Ulas Demir, Semsa Kantaroglu, Ozgur Babur, Gozde Bozdagi
Anil Aksay, Mehmet B. Akhan, University of Hertfordshire, Hatfield, Herts, UK

The idea behind wavelet compression lies in selectively transmitting and reconstructing only those spatial frequencies that are most significant to the eye. Due to this fact, wavelet compression has the best compression rate for 2-D images. However if a sequence of images is to be compressed, temporal correlation must also be utilized to decrease the bit-rate while keeping the visual quality. The aim of this work is to compare several algorithms to code a sequence of images using wavelet transform and evaluate their performances.

The literature on video coding using wavelet transform can be divided into 2 categories: 2-1/2 D and 3 D transforms. 3 D transforms assume the video signal as a 3 D signal in x, y and t and perform transformation in 3 D [1]. These techniques bring complexity and also do not give promising results. In 2-1/2 D wavelet schemes, motion information either in the time or wavelet domain is combined with the 2 D wavelet transform. For time domain motion estimation techniques [2], wavelet transform is applied to motion compensated residue images. This technique distorts the perceptual quality and coding efficiency because of the sharp edges found in the motion compensated residue images. In order to overcome this problem, overlapped block matching techniques can be employed [3], [4]. By this technique, sharp edges found in the residue image disappear, since the algorithm is somewhat averaging the possible candidates for each pixel. Motion estimation in wavelet domain is also possible [5], [6] . In this case, previous and current images are wavelet transformed and in that domain motion estimation and difference is employed. The third possibility is to extract the time-domain motion vectors in wavelet domain. First problem in this scheme is that due to subsampling in wavelet transform. Since the transformation is shift variant, correct time domain motion vectors can not be found in case they are not power of 2 . To make the transform shift invariant, complex wavelet transform is introduced with the cost of redundancy of 4:1 in wavelet coefficients [7], [8]. Thus, this transform enables one to find real valued motion vectors. However, in the case of video compression, the main aim is to decrease the bit-rate while keeping the visual quality high. Due to this fact, motion vectors do not have to match with the correct ones if they decrease the bit-rate. In this work, we do not experiment on the complex wavelet transform due to this fact.

Our results show that by using motion estimation in wavelet domain, we decrease the energy and subsequently the bitrate with the expense of more motion information. Wavelet domain motion estimation performs better than time domain motion estimation in both sequences. Fast motion estimation performs better than motion estimation in sequences having less objects with motion. Entropy of wavelet domain motion estimation is greater than time domain motion vectors, but this is due to the increase in the number of vectors.
Energy (average) Image 1 Image 2 Predictive Error Time domain error wavelet domain error (I)  wavelet domain error (II)
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Entropy of motion vectors (average) Time domain motion vectors wavelet domain vectors (I)  wavelet domain vectors (II) wavelet domain vectors (II)


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