IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 14, NO. 8, AUGUST 2005 1033 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 artifacts. The method employs odd tile sizes ( samples) rather than the conventional even tile sizes ( samples). It is 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. Index Terms—Boundary artifacts, image coding, JPEG2000, wavelet transforms. I. INTRODUCTION T 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 intro- duces distortion. This distortion becomes especially pronounced along the tile boundaries [2]. The problem of tile-boundary ar- tifact reduction has been addressed by several post-processing and detiling techniques [3]–[6]. However, these techniques re- duce the tile-boundary artifacts at the cost of increased compu- tational 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 publica- tion 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 Univer- sity of New South Wales, Australian Defence Force Academy, Canberra ACT 2600, Australia (e-mail: j.wei@adfa.edu.au; m.pickering@adfa.edu.au; m.frater@adfa.edu.au; j.arnold@adfa.edu.au; j.boman@adfa.edu.au). 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 In this paper, a close examination of the wavelet transform is carried out and it is shown that the boundary artifacts are an in- escapable consequence of the method used to choose the data length and the symmetric extension of the data for decomposi- tion. 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 arti- facts can be reduced using an odd data length. In Section IV, results are presented showing the improvement in MSE and sub- jective quality when using the technique. Section V shows how the technique can be implemented in JPEG2000. Finally, con- clusions are drawn in Section VI. II. BOUNDARY ARTIFACTS IN EVEN LENGTH DATA A. Wavelet Transform 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 high- pass filtered versions of the input signal. The outputs of the de- composition filters are then subsampled by a factor of two to produce a critically sampled set of subband samples. The sub- sampling adopted in JPEG2000 follows the low-pass first con- vention 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 odd- indexed 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 sam- ples 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 symmetri- cally extended about the first and last samples before performing 1057-7149/$20.00 © 2005 IEEE