**4. Our proposed method**

The motion estimation and compensation are the most important parts in the video coding process. For this, many works have focused on these video coding parts aiming to improve them. But, the results reached still insufficient especially for the real time applications. That is what encourages us to work on these parts and improve them.

The Block Matching Algorithm still one of the most efficient and the most used method for motion estimation since it works directly on image pixels and it accelerates the estimation process by working on pixels blocks. This method suffers like all others methods from some problems such as the Blocking effect (discontinuity across block boundary) in the predicted image. But, we have overcome this problem in our system with several motion estimation improvement techniques.

Thanks to its proprieties and its suitability as a domain to apply motion estimation and compensation, the multiresolution domain has been adopted in our system to conduce the motion estimation directly on its coefficients. Among the method to obtain a multiresolution representation for the image, we have the DWT that has proved its efficiency not only for data compression but also for motion estimation.

Exploiting the hierarchical relationship between the wavelet coefficients of the different subbands in different levels, different hierarchical ME methods were developed which are adapted to the wavelet transformation. The hierarchical relationship gives that every wavelet coefficients has four descendants in the lower level of the DWT. The motion estimation is conduced hierarchically so that it is calculated firstly in one of the DWT level

In fact, there are two main ME categories of approaches for DWT based: forward and backward approaches. The forward approach consists on conducting the ME in the DWT details subbands of the low level and using it to determine the motion in the higher level subbands (coarse-to-fine). Researchers like Meyer and al (Meyer, 1997) have followed the forward approach to propose a ME method with a new pyramid structure. They have taken the aliasing effect, caused by the BMA used, into consideration and build a ME system given a good perceptual quality after MC. Also, P.Y Cheng and al (Cheng, 1995) has proposed a multiscale forward ME working on the DWT coefficients. They have built a new pyramidal

Nosratinia and Orchard (Nosratinia, 1995) were the first researchers who developed a ME system based on DWT following a backward approach (coarse-to-fine) where they estimated the motion in the finest DWT resolution (higher level) and then progressively refined the ME by incorporating the finer level. Furthermore, Conklin and Hemami (Conklin, 1997) have proved the superiority of the backward ME approach over the forward one in terms of compression rate and visual quality after compensation. This is what encourages more recent researchers (Lundmark, 2000; Yuan, 2002) to follow this approach in

The effectiveness of the BMA and the suitability of the DWT in the video coding, have led us to develop a block matching based motion estimation method in the wavelet domain.

The motion estimation and compensation are the most important parts in the video coding process. For this, many works have focused on these video coding parts aiming to improve them. But, the results reached still insufficient especially for the real time applications. That

The Block Matching Algorithm still one of the most efficient and the most used method for motion estimation since it works directly on image pixels and it accelerates the estimation process by working on pixels blocks. This method suffers like all others methods from some problems such as the Blocking effect (discontinuity across block boundary) in the predicted image. But, we have overcome this problem in our system with several motion estimation

Thanks to its proprieties and its suitability as a domain to apply motion estimation and compensation, the multiresolution domain has been adopted in our system to conduce the motion estimation directly on its coefficients. Among the method to obtain a multiresolution representation for the image, we have the DWT that has proved its efficiency not only for

and it is corrected with the estimation obtained, thereafter, at the others levels.

structure overcoming the shift variant problem of the DWT.

is what encourages us to work on these parts and improve them.

their ME systems.

**4. Our proposed method** 

improvement techniques.

data compression but also for motion estimation.

The proposed method makes use of the wavelet properties to apply the motion estimation directly in the wavelet coefficients. We have adopted the fine-to-coarse motion estimation strategy which has shown its success by many previous works. After applying the DWT on both CF and RF, the motion is estimated firstly between the DWT approximations of the two images. So, we have provided a better estimation since the approximation contains the most visual information. The motion vectors of the approximation are directly calculated. We have exploited that every DWT coefficient has four descendants in the lower DWT level (Quadtree structure). So, the motion vectors of the details subbands are deducted using the hierarchical relationship that exists between the DWT subbands as shown in Figure 5. We compute the motion vectors of the details subbands following this formula:

$$V\_{i,j} = \mathbf{2}^{L-i} V\_{L,1}(\mathbf{x}, y) + \delta\_{i,j} \tag{1}$$

Working on a three level DWT (L=3), we will have i={1, 2, 3} which is the level, j={1, 2, 3, 4} representing the subband number, Vi,j(x, y) is the motion vector for the subband "j" at the level "i" and *i*, *<sup>j</sup>* is the refinement factor (equal to 0 if "i" is equal to L). The displacement of every subband block is the double of the displacement of the same subband block in the lower DWT level where we add to it a refinement factor *i*, *<sup>j</sup>* which correct the estimation error as given in the equation and presented in the Figure above.

Fig. 5. DWT subbands motion vectors representation (L=3)

Moreover, by predicting the motion only in the approximation which has a small size compared to the original frame and contains the most significant information, not only the

Wavelet Transform Based Motion Estimation and Compensation for Video Coding 31

This temporal segmentation based moving zones detection has allowed us to estimate the motion only on limited zones. Thereby, this technique will reduce the computational time of the ME process and gives a more precise estimation with the assumption that the motion vectors of the blocks which are out of the detected zones will have a null value. This gain is

Block based motion estimation assumes that every block have an integer pixel displacement which is, in reality, not true. Therefore, to improve the motion estimation and to increase the accuracy of the prediction, we have moved to sub-pixel precision by developing a sub-pixel technique with a bilinear interpolation process. This is done by interposing a line between each two lines of the image I (see Figure.7) and a column between each two columns of the

The values of the pixels that are in the 1/2 pixel positions are determined relatively to their

Fig. 6. Background subtraction results with the method of Zivkovic

increased if the movement is concentrated in very limited zones.

image. Then, ME is applied to the new image O.

Fig. 7. Bilinear Interpolation for 1/2 pixel precision

neighbouring pixels in the integer positions as follows:

**5.2 Sub-pixel precision** 

computation requirement is highly reduced and the compression ratio is increasing, but also our method maintains a good prediction quality.

The BMA is an efficient method for motion estimation which encourages us to use it in our multiresolution based method. Unfortunately, despite their encouraging proprieties and their promising results, the BMA and DWT suffer from some problems. For this, a several improvement techniques have been implemented to surmount these problems and make our method more robust giving best results.
