Tile-Boundary Artifact Reduction Using Odd Tile Size ... - IEEE Xplore

IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 14, NO. 8, AUGUST 2005

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Tile-Boundary Artifact Reduction Using Odd Tile Size and the Low-Pass First Convention Jianxin Wei, Member, IEEE, Mark R. Pickering, Member, IEEE, Michael R. Frater, Member, IEEE, John F. Arnold, Senior Member, IEEE, John A. Boman, and Wenjun Zeng, Senior Member, IEEE

Abstract—It is well known that tile-boundary artifacts occur in wavelet-based lossy image coding. However, until now, their cause has not been understood well. In this paper, we show that boundary artifacts are an inescapable consequence of the usual methods used to choose tile size and the type of symmetric extension employed in a wavelet-based image decomposition system. This paper presents a novel method for reducing these tile-boundary samples) artifacts. The method employs odd tile sizes ( samples). It is rather than the conventional even tile sizes ( shown that, for the same bit rate, an image compressed using an odd tile length low-pass first (OTLPF) convention has significantly less boundary artifacts than an image compressed using even tile sizes. The OTLPF convention can also be incorporated into the JPEG 2000 image compression algorithm using extensions defined in Part 2 of this standard.

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Index Terms—Boundary artifacts, image coding, JPEG2000, wavelet transforms.

In this paper, a close examination of the wavelet transform is carried out and it is shown that the boundary artifacts are an inescapable consequence of the method used to choose the data length and the symmetric extension of the data for decomposition. We will show in the next section that simply changing the length of the input data sequence will eliminate these boundary artifacts and, hence, the need for any post-processing techniques. Section II describes the cause of boundary artifacts in data with even length. Section III shows how these boundary artifacts can be reduced using an odd data length. In Section IV, results are presented showing the improvement in MSE and subjective quality when using the technique. Section V shows how the technique can be implemented in JPEG2000. Finally, conclusions are drawn in Section VI. II. BOUNDARY ARTIFACTS IN EVEN LENGTH DATA

I. INTRODUCTION

A. Wavelet Transform

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HE DISCRETE wavelet transform (DWT) has gained wide application in image compression algorithms in recent years and has recently been adopted as the transform method in the JPEG 2000 image compression standard [1]. If there are no memory restrictions, the wavelet transform is usually performed on a whole image. However, when the amount of memory available for the transformation is limited, one solution is to partition the input image into tiles and then process each tile independently. Dividing the input image into tiles also allows the use of different coding techniques for separate regions in compound documents and different levels of compression for separate regions of interest in the image. In a lossy image compression system, quantization, which typically follows the transformation procedure, inevitably introduces distortion. This distortion becomes especially pronounced along the tile boundaries [2]. The problem of tile-boundary artifact reduction has been addressed by several post-processing and detiling techniques [3]–[6]. However, these techniques reduce the tile-boundary artifacts at the cost of increased computational complexity at the decoder.

Manuscript received February 9, 2003; revised January 8, 2004. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. David S. Taubman. J. Wei, M. R. Pickering, M. R. Frater, J. F. Arnold, and J. A. Boman are with the School of Electrical Engineering, University College, The University of New South Wales, Australian Defence Force Academy, Canberra ACT 2600, Australia (e-mail: [email protected]; [email protected]; [email protected]; [email protected]; [email protected]). W. Zeng was with Sharp Labs of America, Camas, WA 98607 USA. He is now with the Department of Computer Science, University of Missouri-Columbia, Columbia, MO 65201 USA. Digital Object Identifier 10.1109/TIP.2005.849772

The wavelet transform is essentially a subband filtering process as shown in Fig. 1. Since the two-dimensional (2-D) DWT is typically a combination of a horizontal and vertical one-dimensional (1-D) DWT, in the following examples, we use the 1-D DWT. The input data signal is filtered to produce low-pass and highpass filtered versions of the input signal. The outputs of the decomposition filters are then subsampled by a factor of two to produce a critically sampled set of subband samples. The subsampling adopted in JPEG2000 follows the low-pass first convention which mandates that the low-pass subband samples are formed from the even-indexed output samples of the low-pass filter and high-pass subband samples are formed from the oddindexed output samples of the high-pass filter. These subband samples then form the representation of the signal in the wavelet transform domain and are sometimes referred to as the wavelet coefficients of the data signal. To produce the reconstructed data signal, the subband samples are first upsampled by a factor of two and then filtered to produce reconstructed low-pass and high-pass versions of the original signal. The outputs of the reconstruction filters are then summed to produce the final reconstructed signal. The two-channel decomposition process can be repeated on the low-pass subband samples of a previous filtering stage to provide a multiresolution decomposition of the original signal. For 2-D data, such as images, 1-D wavelet transforms in the horizontal and vertical directions are typically applied. In order to keep the number of subband samples the same as the number of input data samples, the input data is symmetrically extended about the first and last samples before performing

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Fig. 1.

One-dimensional, single-level wavelet decomposition and reconstruction process.

TABLE I FILTER COEFFICIENTS FOR THE 5/3 WAVELET TRANSFORM

Consider the following set of eight data points:

A single-level wavelet decomposition process would then produce the following sets of subband samples:

For analysis purposes, it is convenient to interleave these lowpass and high-pass samples to give the following sequence: the wavelet transformation. With symmetrically extended data, the resulting subband samples are also symmetrical and only those samples that correspond to the nonextended data are required to reconstruct the original signal. In JPEG2000, a whole sample symmetric extension is used to extend the data. For example, if the input data is

then a whole sample extension would give

By representing the subband samples as a single sequence, we can think of the wavelet transform as a mapping from the input data sequence to a sequence of subband samples. For an even number of input samples, one end of the sample sequence must be a high-pass sample and the other end must be a low-pass sample. Furthermore, if we are following the lowpass first convention, then the start of the sequence is a low-pass sample and the end of the sequence is a high-pass sample. Now, let these subband samples be quantized using deadzone scalar quantization with a central quantization interval that is double the width of all other intervals. This is the quantization process used in JPEG2000 and can be defined by (1)

For a more detailed explanation of wavelet transforms for image compression and, in particular, the use of wavelet transforms in the JPEG2000 standard, see [7]. The focus of this paper is the analysis and reduction of the so-called boundary artifacts that occur at the edges of reconstructed images when wavelet transforms are used to perform lossy image compression. These boundary artifacts are particularly noticeable when the image is divided up into tiles that are coded as separate images. The boundary artifacts result from an increase in the error between the reconstructed and original images for samples close to the edge of a tile. To determine the cause of this increased error we investigate the error introduced by the lossy compression process at the edge of a 1-D signal that has been coded using the 5/3 wavelet transform. The filter coefficients for the 5/3 transform are given in Table I. The coefficients of and correspond to decomposition filters with a nominal gain of 1 in accordance with the convention adopted in the JPEG2000 standard. Part 1 of the JPEG2000 standard allows two wavelet transforms: the 9/7 and the 5/3 transform. To simplify the analysis, we consider only the 5/3 transform but the process is easily extendable to the 9/7 transform and other commonly used wavelet filter sets.

is the subband sample in subband , is the where quantization index, is the quantizer step-size, and the function is defined by if if if

(2)

After the inverse quantization process, the reconstructed subband samples in subband are given by (3) where is usually set to . The reconstructed subband samples can then be expressed as (4) is the error between the original subband sample where and the reconstructed sample caused by the quantization process. B. Boundary Artifact Analysis Now, let us analyze how this quantization error affects the reconstructed data. To do this, we will investigate in detail the

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reconstructed data errors at three different positions in the output data sequence. 1) Middle of the Sequence: First, consider an odd-indexed reconstructed data value where the region of support for the reconstruction filters does not include any extended subband samples. If the output data has an odd-index this means that a high-pass subband sample coincides with the center coefficient of the reconstructions filters. which is given by For this case, we choose

(5) Now, leaving out the zero-valued reconstructed samples introduced by the upsampling process and applying (4), we can rewrite this equation to give

(6) The quantization error associated with any particular subband sample effectively has a random value. If we are to qualitatively analyze the nature of this quantization error, we need to observe a large number of these error values and observe the statistical properties of this sample population. . First, let us look at a typical probability distribution for To do this, we generated approximately 50 000 sets of eight data values by picking random starting positions in the 512 512 Lena image and taking the eight consecutive sample values along the row to the right of the starting position. A single-level wavelet decomposition process was then performed on these data sets. The resulting subband samples were then quantized and inverse quantized using (1) and (3) with a step-size of 16. The quantized subband samples were then used to produce sets of reconstructed data values. The low-pass subband samples will have a uniform probability distribution with values ranging from minus half the quantizer step-size to plus half the quantizer step-size. For such a distribution, it is well known that the mean will be zero and the standard deviation is given by

Fig. 2. Probability distribution for the quantization error in high-pass subband samples.

The means of the distributions shown in Fig. 2 are zero, but, unlike the distributions for the low-pass errors, the standard deviation for the high-pass errors depends on the original data values. The higher the correlation between successive data values, the lower the standard deviation will be for the high pass subband samples and consequently the lower the standard deviation of the high-pass quantization errors. So a very “smooth” image will have many small high-pass subband samples, and, hence, the standard deviation of the high-pass quantization errors will be smaller than in an image which has many “sharp edges.” Using this information we have gathered on the statistical properties of the sample quantization errors, we can determine an approximation for the standard deviation of the errors in the reconstructed data. Taking the error terms from (6), we can deas fine the quantization error for

(8) To find an approximation for the standard deviation of , we can use the following formulae for the standard deviation of the sum of two uncorrelated random variables [8]:

(7)

(9)

The probability distributions for the quantization error in the high-pass subband samples are shown in Fig. 2. From Fig. 2, we can see that the error in the high-pass sample at the end of the sequence has a different distribution to all other high-pass has a larger standard deviation errors. The distribution of than the distributions of the other high-pass errors because has a larger standard deviation than the other high-pass subband samples. In other words, the magnitudes of are, on average, larger than the magnitudes of the other high-pass subband samis caused by the mechaples. This increase in the values of nism for extending the original data set. The whole sample symmetric extension is effectively introducing extra high frequency energy into the data values at the end of the data set.

In (9), and are the standard deviations of two uncorreis the standard deviation of the lated random variables and sum of these two variables. So using (9), the standard deviation can be approximated by of

(10) where is the standard deviation for the error in any low-pass subband sample and is the standard deviation for the error in

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any high-pass subband sample that is not at the end of the data set. Then, using (7), we can rewrite this equation to give (11) 2) End of the Sequence: Now, consider the odd-indexed reconstructed data value at the end of the data, which is given by

(12) Leaving out the zero-valued reconstructed samples and applying (4), we can rewrite this equation to give (13) Then, using (7) and (9), the standard deviation of approximated by

can be

(14) is the standard deviation of the error in the high-pass where sample at the end of the data set. There are two things to note from (14). First, because of the symmetric extension, the low-pass quantization errors conare no longer uncorrelated and produce a larger tributing to than for . Second, the standard deviation value for of the error for the high-pass sample at the end of the data set is larger than for the other high-pass errors also resulting in a than for . larger value for 3) Start of the Sequence: Now, consider the even-indexed reconstructed data value at the start of the data set, which is given by

(15) Leaving out the zero-valued reconstructed samples and applying (4), we can rewrite this equation to give (16) Then, using (7) and (9), the standard deviation of approximated by

can be

Fig. 3. Estimated and actual values of the error standard deviation for 50 000 sets of data from the 512 512 Lena image (Q = 16,  = 3:38, and  = 4:36).

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the actual values for the data obtained from the 512 512 Lena image. The results of this comparison are shown in Fig. 3. From Fig. 3, we can also see typical values for the standard deviation of the errors in the reconstructed data. Particularly noticeable is the large standard deviation for the data value at the end of the sequence. This large standard deviation results in larger errors for values at the end of the reconstructed data sequence. However, this is not the end of the problem. A typical wavelet decomposition consists of multiple levels where the input samples for each level are the low-pass samples from the previous level. So, now, let us consider the error at the end of the sequence when a two-level wavelet transform is performed. 4) Multilevel Transforms: From (13), we know that the is given by quantization error for (18) will be reFor a two-level transform, the low-pass sample constructed from a previous wavelet transform. So, the standard can be approximated by deviation for (19) where is the standard deviation of the high-pass samples that are not at the end of the second-level sample sequence and is the standard deviation of the high-pass sample at the end is given by of the second-level sequence. So, using (19),

(17) will be smaller than since From (14), we can see that is less than for the contribution of the high-pass errors to and does not include the larger errors for the high-pass sample at the end of the data set. To assess the accuracy of these approximations for typical image values, we used similar methods to analyze the remaining five data positions. We then compared the estimated values to

(20) Then, from (20), we can see that, because the second-level sample sequence will have a high-pass sample at the same end as the first-level sequence, the larger quantization errors at the end of the sequence accumulate as successive levels of the reconstruction process are performed.

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Fig. 4. Values of the error standard deviation for a single-level (l = 1) and two-level (l = 2) wavelet transform performed on 50 000 sets of data from the 512 512 Lena image.

Fig. 5. Values of the error standard deviation for a two-level wavelet decomposition using an odd data length of 9 and an even data length of 8 performed on 50 000 sets of data from the 512 512 Lena image.

Alternatively, for a two-level transform, the standard deviation for the error at the start of the sequence is given by

and use the low-pass first convention when subsampling the subband samples. We will refer to this approach as the odd tile length low-pass first (OTLPF) convention.

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(21) Fig. 4 shows the standard deviation of the reconstruction errors when a single-level and two-level wavelet transform is performed on the data obtained from the 512 512 Lena image. From Fig. 4, we can see that the errors at the end of the reconstructed data sequence tend to be larger than those at the start of the sequence. We have demonstrated that these larger errors are caused by the symmetric extension at the end of the sample sequence that contains a high-pass sample. We can also see from Fig. 4 that the problem is compounded for multilevel transforms when the length of the sequence is . If this is the case, there is a high-pass sample at given by the end of the sample sequence produce by every level of the decomposition process. III. TILE-BOUNDARY ARTIFACT REDUCTION USING ODD DATA LENGTHS One way to avoid producing a high-pass sample at the end of every sample sequence is to choose an odd data length given rather than an even data length of . This case is by illustrated in Fig. 5, where the data length has been extended to nine values rather than the previous eight. , we Fig. 5 shows that, by choosing a data length of avoid the problems caused by symmetrically extending around a high-pass sample at all levels. Consequently, the standard deviation of the reconstruction errors at the end of the sequence is significantly reduced. If the previous analysis is conducted using the 9/7 transform, similar results are obtained. These results are illustrated in Fig. 6(b), which shows the error standard deviation values when using a four-level 9/7 transform on both even and odd-length data sets. For comparison, Fig. 6(a) shows error standard deviation values when using a four-level 5/3 transform on both even and odd-length data sets. The solution we are proposing, to reduce tile-boundary artifacts in wavelet coded images, is to use an odd tile size given by

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IV. TILE-BOUNDARY ARTIFACTS IN JPEG2000 As demonstrated above, tile-boundary artifacts occur in lossy, wavelet-based image coding when even tile sizes are used. As it is a wavelet-based coding system, the base model of the JPEG2000 standard (i.e., JPEG2000 Part 1) suffers from these artifacts. In this section, the tile-boundary artifact problems of JPEG2000 Part 1 are demonstrated and a novel method to reduce these tileboundary artifacts is presented. This method is based on the theory presented in the previous sections. A. Tile-Boundary Artifacts in JPEG2000 Part 1 Fig. 7 shows the mean-square errors (MSEs) for each row and column of the reconstructed image of the 512 512 Lena image compressed at a bit rate of 0.5 bits-per-pixel using JPEG2000 Part 1 [1]. Tile sizes of 64 64 were used and the tiles can be distinguished as alternating light and dark sections in the plots. In the down-sampling process, low-pass coefficients were kept in the far left column and top row of each tile. Since the tile sizes are even, high-pass coefficients populate the far right column and bottom row of each tile. Large MSE spikes at the tile boundary can be seen in both plots. These spikes are associated with the right and bottom sides of each tile, indicating that there are large errors in each tile’s far right and bottom sides. B. Odd Tile Size As we have seen in the previous section, one way to avoid these errors on the tile boundary associated with high-pass coefficients is to locate low-pass coefficients along all four sides of the tile. This can be achieved by using an odd tile size. Fig. 8 shows a plot of the MSE for the same Lena image compressed at 0.5 bits-per-pixel but with a tile size of 65 65. Now, instead of a MSE spike associated with one side of a tile boundary, in the two plots for the rows and columns, there are now large MSE spikes along two sides of every second tile in both plots. The result of this effect is a “good tile” such as

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Fig. 6. Values of the error standard deviation for 50 000 sets of data from the 512 (a) the 5/3 transform and (b) the 9/7 transform.

2 512 Lena image. A four-level wavelet decomposition was performed using

the “good tile,” however, is a “bad tile” such as the second tile in both of the plots, where there are large MSE spikes associated with both sides of the tile boundary. C. OTLPF

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Fig. 7. Average MSE for each row and column of the 512 512 Lena image after compression at a bit rate of 0.5 bits-per-pixel using JPEG2000 Part 1 with a tile size of 64 64.

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Fig. 8. Average MSE for each row and column of the 512 512 Lena image after compression at a bit rate of 0.5 bits-per-pixel using JPEG2000 Part 1 with a tile size of 65 65.

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the first tile in both of the plots, where the boundary MSE is about the same magnitude as the interior of the tile. Following

This good-tile/bad-tile effect is caused by the canvas coordinate system used in JPEG2000. In the JPEG2000 standard, the input image is positioned in a 2-D space called the canvas and the location of each pixel in this space is specified using the canvas coordinate system. This means that each pixel has a corresponding canvas coordinate. This canvas coordinate determines the subsampling to be used. Low-pass samples must be located on even canvas coordinates and high-pass samples on odd canvas coordinates regardless of the tile and image position in the canvas coordinate system (for a more detailed explanation of the canvas coordinate system, see [7]). Thus, if the first column of the first tile is located on an even canvas coordinate, then the last column will end on an even coordinate as well due to the odd tile size. Hence, this tile starts and ends with low-pass samples. It has already been demonstrated that this will reconstruct a good tile without a large MSE rise at the tile boundary. However, the second tile, having its first and last columns located on odd canvas coordinates, therefore, has high-pass samples located at both the left and right sides of the tile boundary. Hence, a large MSE will be produced on both left and right hand sides of the tile. As discussed in the previous section, the MSE at the tile boundary is reduced if the proposed OTLPF convention is used. Fig. 9 shows a plot of the MSE for the Lena image reconstructed using the OTLPF convention with tile sizes of 65 65. In the down-sampling process, the subsampling convention enforced by the canvas coordinate system was ignored and low-pass coefficients were kept in the far left column and top row of each tile (the next section describes how to implement the OTLPF convention while still complying with the subsampling imposed by the canvas coordinate system). The benefits of the OTLPF convention are not dependent on the choice of image, tile size or compression factor. Using the standard even tile size approach always results in large errors 512 Lena occurring at tile boundaries. Results for the 512 image coded at 0.25 bits-per-pixel are shown in Figs. 10 and 11,

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Fig. 9. Average MSE for each row and column of the 512 512 Lena image after compression at a bit rate of 0.5 bits-per-pixel using JPEG2000 Part 1 with the OTLPF convention and a tile size of 65 65.

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Fig. 10. Average MSE for each row and column of the 512 512 Lena image after compression at a bit rate of 0.25 bits-per-pixel using JPEG2000 Part 1 with a tile size of 64 64.

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Fig. 12. Average MSE for each row and column of the 512 512 Lena image after compression at a bit rate of 1.0 bits-per-pixel using JPEG2000 Part 1 with a tile size of 64 64.

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Fig. 13. Average MSE for each row and column of the 512 512 Lena image after compression at a bit rate of 1.0 bits-per-pixel using JPEG2000 Part 1 with the OTLPF convention and a tile size of 65 65.

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with results for 1.0 bit-per-pixel shown in Figs. 12 and 13. It can be seen, in both high and low bit-rate cases, that using the OTLPF convention has significantly reduced the error at the tile boundary compared to the traditional coding approach of even tile sizes. Figs. 14–17 show plots of the MSE of the Café image coded at 0.5 bits-per-pixel but with different tile sizes. Results for the traditional coding approach using even sized tiles are shown 64 tiles) and Fig. 16 (256 256 tile). Alin Fig. 14 (64 though tile sizes are quite different, large MSE spikes occur at the tile boundaries in both cases. Results using the OTLPF convention with tile sizes 65 65 and 257 257 are shown in Figs. 15 and 17, respectively. The improvement in the MSE at tile boundaries in both cases is clear.

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Fig. 11. Average MSE for each row and column of the 512 512 Lena image after compression at a bit rate of 0.25 bits-per-pixel using JPEG2000 Part 1 with the OTLPF convention and a tile size of 65 65.

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D. Subjective Results Boundary artifacts often form a significant proportion of the perceived degradation introduced by image compression. It has

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Fig. 14. Average MSE for each row and column of the Cafe image after compression at a bit rate of 0.5 bits-per-pixel using JPEG2000 Part 1 with a tile size of 64 64.

Fig. 16. Average MSE for each row and column of the Cafe image after compression at a bit rate of 0.5 bits-per-pixel using JPEG2000 Part 1 with a tile size of 256 256.

Fig. 15. Average MSE for each row and column of the Cafe image after compression at a bit rate of 0.5 bits-per-pixel using JPEG2000 Part 1 with the OTLPF convention and a tile size of 65 65.

Fig. 17. Average MSE for each row and column of the 512 512 Lena image after compression at a bit rate of 0.5 bits-per-pixel using JPEG2000 Part 1 with the OTLPF convention and a tile size of 257 257.

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been demonstrated that the implementation of the OTLPF convention can greatly reduce the MSE associated with samples at tile boundaries. The difference in subjective quality is illustrated in Figs. 18 and 19, which show a reconstructed Lena image compressed at 0.25 bits-per-pixel using JPEG2000 Part 1 with a tile size of 64 64 (Fig. 18) and the OTLPF convention with a tile size of 65 65 (Fig. 19). V. OTLPF WITH SINGLE-SAMPLE OVERLAP From the previous section, we can see that using the OTLPF convention significantly reduces the errors at the tile boundaries. However, simply using the OTLPF convention conflicts with the subsampling enforced by the canvas coordinate system. As discussed previously, using the canvas coordinate system dictates that low-pass samples must be located on even canvas coordinates and high-pass samples on odd canvas coordinates. To use the OTLPF convention, and also meet this requirement, an overlap method is employed. Tiles are now overlapped by one

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sample with neighboring tiles to the right and bottom of the tile currently being coded. A decoder conforming to the core coding system of the JPEG2000 standard is not required to allow this type of tile overlap. However, a tile overlapping system (known as the single-sample overlap or SSO technique) is defined in Part 2 of the standard, which describes optional extensions to the core coding system [9]. As a result of this overlap, odd tile sizes can be used with the top left sample of every tile located at an even coordinate in the canvas system. Fig. 20 shows the row and column MSE results for the OTLPF convention when using this overlap technique. By comparing Figs. 9 and 20, we can see that there is a very small improvement in the MSE of samples at the tile boundaries when using the SSO technique. This is not surprising since we have shown that it is the odd tile size, not overlapping the tiles, that causes the reduction in MSE at the tile boundary. However, the tile overlapping technique must be implemented in order to comply with the subsampling convention imposed by the JPEG2000 canvas coordinate system.

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Fig. 20. Average MSE for each row and column of the 512 512 Lena image after compression at a bit rate of 0.5 bits-per-pixel using JPEG2000 Part 2 with the OTLPF convention, SSO, and a tile size of 65 65.

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Fig. 18. Decoded 512 512 Lena image after compression at a bit rate of 0.25 bits-per-pixel using JPEG2000 Part 1 with a tile size of 64 64.

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Fig. 19. Decoded 512 512 Lena image after compression at a bit rate of 0.25 bits-per-pixel using JPEG2000 Part 1 with the OTLPF convention and a tile size of 65 65.

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The proposed method is very simple and involves no changes to the wavelet transform. This method not only reduces tileboundary artifacts but also reduces the bit rate needed for a given PSNR in a compressed image. Table II shows the PSNR for all of the methods discussed. It can be seen that overall there is a 0.1 to 0.3-dB improvement for the new technique. It should be pointed out that this is a comparison of the PSNR for the entire image. Our new approach only reduces errors for the samples at the tile boundary and these samples correspond to a small fraction of the total number of samples in the image. Hence, a

TABLE II PSNR VERSUS BITS/PIXEL FOR THE 512

2 512 LENA IMAGE

significant reduction in the errors at the tile boundary is required to affect the PSNR of the entire image. The slight reduction in PSNR for the overlap technique is due to the extra bits required to code the overlapping samples. VI. CONCLUSION It has been demonstrated that using the proposed OTLPF convention provides a simple method to significantly reduce coding artifacts at tile boundaries in wavelet-based image compression. This reduction can be observed in subjective results and in the PSNR of decoded images regardless of the size of the tiles and the compression factor. The technique can also be incorporated into the JPEG 2000 image compression algorithm using extensions defined in Part 2 of this standard.

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REFERENCES [1] JPEG 2000 Image Coding System, Part 1: Core Coding System. [2] N. C. Kim, I. H. Jang, D. H. Kim, and W. H. Hong, “Reduction of blocking artifact in block-coded images using wavelet transform,” IEEE Trans. Circuits Syst. Video Technol., vol. 8, no. 3, pp. 253–257, Jun. 1998. [3] B. Jeon and J. Jeong, “Blocking artifacts reduction in image compression with block boundary discontinuity criterion,” IEEE Trans. Circuits Syst. Video Technol., vol. 8, no. 3, pp. 345–357, Jun. 1998. [4] H. Paek, R.-C. Kim, and S.-U. Lee, “On the POCS-based postprocessing technique to reduce the blocking artifacts in transform coded images,” IEEE Trans. Circuits Syst. Video Technol., vol. 8, no. 3, pp. 358–367, Jun. 1998. [5] C. M. Brislawn, “Symmetric Extension Transforms,” in Wavelet Image and Video Compression, P. N. Topiwala, Ed. Boston, MA: Kluwer, 1998. [6] K. Berkner and E. L. Schwartz, “Removal of tile artifacts using projection onto scaling function for JPEG 2000,” presented at the IEEE Int. Conf. Image Processing, Rochester, NY, Sep. 2002. [7] D. S. Taubman and M. W. Marcellin, JPEG2000: Image Compression Fundamentals, Standards and Practice. Boston, MA: Kluwer, 2002. [8] R. G. Brown and P. Y. C. Hwang, Introduction to Random Signals and Applied Kalman Filtering, 3rd ed. New York: Wiley, 1997. [9] JPEG 2000 Image Coding System, Part 2: Extensions.

Jianxin Wei (M’97) received the B.Sci. degree in semiconductor engineering and the M.Sci degree in nuclear physics from Hunan University, Hunan, China, in 1981 and 1986, respecitvely, and the Ph.D. degree from the Australian National University, Canberra, in 1993. Since 1993, he has been with the Australian Defence Force Academy, Canberra, excluding the period from 1994 to 1996, when he was a Researcher at the University of Manchester, Manchester, U.K. His current research interests are image and video coding/compression, processing, transmission, video object segmentation, pattern recognition, remote sensing, and satellite oceanography. He has been an active contributor to the JPEG 2000 image coding standard.

Mark R. Pickering (M’96) received the B.E. degree from the Capricornia Institute of Advanced Education, Rockhampton, Australia, in 1988 and the M.E. and Ph.D. degrees in electrical engineering from the University of New South Wales, Sydney, Australia, in 1991 and 1995, respectively. He is currently a Senior Lecturer with the School of Information Technology and Electrical Engineering, Australian Defence Force Academy, Canberra, Australia. His research interests include video and audio coding, data compression, information security, data networks, and error-resilient data transmission.

Michael R. Frater (S’89–M’91) was born in Sydney, Australia, in 1965. He received the B.Sc. degree in mathematics and physics and the B.E. (Hons.) degree in electrical engineering from the University of Sydney, Sydney, Australia, in 1986 and 1988, respectively, and the Ph.D. degree from the Australian National University, Canberra, in 1991. He is currently an Associate Professor in the School of Information Technology and Electrical Engineering at the University College, University of New South Wales, Australian Defence Force Academy, Canberra. His research interests include aspects of the coding and transmission of video services, teletraffic and queuing theory, stochastic processes, signal processing, and control. Dr. Frater has served as an Associate Editor of the IEEE TRANSACTIONS ON IMAGE PROCESSING.

John F. Arnold (S’77–M’85–SM’96) received the B.E. and M.Eng.Sc. degrees from the University of Melbourne, Melbourne, Australia, in 1976 and 1979, respectively, and the Ph.D. degree from the University of New South Wales, Sydney, Australia, in1984. Since 1978, he has been with the University of New South Wales, initially at the Royal Military College, Duntroon, Australia, and, more recently, at the Australian Defence Force Academy, Canberra, Australia. He is currently a Professor of electrical engineering and Head of the School of Information Technology and Electrical Engineering, University of New South Wales. His research interests lie in the fields of video coding, error resilience of compressed digital video, and coding of remotely sensed data, and he has published widely in these areas. Prof. Arnold is an Associate Editor of the IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY.

John A. Boman is currently pursuing the M.Eng. degree at the School of Information Technology and Electrical Engineering, Australian Defence Force Academy, Canberra, Australia.

Wenjun Zeng (S’94–M’97–SM’03) received the B.E. degree from Tsinghua University, Beijing, China, in 1990, the M.S. degree from the University of Notre Dame, Notre Dame, IN, in 1993, and the Ph.D. degree from Princeton University, Princeton, NJ, in 1997, all in electrical engineering. He is currently an Associate Professor with the Computer Science Department, University of Missouri-Columbia. From 1997 to 2000, he was with Sharp Labs of America, Camas, WA. He was with PacketVideo Corporation, San Diego, CA, from December 2000 to August 2003, where he was leading R&D projects on wireless multimedia streaming, encoder quality optimization, and digital rights management. His current research interests include multimedia communications and networking, content and network security, and wireless multimedia. He has been an active contributor to the JPEG 2000 image coding standard and the MPEG4 IPMP Extension standard. Dr. Zeng has served as a Technical Program Committee Member, Special Session Chair, and Panel Session Organizer for several IEEE international conferences. He was the Lead Guest Editor of IEEE TRANSACTIONS ON MULTIMEDIA April 2004 Special Issue on Streaming Media published. He is the Technical Program Co-Chair of the Multimedia Communications and Home Networking Symposium, IEEE International Conference on Communications 2005. He is a member of the IEEE COMSOC Multimedia Communications Technical Committee.