IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 9, NO. 4, APRIL 2000 577 Motion Estimation Using Low-Band-Shift Method for Wavelet-Based Moving-Picture Coding Hyun-Wook Park, Senior Member, IEEE, and Hyung-Sun Kim Abstract—The discrete wavelet transform (DWT) has several advantages of multiresolution analysis and subband decomposi- tion, which has been successfully used in image processing. How- ever, the shift-variant property is intrinsic due to the decimation process of the wavelet transform, and it makes the wavelet-domain motion estimation and compensation inefficient. To overcome the shift-variant property, a low-band-shift method is proposed and a motion estimation and compensation method in the wavelet do- main is presented. The proposed method has a superior perfor- mance to the conventional motion estimation methods in terms of the mean absolute difference (MAD) as well as the subjective quality. The proposed method can be a model method for the mo- tion estimation in wavelet domain just like the full-search block matching in spatial domain. Index Terms—Block matching, discrete wavelet transform (DWT), low-band-shift, motion estimation and compensation, wavelet block. I. INTRODUCTION T HE DISCRETE wavelet transform (DWT) has received considerable attentions in the field of image processing due to its flexibility in representing nonstationary image sig- nals and its ability in adapting to human visual characteristics [1]. It is closely related to multiresolution analysis and subband decomposition, which has been successfully used in image pro- cessing for a decade [2]–[4]. The wavelet transform decomposes a nonstationary signal into a set of multiresolutional wavelet coefficients where each component becomes relatively more stationary and hence easier to code. Also, coding schemes and parameters can be adapted to the statistical properties of each wavelet coefficient, thereby im- proving the coding efficiency. In subband coding, the frequency band of an image signal is decomposed into a number of sub- bands by a bank of bandpass filters. Each subband is then deci- mated and encoded separately. For reconstruction, the subband signals are decoded and expanded back to the original frequency band by interpolation. The subband-coding approach provides a signal-to-noise ratio comparable to the transform-coding ap- proach and yields a superior subjective perception due to the lack of the blocking effect. In video coding, several types of interframe predictions [5], [6] have been used to reduce the interframe redundancy. Motion- compensated prediction has been used as an efficient scheme Manuscript received March 20, 1998; revised August 19, 1999. The associate editor coordinating the review of this manuscript and approving it for publica- tion was Prof. Steven D. Blostein. The authors are with the Department of Electrical Engineering, Korea Ad- vanced Institute of Science and Technology, Taejon 305-701, Korea (e-mail: hwpark@athena.kaist.ac.kr). Publisher Item Identifier S 1057-7149(00)02683-X. for temporal prediction. In order to perform the motion com- pensation in the wavelet domain, block matching can be ap- plied to the wavelet coefficients. There have been many attempts to predict the wavelet coefficients by motion compensation in the wavelet domain [7]–[11]. However, motion compensation in the wavelet domain is highly dependent on the alignment of the signal and the discrete grid chosen for the analysis. There exist very large differences between the wavelet coefficients of the original image and the one-pixel-shifted image [12], [13]. This shift-variant property happens frequently around the image edges, so motion compensation of the wavelet coefficients can be difficult. To overcome the shift-variant property of the wavelet trans- form, a new method is presented for motion estimation and compensation in the wavelet domain. For motion estimation and compensation in the wavelet domain, the reference frame is shifted by one pixel along the , the , and the diagonal di- rections, respectively, in the spatial domain. The shifted frames are transformed to the wavelet domain for motion estimation. These shift and wavelet-transform processes are named the low- band-shift method. The next-level low-band-shift operations are repeated iteratively to the low–low band of each level. This low-band-shift method avoids the shift-variant property of the wavelet transform and performs the motion compensation more precisely and efficiently. This paper is organized as follows: Section II briefly reviews the motion estimation and compensation in the spatial domain and the wavelet domain. Section III describes the proposed mo- tion estimation and compensation scheme for overcoming the shift-variant property. Comparative studies of the various mo- tion compensation techniques for wavelet-based coding are pre- sented in Section IV. Finally, conclusions are given in Section V. II. MOTION ESTIMATION AND COMPENSATION IN SPATIAL AND WAVELET DOMAINS A. Motion Estimation and Compensation in Spatial Domain Video compression standards, such as MPEG-1 and MPEG-2, use a two-dimensional (2-D) discrete cosine trans- form (DCT) to reduce the spatial redundancy and use a block-matching algorithm to reduce the temporal redundancy [5]. However, block-based coding suffers from blocking effects, in particular, in low-bitrate applications. In wavelet-based video coding [14], a motion estimation can be performed in the spatial domain, which is just the block- based motion estimation introduced in the MPEG standards. However, the block-based motion estimation often produces dis- continuities between the motion-compensated blocks because 1057-7149/00$10.00 © 2000 IEEE