31
38
43
50
56
60
65
67
68
68
66
64
57
56
8
10
10
13
14
18
20
27
31
38
43
50
56
61
64
67
68
68
66
64
57
55
42
10
10
13
14
18
20
27
31
38
43
51
56
61
64
67
68
68
66
64
58
55
43
41
10
13
14
18
20
27
31
39
42
51
55
61
64
67
68
68
67
64
58
54
44
40
27
13
14
19
20
28
31
39
42
51
55
61
64
67
68
68
67
63
59
53
45
39
28
26
13
19
20
28
30
39
42
52
55
62
64
68
68
68
67
63
59
53
46
38
29
24
19
19
29
30
39
41
52
55
62
63
68
68
68
67
63
60
52
47
37
30
20
19
29
30
40
41
53
55
62
63
68
68
68
67
62
60
51
48
36
31
29
30
40
41
53
54
62
63
68
68
68
68
62
61
51
48
35
32
30
40
41
54
54
62
63
68
68
68
68
61
61
50
49
34
33Table 3
The quantization value on each frequency order for chrominance.
17
13
10
9
9
8
8
8
8
8
9
9
10
10
12
12
17
18
27
27
43
44
68
12
10
9
9
8
8
8
8
8
9
9
10
10
12
12
17
18
27
28
43
44
67
69
11
9
9
8
8
8
8
8
9
9
9
10
12
12
17
18
26
28
42
45
67
69
97
9
9
8
8
8
8
8
9
9
9
10
12
12
17
18
26
28
42
45
66
70
96
97
9
8
8
8
8
8
9
9
9
10
12
13
16
18
26
29
41
46
66
70
95
98
123
8
8
8
8
8
9
9
9
10
11
13
16
19
26
29
41
46
65
71
94
99
123
124
8
8
8
8
9
9
9
10
11
13
16
19
25
29
40
47
65
72
94
99
122
125
142
8
8
9
9
9
9
10
11
13
16
19
25
30
40
47
64
72
93
100
122
125
142
143
8
9
9
9
9
10
11
13
16
19
25
30
40
48
64
73
92
101
121
126
142
143
149
9
9
9
9
10
11
13
16
20
24
30
39
48
63
73
92
102
121
126
141
143
149
150
9
9
9
10
11
13
15
20
24
31
39
49
63
74
91
102
120
127
141
144
149
150
143
9
9
10
11
14
15
20
24
31
38
49
62
75
91
103
119
128
141
144
149
150
143
142
9
10
11
14
15
21
24
32
38
50
62
75
90
104
119
129
140
145
149
150
145
141
122
11
11
14
15
21
23
32
37
50
61
76
89
105
118
129
140
145
149
149
144
141
123
121
11
14
15
21
23
32
37
51
61
77
89
105
118
130
139
145
149
149
145
140
124
119
89
14
14
21
23
33
37
52
61
77
88
106
118
130
139
146
149
149
145
140
126
118
91
87
14
22
23
33
36
52
60
78
87
107
117
131
138
146
149
149
146
139
127
116
93
84
48
22
23
33
36
53
60
79
86
108
116
131
138
146
149
149
146
138
128
115
95
82
51
46
22
34
35
54
59
79
85
109
116
132
137
147
149
149
146
137
129
113
97
79
54
43
34
35
55
59
80
85
109
115
132
136
147
149
149
147
137
130
112
99
77
57
41
35
56
58
81
84
110
114
133
136
147
149
148
147
136
131
110
101
74
60
56
58
81
83
111
114
134
135
148
149
148
148
135
132
108
103
72
63
57
82
83
112
113
134
135
148
149
148
148
134
133
107
105
69
66Figure 5
The256
×
256 DCT quantization table for luminance and chrominance for image compression.These new finer256
×
256 quantization tables have been generated from the psychovisual threshold functions in (7). Each traversing array in zigzag pattern represents the quantization value on each quantization order from order 0 to order 510. This new smoother 256
×
256 quantization table for luminance is designed to take smaller value than a quantization table for chrominance. Any slight changes on respective frequency order in the luminance channel will generate significantly greater reconstruction error than a change in chrominance channel. The slight changes by the image intensity on the luminance channel will provide visible textures that can be perceived by human visual systems.The contribution of the frequency signals to the reconstruction error is mainly concentrated in the low frequency order. Referring to Figure1, the SPL values on frequency from 2 kHz to 5 kHz are significantly lower. These quantization tables follow the same pattern in order to capture the concept of the psychoacoustic absolute hearing threshold. The quantization values from the psychovisual threshold on chrominance channel are designed to be larger than the quantization values on luminance channel. The human visual system is less sensitive to the chrominance channels as they provide significantly irrelevant image information. The smoother quantization tables will be tested and verified in image compression.


## 5. Quality Measurement

Two statistical evaluations have been conducted in this research project to verify the performances of psychovisual threshold in image compression. In order to gain significantly better performance, the image compression algorithm needs to achieve a trade-off between average bit rates and quality image reconstruction. The conventional quality assessments are employed in this paper. They are average absolute reconstruction error (ARE), means square error (MSE), and peak signal to noise ratio (PSNR). The average reconstruction error can be defined as follows:(8)
ARE
(
s
)
=
1
MNR
∑
i
=
0
M
-
1
∑
j
=
0
N
-
1
∑
k
=
0
R
-
1
g
(
i
,
j
,
k
)
-
f
(
i
,
j
,
k
)
,where the original image size M
×
N
×
R refers to the three RGB colors. The MSE calculates the average of the square of the error defined as follows [21]: (9)
MSE
=
∑
i
=
0
M
-
1
∑
j
=
0
N
-
1
∑
k
=
0
R
-
1
g
(
i
,
j
,
k
)
-
f
(
i
,
j
,
k
)
2
.The standard PSNR is used and calculated to obtain the measure of the quality of the image reconstruction. A higher PSNR means that the image reconstruction is more similar to the original image [22]. The PSNR is defined as follows:(10)
PSNR
=
20
lo
g
10
Max
⁡
i
MSE
=
10
lo
g
10
25
5
2
MSE
,where Max
⁡
i is the maximum possible pixel value of the image. Structural similarity index (SSIM), another measurement of image quality, is a method to measure quality by capturing the similarity between original image and compressed image [23]. The SSIM is defined as follows:(11)
SSIM
x
,
y
=
l
x
,
y
α
·
c
x
,
y
β
·
s
x
,
y
γ
,where α
>
0, β
>
0, γ
>
0 are parameters to adjust the relative importance of the three components. The detailed description is given in [23].


## 6. Experimental Results

This quantitative experiment has been conducted to investigate the performance of a psychovisual threshold on the large image block. The new finer256
×
256 quantization tables have been generated from the psychovisual threshold on 256
×
256 DCT. They are tested on 40 real and 40 graphical high fidelity images. An input image consists of 512
×
512 colour pixels. The RGB image components are converted to YCbCr color space. In this experiment, each image is divided into 256
×
256 image block pixels; thus each block is transformed into 256
×
256 DCT. The DCT coefficients are quantized by new finer 256
×
256 quantization tables from psychovisual threshold. The frequency distribution of the transformed coefficients after the quantization process is summarised by histograms in Figures 6 and 7. The histogram of the frequency distribution is obtained after quantization processes. Figures 6 and 7 show a histogram of the frequency distribution after quantization process of 8
×
8 default JPEG quantization tables and 256
×
256 quantization tables from psychovisual threshold for luminance and chrominance, respectively.Figure 6
Frequency distribution of the alternating current (AC) coefficients using8
×
8 DCT quantization (a) and 256
×
256 DCT quantization from psychovisual threshold (b) on luminance for 40 real images.
(a)
(b)Figure 7
Frequency distribution of the alternating current (AC) coefficients using8
×
8 default JPEG quantization tables (a) and 256
×
256 DCT quantization from psychovisual threshold (b) on chrominance for 40 real images.
(a)
(b)The compression rate focuses mainly on the contribution of the AC coefficients to image compression performance. The frequency coefficients after quantization process consist of many zeros. The frequency distribution of the AC coefficients given by its histogram may predict the compression rate. The higher zeros value on the histogram of frequency distribution means that the image compression output provides lower bit rate to present an image.According to Figures6 and 7, the distribution of the frequency coefficients after the quantization process by smoother 256
×
256 quantization tables from psychovisual thresholds produces significantly more zeros for both luminance and chrominance channels, respectively. These finer quantization tables produce a smaller standard deviation on AC coefficients from the large 256
×
256 image block than the small 8
×
8 image block. Hence, it is possible to code large transformed block using smaller number of bits for the same image.The256
×
256 transform coding consists of 65535 AC coefficients for each regular block. Most AC coefficients are naturally small coming out of quantization process. The psychovisual threshold on large DCT determines an optimal contribution of the AC coefficients of large transform coding. The new 256
×
256 quantization tables from psychovisual threshold are able to reduce down the irrelevant AC coefficients. The distribution of the transform coefficients gives an indication on how much transform coefficients will be encoded by a lossless Huffman coding.An average Huffman code is calculated from the quantized transform coefficients. After the transformation and quantization of256
×
256 image block are over, the direct current (DC) coefficient is separated from the AC coefficients. The AC coefficients are listed as a traversing array in zigzag pattern as shown in Figure 8.Figure 8
Zigzag order of256
×
256 image block.Next, run length encoding is used to reduce the size of a repeating coefficient in the sequence of the AC coefficients. The coefficient values can be represented compactly by simply indicating the coefficient value and the length of its run wherever it appears. The output of run length coding represents the symbols and the length of occurrence of the symbols. The symbols and variable length of occurrence are used in Huffman coding to retrieve code words and their length of code words. Using these probability values, a set of Huffman code of the symbols can be generated by Huffman tree. Next, the average bit length is calculated to find the average bit length of the AC coefficients.There are only four DC coefficients under regular256
×
256 DCT. The maximum code length of the DC coefficient is 16 bits. The DC coefficients are reduced down by 4 bits. The average bit length of the DC coefficients produces 12 bits after the quantization process in image compression. The average bit length of image compression based on default 8
×
8 JPEG quantization tables and the finer 256
×
256 quantization tables from psychovisual threshold is shown in Table 4. The experimental results show the new large quantization tables from psychovisual threshold produce a lower average bit length of Huffman code than the default JPEG quantization tables.Table 4
Average bit length of Huffman code of image compression using 8 × 8 JPEG compression and 256 × 256 JPEG compression using psychovisual threshold for 40 real images and 40 graphical images.
Average bit length of Huffman code
8 × 8 JPEGcompression
256 × 256 JPEGcompression
40 real images
40 graphic images
40 real images
40 graphic images
DC luminance
5.7468
5.6722
12
12
DC chrominance Cr
2.7941
3.8663
12
12
DC chrominance Cb
3.1548
4.0730
12
12
AC luminance
2.8680
2.9653
2.3031
2.6582
AC chrominance Cr
2.0951
2.5059
1.2931
2.1450
AC chrominance Cb
2.1845
2.5158
1.3656
2.1855The DCT coefficients from a large image block have been greatly discounted by quantization tables in image compression. An optimal amount of DCT coefficients is investigated by reconstruction error and average bit length of Huffman code. The effect of incrementing DCT coefficient has been explored from this experiment. The average reconstruction error from incrementing DCT coefficients is mainly concentrated in the low frequency order of the image signals.The new256
×
256 quantization table from the psychovisual threshold produces a lower average bit length of Huffman code in image compression as shown in Table 4. At the same time, the compressed output images produce a better quality image reconstruction than the regular 8
×
8 default JPEG quantization tables as listed in Table 5. The new design on quantization tables from psychovisual threshold performs better by producing higher quality in image reconstruction at lower average bit length of Huffman code.Table 5
The average image reconstruction error using 8 × 8 JPEG compression and 256 × 256 JPEG compression using psychovisual threshold for 40 real images and 40 graphical images.
Image measurement
8 × 8 JPEGcompression
256 × 256 JPEG compression
40 real images
40 graphic images
40 real images
40 graphic images
ARE
5.535
5.648
5.074
5.050
MSE
70.964
92.711
51.841
59.625
PSNR
31.190
31.636
32.363
33.421
SSIM
0.956
0.957
0.961
0.960The average bit size of image compression as presented in Table6 shows that the finer 256
×
256 quantization tables from psychovisual threshold use fewer bits. Therefore, the compression ratio of the difference between a compressed image from the new large quantization table and the original image produces a higher compression ratio than standard JPEG image compression as shown in Table 7. In order to observe the visual quality of the output image, a sample of original baboon right eye is zoomed in to 400% as depicted on the right of Figure 9.Table 6
The average bit size of 8 × 8 JPEG compression and 256 × 256 JPEG compression using psychovisual threshold.
8 × 8 JPEG compression
256 × 256 JPEG compression
40 real images
40 graphic images
40 real images
40 graphic images
230.997 Kb
258.394 Kb
158.792 Kb
223.652 KbTable 7
The average compression ratio score of 8 × 8 JPEG compression and 256 × 256 JPEG compression using psychovisual threshold.
8 × 8 JPEG compression
256 × 256 JPEG compression
40 real images
40 graphic images
40 real images
40 graphic images
3.3247
2.9722
4.8365
3.4339Figure 9
Original baboon image (a) zoomed in to 400% (b).
(a)
(b)The image compression output of256
×
256 quantization table from psychovisual threshold is shown on the right of Figure 10. A visual inspection on the output image using 256
×
256 quantization tables from psychovisual threshold produces the richer texture on the baboon image. The psychovisual threshold on 256
×
256 image block gives an optimal balance between the fidelity on image reconstruction and compression rate. The experimental results show that the psychovisual threshold on large DCT provides minimum image reconstruction error at lower bit rates. The JPEG image compression output as depicted on the left of Figure 10 contains artifact image or blocking effect under regular 8
×
8 block transform coding. At the same time, the smoother 256
×
256 quantization tables from psychovisual threshold manage to overcome the blocking effects along the boundary blocks. These finer 256
×
256 quantization tables from psychovisual threshold provide high quality image with fewer artifact images. The psychovisual threshold is practically the best measure of an optimal amount of transform coefficients to the image coding.Figure 10
The comparison of visual outputs between8
×
8 JPEG quantization table (a) and 256
×
256 quantization tables from psychovisual threshold (b) zoomed in to 400%.
(a)
(b)


## 7. Conclusion

This research project has been designed to support large block size in a practical image compression operation in the near future. A step-by-step procedure has been developed to produce psychovisual threshold on256
×
256 block transform. The use of the psychovisual threshold on a large image block is able to overcome the blocking effect or artifact image which often occurs in standard JPEG compression. The psychovisual threshold on discrete transform has been used to determine an optimal amount of frequency transform coefficients to code by generating the much needed quantization tables. Naturally, a frequency transform on large image block is capable of reducing redundancy and better exploiting pixel correlation within the image block. The new set of quantization tables from psychovisual threshold produces better performance than JPEG image compression. These quantization tables from psychovisual threshold practically provide higher quality images at lower bit rate for image compression application.



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*Source: 821497-2015-03-22.xml*