Chapter 5

CHAPTER 6

Chapter 7

A brief but complete and exhaustive introduction to JPEG 2000, that will be discussed in this chapter, is given in appendix D.

6.1. INTRODUCTION

In some previous chapters and in appendices B to D, the concept of wavelets is explained, the benefit introduced by them within the image compression field, and the new image compression standard JPEG 2000 is introduced, compared to other old and more recent standards, and some coding methods on the basis of some pre-constituted test images; the AutoMERS project was also introduced with the images based on this project and their peculiar features. The main idea of this chapter is to compare the JPEG 2000 Standard with some other standards and image coding methods, especially the precursor JPEG, on the base of these AutoMERS images, with the aim of understanding better how much this new standard could be useful from the point of view of this project. In this chapter some kinds of compression are explored, such as lossless compression, downsampling and interpolation. Different operations are developed on different image plane components, from the quality, subjective and objective, point of view; this for obtaining more information as regards test images. An explanation of the AutoMERS-based test images and the software utilised in the tests is done in a previous chapter, and we refer to the explanation in that chapter. Other, more detailed, explanations about some software programs used will be given from time to time in the different sections of that chapter.

6.2. DOWNSAMPLING COMPRESSION

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6.3. STANDARDS AND RESULTS

In this section the three image coding standards and algorithms chosen for the tests are explained in more detail. the decision is to compare the JPEG 2000 standard (which, as mentioned previously, is the most important new image coding standard) with the most widely-used standard, JPEG, and the SPIHT algorithm, as a good example of a wavelet based algorithm. The comparison can be made with these three software programs in both the lossless and lossy cases. In the lossless compression case some applications, WinZip and Gzip, developed for file compression and other standards and methods as JPEG-LS and PNG are also used.
 

Quality	100	99	98	95	90	80	70	60	50	40	30	20	10
C.R.[X:1]	3.24	3.66	4.47	6.86	10.92	18.19	24.39	30.47	36.22	43.59	54.83	76.29	117.53
I.C.R.[1:Y]	0.309	0.273	0.224	0.146	0.0916	0.0550	0.0410	0.0328	0.0276	0.0229	0.0182	0.0131	0.00851
B.R.[bpp]	2.469	2.186	1.790	1.166	0.733	0.440	0.328	0.263	0.221	0.184	0.146	0.105	0.0681

Quality	5	2	/	/	/	/	/	/	/	/	/	/
C.R.[X:1]	145.38	160.41	180	210	250	300	370	450	550	700	850	1000
I.C.R.[1:Y]	0.00688	0.00623	0.005556	0.004762	0.0040	0.003333	0.002703	0.002222	0.001818	0.001486	0.001176	0.0010
B.R.[bpp]	0.0550	0.0498	0.0444	0.03809	0.0320	0.02667	0.02161	0.01778	0.01455	0.01143	0.00941	0.008

6.3.1. JPEG

For the JPEG tests Matlab’s Image Processing Toolbox is used because it allows to transform each bitmap file into a JPEG compressed file using lossy methods with a simple operation that requires only a few Flops. On the other hand, this operation is not very flexible, since it takes only one input parameter: the quality of the compression, Q. This parameter Q is a number in the range of 0 to 100 that permits to modify the quality of the compression algorithm and consequently the compression ratio obtained; higher number means higher quality of the reconstructed image, and therefore less image degradation due to compression. For the tests we have decided to obtain the parameters PSNR, size and compression ratio of each of the 5 images for these 15 different values of the quality parameter Q, chosen to cover a wide range of image quality:

• Q = {100, 99, 98, 95, 90, 80, 70, 60, 50, 40, 30, 20, 10, 5, 2}.

Given that and given the impossibility for the JPEG function in Matlab to act directly on the bit rate, the 15 values of bit rate and compression ratio shown in Table 6.3 are used, as parameter values for the other software applications, such as JPEG 2000 and SPIHT software programs, which allow the use of compression ratio as input parameter. The terms quality, compression ratio and bit rate are used without distinction for this reason, within this and the next sections. A first example of the JPEG compression on test images is shown in Figure 6.4; there is a small part of the original image “Ima3” and its compressed copies with quality values of 100, 90, 80, 60, 30, 10, 5 and 2. From this Figure the visual quality of the image remains very good for the first two compressed images, Q = 100 and 90, where the values of the PSNR is above 32 dB, respectively 35.13 dB and 32.46 dB, and the compression ratio is 3.24 : 1 and 10.92 : 1.

The quality remains good, both from a subjective and objective point of view, for the next three compressed images, with Q equal to 80, 60 and 30 and compression ratio equal to 18.19 : 1, 30.47 : 1 and 54.83 : 1, showing PSNR values between 29.5 and 32 dB, respectively 31.29 dB, 30.42 dB and 29.48 dB. Among these three images the visual quality remains quite good also for the image with Q = 30, in which some little distortion artefacts appear, although it is worse than the other two images. For the last three images of Figure 6.4, with Q = 10, 5 and 2, the quality is beginning to become less acceptable from a visual point of view, because the blocking artefacts introduced by the distortion, are quite annoying and they tend to change the shape of the objects, especially in the last image. For these three reconstructed images the PSNR values are quite low, 27.28 dB, 25.26 dB and 22.71 dB respectively, even if the compression ratio is very high, 117.53 : 1, 145.38 : 1 and 160.41 : 1.

After this first visual evaluation, the PSNR values for all 5 images and their mean are shown in Figure 6.5 with compression ratio as parameter. In this case the PSNR parameter shown is taken as the mean value of the PSNR values of the 3 RGB components of the image; this is valid for all the results of the next sections if not specified to the contrary. From these diagrams one can observe that to have a high visual quality, with PSNR higher than 33 dB or Q higher than 90, the compression ratio will be lower than 11 : 1.

An acceptable visual quality with PSNR in the range roughly 29-32 dB, can be chosen; in this case Q varies between 20 and 80, and the compression ratio goes from 80 : 1 up to 20 : 1. From these results there is clearly a trade-off between desired visual quality desired and compression ratio: for example, the quality can be reduced a little, with a decrement of PSNR of 1 or 2 dB, to gain a lot in compression ratio, and introducing little distortion. Higher value of compression ratio, higher than 80 : 1, can be achieved reducing a lot the quality of the compressed images, dropping to PSNR values of 27 dB and less; this fact is shown in Figure 6.5 and in Table 6.4 both visually and with the PSNR values. From the visual point of view, when the quality of the compression decreases a typical feature of this kind of compression emerges as shown clearly in Figure 6.4: the introduction of block distortion artefacts. Comparison with other compression techniques, as seen in following sections, shows that at the same level of PSNR values this characteristic is most annoying for the human vision and the image looks more distorted. Another feature is clearly shown in the diagram of Figure 6.5: the different range of PSNR values found for the different images at the same compression ratio values. For example for the range of values of quality, RQx, found before, RQ1 = {Q > 90}, RQ2 = {20 < Q < 80} and RQ3 = {Q < 20}, totally different ranges of PSNR values are found for the images “Ima1” and “Ima2”:

• {30.8-32.8}, {28-29.7} and {< 27} for “Ima1”,
• {34-37}, {31-33.5} and {< 30} for “Ima2”.

6.3.2. SPIHT

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6.3.3. JPEG 2000

The third image compression standard used in the test is the JPEG 2000 Standard; a detailed explanation of this standard is in appendix D. The software used in the tests is the JasPer software, a collection of library and application programs written in the C language, used for coding the test images in a JPEG 2000 based mode. There is the possibility with the “Jasper” executable file to code and decode images in lossless compression mode, with a file extension “.JP2” for the compressed file; we have used this mode to develop tests in a way to compare this standard with the other lossless compression standards and applications; the results of this comparison will be placed in the next section in this chapter. There is also obviously the possibility with the same application file to compress colour images in a lossy mode, given the input rate parameter as inverse of compression ratio, saving the compressed files with the extension “.JPC” and obtaining with the “imgcmp” application file the PSNR values compared with the original images.

Figure 6.8 shows, as with Figure 6.4 and 6.6 for JPEG and SPIHT, the original test image and its compressed copies at different compression ratio. The same values of compression ratio are used for all three methods. Until a compression ratio value of 10 : 1 the difference between the reconstructed images and the original remains imperceptible, whereas in the range of compression ratio between 20 : 1 and 80 : 1 the quality of the compressed images decrease a little bit, although remaining very good. For compression ratio values between 80 : 1 and 160 : 1 the images begin to become a little bit blurred, retaining however quite good quality and showing totally the features of the objects within the image. At this point of compression ratio, about 160 : 1, the images from JPEG and SPIHT are distorted and the artefacts introduced are very annoying, but the images from JPEG 2000 stay almost faithful to the original; both from the PSNR and the quality point of view they could be compared at images obtained with JPEG and SPIHT with compression ratio around 40-50 :1.

For this reason it is of interest to increase the compression ratio, looking for limiting values, performing more tests with higher compression ratio, but only with JPEG 2000 software. In Figure 6.9 the images reconstructed from the original “Ima3”, obtained with compression ratio values from 110 : 1 up to 1000 : 1 are shown. As seen in the first two reconstructed images in the range of compression ratio values between 110 : 1 and 200-250 : 1, the visual quality remains good, both from the subjective and the objective point of view, with PSNR values higher than 27 dB. For compression ratio values around 300-400 : 1, as in the third reconstructed image, the quality begins to decrease, with an introduction of even more blurring distortion artefacts and the PSNR values decrease down to 26 dB; in this case the images remain however quite faithful to the original, and this is interesting thinking about the compression performance reachable.

The fourth reconstructed image shows that for values of compression ratio around 500-700 : 1 there is an introduction of ringing-effect distortion artefacts that distort the shape of the objects within the images, but the typical features of the images remain clearly visible; the PSNR values in this case decrease down to 24.5-25 dB. The last image with PSNR of about 23.1 dB and compression ratio of 1000 : 1, shows that the distortion artefacts introduced are annoying, even if the shape of the objects remains quite visible. Comparison of images obtained with JPEG 2000 with images obtained with JPEG and SPIHT for the same PSNR values shows that the quality of the JPEG 2000 reconstructed images is visually better than the others. Adding this feature to the fact that the value of compression ratio is remarkably higher, 1000 : 1 compared to 130 : 1 for JPEG and 400 : 1 for SPIHT, it is possible to see how big is the improvement brought by the JPEG 2000 standard within the image compression field.

The diagram in Figure 6.10 show the curves of the PSNR values for the five images and their mean at different compression ratios, from about 3 : 1 up to 1000 : 1. A first look at this diagram, compared with the two diagrams in Figure 6.7 and 6.5, shows that the PSNR values are on the whole higher than the values found for JPEG and SPIHT; the improvement of the objective and subjective visual qualities is actually the most important feature, as seen previously in this section and as it will be explored in detail during the next sections. The other two features met in the previous sections still remain in this diagram: the possibility to see 3 range of PSNR values and the differences of PSNR values within the ranges for the different images.

Table 6.6 shows the PSNR values of the mean of 5 images for JPEG 2000, JPEG and their difference for different values of compression ratio; whereas the JPEG PSNR values are obtained only for compression ratio lower than 160 : 1, the JPEG 2000 PSNR values are obtained for compression ratio values up to 1000 : 1, so in the last range there is no comparison of values. From Table 6.6, for low values of compression ratio, less than 4 : 1, the PSNR values of JPEG 2000 are higher than the JPEG values, more than 4 dB; incrementing the compression ratio until about 15 : 1, the difference between the PSNR values of the two standards decrease until 0.2-0.5 dB. This difference value remains quite constant until the value of compression ratio of 70 : 1 is reached; the visual quality is good for both standards within this range, even if a comparison of the images with the same PSNR value shows a higher subjective visual quality for the JPEG 2000.

Increasing the value of compression ratio from 70 : 1 up to 160 : 1 the difference values between the two standards increase almost linearly, reaching values of about 6 dB and consequently also the subjective quality becomes even more different. A look of the PSNR values for the JPEG 2000 shows that the decrement of these values with the increment of the compression ratio is almost linear and it does not present unexpected sudden decrement, as happens for the JPEG standard.

6.3.4. LOSSLESS COMPRESSION

6.3.4. LOSSY COMPRESSION

Most of the results obtained in tests, compressing the images in a lossy mode, are already seen within the sections regarding JPEG, 6.3.1, SPIHT, 6.3.2 and JPEG 2000, 6.3.3. In this section with the help of the diagrams shown in the next figures some important aspects, already briefly explained, are underlined, and other interesting features of the tests are found. Figure 6.12 shows the PSNR values obtained for the 3 different methods, on the left, and as differences between SPIHT and JPEG 2000 with JPEG, on the right, as the mean of the values of the 5 test images, for different values of bit rates. All the figures in this section are arranged in the way just described, with on the left the PSNR values of the reconstructed images and on the right the PSNR value differences with the JPEG values, unless otherwise stated. All the PSNR results obtained for the 5 images and their mean, for the 3 different compression methods at various compression ratios are also summarised in Table 6.8.
 

Q	100	99	98	95	90	80	70	60	50	40	30	20	10	5	2
C.R.[X:1]	3.24	3.66	4.47	6.86	10.92	18.19	24.39	30.47	36.22	43.59	54.83	76.29	117.53	145.38	160.41
JPEG	35.44	35.37	35.14	34.02	32.91	32.01	31.56	31.25	31.02	30.75	30.38	29.79	28.50	25.59	23.59
SPIHT	35.13	34.64	33.93	32.76	31.82	31.05	30.67	30.41	30.22	30.02	29.78	29.40	28.86	28.58	28.45
JPEG2000	40.97	39.73	38.16	35.45	33.65	32.38	31.82	31.48	31.25	31.01	30.75	30.37	29.88	29.64	29.53

From Figure 6.12 and Table 6.8, the difference between JPEG 2000 and SPIHT is, almost for every compression ratio value, about 1-1.2 dB, and this value increases at low compression ratio. The difference between JPEG 2000 and JPEG is instead very high, both for low compression ratio, with values higher than 0.8 bpp, and for high compression ratio, values lower than 0.08 bpp, reaching in some points values of more than 4-5 dB; within the range 0.08-0.8 bpp, the difference is instead less than 1 dB. The diagram on the right of Figure 6.12 shows also that for bit rate higher than 0.08 bpp the JPEG standard performs better than SPIHT, but this is only from the PSNR values point of view, because comparing the reconstructed images at the same compression ratio the quality of the SPIHT seems higher.

Another important feature can be obtained from the diagrams: the sudden decreasing of the JPEG PSNR values around compression ratio values of 0.07-0.09 bpp; this feature is typical for the DCT-based standards, because for high compression ratio there are not enough bits to perform a correct DCT transform. Whereas for the JPEG standard there is a sudden worsening of the performance, for the JPEG 2000 the decrease of PSNR values, as in Figure 6.12 for bit rate values higher than 0.05 bpp, continues almost linearly; this trend is also noticed for bit rate values lower than 0.05 bpp until at least 0.008 bpp, and the same trend is visible for subjective quality performances. This is clearly visible in Figure 6.13 where the PSNR values for the 5 images and the mean, for the JPEG 2000 compressed method only, are depicted. Apart from “Ima1”, the slopes of the curves of the different images, having quite different PSNR values, are almost similar. “Ima3”, which has a lot of edges and changes of luminance, has the steepest curve, whereas “Ima1”, which shows the background with less edges and little change of luminance, has the least sloping curve.

6.4. REGION OF INTEREST CODING

6.4.1. INTRODUCTION

In this section an useful functionality of the JPEG 2000 Standard is used: the possibility to compress two parts of the image, the Region of Interest (ROI) and the Background (BG), with different compression ratio and quality; this interesting feature, called ROI Coding, is explained in detail in section D.6. Whereas “JasPer”, the JPEG 2000 codec software used in previous tests, does not have this functionality, “JJ2000”, the software used in this section, give the possibility to perform ROI coding; this software utilises the MAXSHIFT method as default in the bit-plane coding to scale the ROI coefficients, and it defines a ROI within the image in these three different ways:

• As a rectangular shaped area, defined by its upper-left pixel coordinates and its width and height values,
• As a circular shaped area, defined by the coordinates of its centre pixel and the radius value,
• As an arbitrary shaped area, defined by a bi-level-greyscale mask image; its zero values, black coloured, correspond to the BG area, whereas non zero values, usually 255 and white coloured, correspond to the ROI area.

6.4.2. TEST IMAGES AND ROI MASK UTILISED

To perform the ROI coding tests another AutoMERS-based test image, shown in the left part of Figure 6.19 and called “Ima6” is introduced. This image is interesting because it shows a fairly big red object, a life form called “Sea Cucumber”, that stands out from the other parts of the image, formed by the background, the black and white cross, the centre sinker, the brown fish and the white crab. This image is a good example of an object-background image and for this reason it is suitable for ROI coding tests. “Ima6” is 512 ´ 512 sized, 24 bit/pixel RGB colour image, as with all the test images used up to now. In addiction to this new test image, the 5 AutoMERS-based test images, shown in Figure 3.2 has been utilised as in previous experiments.

The tests are developed with, as the ROI mask, three different kind of greyscale ROI mask images, shown in Figure 6.19 and 6.20:

• A greyscale image formed by a rectangular shaped area, square shaped, as shown in the left part of Figure 6.20, where the upper-left corner of the rectangle has pixel coordinates (128,128), and the width and the height have both 256 pixel size; in this way the ROI area has exactly a quarter size compared to the whole image area. In other particular tests various rectangular shaped ROI masks similar to this are used, with different sizes of the rectangle side and area, as shown in Table 6.10,
• A greyscale image formed by a circular shaped area, as depicted in the right part of Figure 6.20, where the centre of the circle has pixel coordinates (256,256) and the radius is 144 pixels; these dimensions are chosen in a way to maintain the ratio between the ROI area size and the whole image area size as approximately a quarter,
• A greyscale image formed by an arbitrary but well defined shaped area, as shown in the right part of Figure 6.19, with the shape of the ROI area coincident with the shape of the red object depicted in “Ima6”; the ratio between the ROI area size and the whole area is, even in this case, about 0.25.

Figure 6.20 : Rectangular shaped, left, and circular shaped, right, ROI Mask bi-level-greyscale images.

The first two kinds of mask, rectangular and circular shaped, are used to perform a ROI coding on the six test images, whereas the third kind of mask, arbitrary shaped, is utilised to perform the ROI coding only on “Ima6” test image. The compression ratio value in the form of bit rate is inserted, as input parameter in the JJ2000 software, both for the ROI coding and the normal coding. In tests this parameter remains in the interval between 3 bpp and 0.008 bpp, and this because under the lower value, compression ratio of 1000 : 1, the ROI parts of the reconstructed images have quality too poor to be considered interesting and useful for our aims.

The reconstructed images obtained from the ROI coding and decoding, give the possibility to extract two different values of the visual quality parameter, PSNR:

• A value of PSNR, as usual, obtained considering the original test image and the whole reconstructed image, called “ROI + BG” in the following diagrams,
• A value of PSNR obtained considering the original test image and only the region of interest area within the reconstructed image, called “ROI” in the diagrams,

Figure 6.21 : Diagram of PSNR values of the reconstructed images from the original “Ima6” image at various bit rates, with and without arbitrary shaped mask ROI Coding.

For each value of bit rate there is a comparison between these two PSNR values with the values obtained from the original test image and the reconstructed images coded in the normal way, without ROI coding, called “JPEG 2000” in the next diagrams.

6.4.3. ARBITRARY SHAPED ROI CODING

The first results seen in this section are the results obtained from the ROI coding with the arbitrary shape ROI mask shown in Figure 6.19; the various PSNR values resulting from this coding are shown in Figure 6.21. Above bit rate values of about 0.7-0.9 bpp, the ROI PSNR values remain very high, about 45 dB, whereas the PSNR values of the total image, “ROI + BG”, decrease rapidly and continuously to a value of 32 dB with an immediate fall down to 20 dB near to those bit rate values. The reason for this trend is that less bits are used to code the BG area, which becomes poorer in quality, while many bits are used to code the ROI area whose quality remains very high. From that bit rate value downwards, the amount of bits used to code the ROI area becomes even smaller and so the PSNR values decrease continuously.

Comparing the PSNR values of “ROI” and “JPEG 2000” curves in Figure 6.21, the latter obtained coding the test image without ROI coding, to obtain the same PSNR value, as long as the quality remains acceptable, the compression ratio shown by the “ROI” values is four times bigger than the “JPEG 2000”; the points A1, A2, B1 and B2, in Figure 6.21 show clearly this feature. Size of the ROI area in the tests with the original image “Ima6” is a quarter of the whole area; this subject will be seen later in this section when some tests using ROI masks with rectangles of different sizes will be performed.

Table 6.9 shows the distribution of bits between ROI and background that the encoder makes during the ROI coding, with the values and the percentage of bits used to code the two different areas; The “JJ2000” software uses the MAXSHIFT coding method, with the bit rate parameter in input; it decides the amount of bit to use for the decoding of the ROI area. It is so possible to count the amount of bits, and their percentage, for both ROI and Background; this number are related to the quality of the reconstructed images, the PSNR values. Above a bit rate of about 0.9 bpp part of the bits amount is used to code the background, to give to it a poor but acceptable quality and this is shown in the first two images, higher-left, of Figure 6.22; this is possible because the amount of bit used to code the ROI is sufficient to give to it a very high quality. From that bit rate value downwards the whole amount of bits are used to code the ROI area with the best quality possible, so no bits are utilised to code the background area.

Comparing the results at low bit rate depicted in Table 6.9 with the images shown in Figure 6.22, in which the reconstructed images at different bit rate are depicted with their compression ratio and PSNR values, it is possible to see that even if no bits are used for the background area, a part of the background is still shown at very low quality. This strange result depends on the building of the ROI mask in the wavelet transform space, and on the method used for the bit plane coding; actually the quality of the image in the background decreases going perpendicularly away from the perimeter of the ROI mask.

Figure 6.22 shows clearly moreover that the visual quality of the ROI remains very good until a compression ratio of 80 : 1, with a PSNR higher than 31 dB and it is still good until 240 :1 with a PSNR value of 29 dB; the quality remains still acceptable up to 480 : 1, where the PSNR remains higher than 27 dB, but the distortion artefacts begin to be visible, and the image begins to become blurred.

6.4.4. RECTANGULAR AND CIRCULAR SHAPED ROI CODING

The second kind of test results shown here are obtained from the coding of the six different test images with a rectangular shaped mask, depicted in Figure 6.20. The curves of the PSNR values from “ROI”, “ROI + BG” and “JPEG 2000”, average of the six images, are depicted in the diagram of Figure 6.23. This diagram is clearly similar to the diagram in Figure 6.21, actually there is an immediate decrement of the “ROI + BG” PSNR values, a stability of the “ROI” PSNR values until bit rate values of about 0.7-0.9 bpp, and a slight decrement after this value; also in this case the same PSNR values are found for a compression ratio four times bigger than “JPEG 2000”, given that the area of the ROI rectangle is a quarter of the whole image. Seeing the curves of the PSNR values of the ROI for the six different test images, depicted in Figure 6.24, for all of them there is a value of PSNR constant until a bit rate value about 0.6-0.9 bpp, depending on the test images, and a slow decrement with the increment of compression ratio after this bit rate value.

The six reconstructed test images for a PSNR of about 38-41 dB, as in Figure 6.25, show that “Ima1”, “Ima3” and “Ima6”, that have a lot of edges and changes of luminance and colour within the ROI area image, need more bits, and so a bit rate higher, to code the ROI area maintaining a similar PSNR value and visual quality, especially “Ima1” that has a big amount of little edges and changes of luminance. “Ima2”, “Ima4” and “Ima5” need less bits to code the ROI, because they have few changes of luminances and they are characterised by large flat white areas within the ROI area, especially “Ima2”: for these reasons they need a bit rate lower than the other images to maintain same PSNR values and visual quality.

From the diagram in Figure 6.24 it is possible to notice this, and also that at the same bit rate value the PSNR difference between different images is quite high, for example about 5-6 dB between “Ima1” and “Ima2”, and so the visual quality between these images within the ROI area at the same compression ratio is very different.

Looking at the diagrams previously depicted and at the results obtained, an interesting test could be done changing the size of the rectangle, the length of the side, that characterise the ROI area; for this reason we have decided to use seven different rectangular shaped ROI masks with seven different side lengths, as shown in Table 6.10, coding the same six test images and using the mean PSNR values. In Table 6.10 the dimensions of the side and of the area are specified, and from these the percentage of the ROI size is calculated, compared to the whole image area and the inverse of this ROI size, not in percentage.

In Figure 6.26 the seven different curves of the PSNR mean values at different bit rate are depicted; decreasing the area of the ROI rectangle there is a decrement of the bit rate values where the PSNR value begin to decrease, and consequently the values of bit rate used to obtain a similar PSNR value. The curves assumes the same appearance with a slow decrement on PSNR values, as they are only translated horizontally. In Figure 6.27 an interesting diagram is depicted: the value of bit rate obtained, related to the ROI area size in percentage, compared to the whole image area, for four different PSNR values.

From this diagram it is clearly possible to notice that there is a linear relation between the size of the ROI area chosen for the coding and the bit rate values necessary to achieve a certain PSNR value and quality; for that reason maintaining the same PSNR and halving the size of ROI, the compression ratio is doubled. This result could be expected and maybe even obvious, thinking about how the JPEG 2000 ROI coding is performed, but the diagram in Figure 6.27 clearly proves it. The same kind of experiments performed with the rectangular ROI mask have been performed with the circular ROI mask shown in Figure 6.20.