**1. Introduction**

22 Advances in Wavelet Theory and Their Applications in Engineering, Physics and Technology

Wu, M., Wei, J., Shih, H. & Ho, C.C. (2009). "2-Level-Wavelet-Based License Plate Edge

*Conference on* , vol.2, no., pp.385-388, 18-20.

Detection," *Information Assurance and Security, 2009. IAS '09. Fifth International* 

With the big evolution in the quantity of video data issued from an increased number of video applications over networks such as the videophone, the videoconferencing, and multimedia devices such as the personal digital assistants and the high-definition cameras, it has become crucial to reduce the quantity of video data which will be stored or transmitted. In fact, since the capacity of the storage Medias has become high and sufficient, the data storage problem was resolved but the transmission of the data remains an important problem especially with the limited channel bandwidth.

Actually, the necessity of the development of an efficient video coding method has made video compression a fundamental task for video-based digital communications. Video compression reduces the quantity of video data by eliminating the spatial and the temporal redundancy. Spatial compression is done by transforming video frames and representing them otherwise using the spatial correlation between frames pixels. In the other side, motion estimation and compensation are employed in video coding systems to remove temporal redundancy while keeping a high visual quality. They are the most important parts of the video coding process since they require the most computational power and the biggest consumption in resources and bandwidth. Therefore, many techniques have been developed to estimate motion between successive frames.

Motion estimation and compensation (ME/MC) was conducted in many domains such as spatial domain by applying it directly on images pixels without any transformation, the frequency domain by driving it on the Discrete Cosine Transform (DCT) or the Discrete Fourier Transform (DFT) coefficients. It can be also done in the multiresolution domain by running it on the Discrete Wavelet Transform (DWT) coefficients. However, giving the promising performances of the multiresolution analysis especially the DWT which provides a multiresolution expression of the signal with localization in both space and frequency, many methods have been developed to construct a wavelet based video coding system (Shenolikar, 2009) and the DWT was integrated in new coding standards such as JPEG2000, MPEG-4, and H.264. Furthermore, recently, many motion estimation and compensation systems (BEN AOUN, 2010) have also confirmed that the DWT is the most suitable and the most efficient domain that gives efficient and precise motion estimation.

For this, we have developed a block based ME/MC method in the wavelet domain. Our method exploits the benefits of DWT and the hierarchical relationship between its subbands

Wavelet Transform Based Motion Estimation and Compensation for Video Coding 25

The DWT decomposes the image into different subbands, as shown in Figure.2, aiming to isolate the high frequencies that are not interesting to the human eyes. So, we will have the most important information concentrated in the subband LL of the highest level called also

The Figure.3 bellow shows the decomposition of the Foreman image into three level of DWT. This example illustrates clearly that the DWT approximation presents the most significant information that the human eyes are sensible to. The others subbands (DWT

details) give the high frequencies existing in the image along different orientations.

(a) Original image (b) DWT decomposition

Fig. 3. Three levels DWT decomposition applied to Foreman

DWT approximation (LL3 in the Fig.2).

Fig. 2. Different DWT subbands (3 levels)

(Quadtree) to drive ME/MC on wavelet coefficients, especially in the low frequency subband where we find the most significant visual information. This method is consolidated by several techniques to ameliorate the results. With this method, we have achieved good results in terms of prediction quality, compression performance and computational complexity.

The goal of this chapter is to introduce new motion estimation and compensation system based on the DWT which has given better and superior results compared with others systems conducted in spatial or frequency domains. Our system is also based on the Block Matching Algorithm (BMA) which is the simplest, the most efficient and the most popular technique for motion estimation and compensation. Additional techniques are introduced to accelerate the estimation process and improve the prediction quality. In Section 2, we introduce the multiresolution domains and especially the DWT as a multiresolution description for the image which has proved its efficiency for ME/MC. Section 3 presents the motion estimation principle and methods focusing on the DWT based systems. Section 4 describes our DWT and BMA based proposed method. In Section 5, we will introduce some supplementary techniques which have been developed to improve our method and give the main causes which have made of them crucial parts for an efficient motion estimation system. In Section 6, we evaluate our method and compare it to others conventional methods conducted in different domains. This will prove that our method outperforms conventional method in many terms. Finally, Section 7 summarizes the key findings and suggests future research possibilities. We should mention that, along this chapter, when we say motion estimation, we imply implicitly the motion compensation.

## **2. Wavelet transform domain**

The wavelet transform, as a multiresolution domain that hybrid the frequency and the spatial domain, has proved that it is a very appropriate and reliable domain for a powerful motion estimation and compensation. For this, we have been encouraged to study and exploit it, and more precisely the DWT, in our motion estimation system.

The DWT consists on applying hierarchically low-pass (L) and high-pass (H) filters after decimation (sub-sampling the image on two parts). This procedure is repeated until reaching a prefixed level. Figure.1 shows the decomposition of an image with DWT. In this example there are two levels of DWT decomposition.

Fig. 1. DWT decomposition (2 levels)

The DWT decomposes the image into different subbands, as shown in Figure.2, aiming to isolate the high frequencies that are not interesting to the human eyes. So, we will have the most important information concentrated in the subband LL of the highest level called also DWT approximation (LL3 in the Fig.2).


Fig. 2. Different DWT subbands (3 levels)

24 Advances in Wavelet Theory and Their Applications in Engineering, Physics and Technology

(Quadtree) to drive ME/MC on wavelet coefficients, especially in the low frequency subband where we find the most significant visual information. This method is consolidated by several techniques to ameliorate the results. With this method, we have achieved good results in terms

The goal of this chapter is to introduce new motion estimation and compensation system based on the DWT which has given better and superior results compared with others systems conducted in spatial or frequency domains. Our system is also based on the Block Matching Algorithm (BMA) which is the simplest, the most efficient and the most popular technique for motion estimation and compensation. Additional techniques are introduced to accelerate the estimation process and improve the prediction quality. In Section 2, we introduce the multiresolution domains and especially the DWT as a multiresolution description for the image which has proved its efficiency for ME/MC. Section 3 presents the motion estimation principle and methods focusing on the DWT based systems. Section 4 describes our DWT and BMA based proposed method. In Section 5, we will introduce some supplementary techniques which have been developed to improve our method and give the main causes which have made of them crucial parts for an efficient motion estimation system. In Section 6, we evaluate our method and compare it to others conventional methods conducted in different domains. This will prove that our method outperforms conventional method in many terms. Finally, Section 7 summarizes the key findings and suggests future research possibilities. We should mention that, along this chapter, when we

The wavelet transform, as a multiresolution domain that hybrid the frequency and the spatial domain, has proved that it is a very appropriate and reliable domain for a powerful motion estimation and compensation. For this, we have been encouraged to study and

The DWT consists on applying hierarchically low-pass (L) and high-pass (H) filters after decimation (sub-sampling the image on two parts). This procedure is repeated until reaching a prefixed level. Figure.1 shows the decomposition of an image with DWT. In this

of prediction quality, compression performance and computational complexity.

say motion estimation, we imply implicitly the motion compensation.

exploit it, and more precisely the DWT, in our motion estimation system.

example there are two levels of DWT decomposition.

**2. Wavelet transform domain** 

Fig. 1. DWT decomposition (2 levels)

The Figure.3 bellow shows the decomposition of the Foreman image into three level of DWT. This example illustrates clearly that the DWT approximation presents the most significant information that the human eyes are sensible to. The others subbands (DWT details) give the high frequencies existing in the image along different orientations.

(a) Original image (b) DWT decomposition

Fig. 3. Three levels DWT decomposition applied to Foreman

Wavelet Transform Based Motion Estimation and Compensation for Video Coding 27

window P. However, the block matching is based on minimizing a criterion like the Mean Absolute Error (MAD) or the Mean Square Error (MSE) which is the most common block distortion measure for matching two blocks and it provides more accurate block matching. The MV will be applicable to every pixels of the same block which reduces the

To identify the best corresponding block, the simplest way is to evaluate every block in the reference frame (exhaustive search, ES). But, although this method finds generally the appropriate block, it consumes a high computation time. Hence, others fast searching strategies (Barjatya, 2004) have been developed where search is done in a particular order. There are the Three Step Search (TSS), the Simple and Efficient Search (SES), the Four Step Search (4SS), the Adaptive Rood Pattern Search (ARPS) and the Diamond Search (DS) which has proved to be the best searching strategies coming close to the ES results. So, the DS was improved in many variants such as the Cross DS (CDS), the Small CDS (SCDS) and the New

In conventional coding systems such as H.261 and MPEG-1/2, BMA is conducted directly on frame which needs a large computing power. That is why many studies have been made and proved that it is better to transform the frame before executing the ME techniques. However, with the development of new video coding standards, wavelets have received an important interest since it has shown good and effective results. The main idea behind wavelet is to generate a space-frequency representation focusing only on the spatial frequencies that are most significant to the human eye. This wavelet decomposition is a reversible procedure which is performed by successive approximations of the initial information (original frame). This process, will improve the coding efficiency since the wavelet coefficients are much correlated and this representation reduces the blocking effects

Initially, the DWT was used to encode the MVs and the estimation errors after conducting the motion estimation in the spatial or the frequency domains (Figure.4.a). Thereafter, given that the DWT is a spatial-frequency representation for the image that concentrates the most important information in one subband (DWT approximation subband) and since the different DWT subbands are hierarchically correlated, the DWT was used as a domain to

conduce the motion estimation and it has shown a great success.

 (a) Conventional ME + DWT based MVs and ME errors encoding

Fig. 4. Video coders based on DWT

(b) Motion estimation in the wavelet

domain

computational requirement.

CDS (NCDS).

especially in the edges.

The fact that the DWT approximation contains the most of the information issued from the original image was encouraging to benefit of this DWT propriety. For this, the motion estimation was conducted principally in this subband which accelerates the motion estimation process.

The discrete wavelet transform (DWT) as a powerful tool for signal processing has found its application in many areas of research. Image compression is still one of the most successful applications in which the DWT has been applied. So, it is natural that researchers are interested in creating a DWT based new technologies for video compression and motion estimation (Kutil, 2003).
