Performance Comparison of Image Compression Using Wavelets

This paper describes how the Fractal image coding takes the long time in its computation. It is its block searching and matching which takes long time. So to overcome this, we use the combination of fractal and wavelet this reduces the computation time. Based on this, we proposed an improved fractal image algorithm based on the wavelet subtree. The algorithm proposed improved fractal image compression technique in wavelet domain with thresholding value. This reduces the encoding time effectively. It has big compression ratio and fast decoding but it is ts encoding that takes long time means searching and matching of block makes its long time. The usual approach is based on the collage theorem. 2. DESIGNING OF FRACTAL[7], [5] 2.1. Image Partitions The square support S of The original image is partitioned into nonoverlapping square range cells of two different sizes, thus forming a two level square partitioned. This type of partitioned is closely related to quad-trees. The larger cellsof size B X B-are referred to as (domain) parents, the smaller ones –of size B/2 X B/2-as (range) children. A parent can be split into up to four non overlapping children. The whole process of fractal image encoding is shown in Fig. 1. Fig.1: One of the Block Mappings in a PIFS Representation Firstly, we have to select the image partition scheme for the formation of range blocks, secondly domain block must be selected from the domain pool in such a way domain blocks must be transformed to cover range International Journal of Computer Science & Communication (IJCSC) 98 blocks. Thirdly, the partition scheme used and the type of domain pool used affect the choice of transforms. Fourthly, Then a suitable candidate from all available domain blocks is searched to encode any particular range block. Fifthly, This step of fractal image compression is computationally very expensive. This computational requirement is the biggest limitation of fractal encoding. A wide variety of techniques have been proposed to fasten the process. 3. FRACTAL IMAGE CODING BASED ON WAVELET SUB-TREE[4] Generally signals are processed in time domain, sometimes time and frequency both representations are required. Wavelet analysis is capable of providing the time and frequency information simultaneously, hence giving a time-frequency representation of the signal. Multi resolution is the beauty of the wavelet i.e. different parts of the signal are viewed through different resolutions. Fig.2: DWT in 2D One Stage 2D Analysis Bank Filter hØ(–n) is a low-pass (half-band) filter, whose output wH (j,m,n) is an approximation of the input hØ(–n) ; hØ (–n) is a high-pass (half-band) filter, whose output wØ D (j,m,n) and wØ V(j,m,n)is a high-frequency or detail part of the input h(–n). Synthesis filters h(n) and h(n) combine two subband signals to produce wØ(j + 1, m, n), which is the original signal. In wavelet domain a square in the image is split up into four equal sized subsquares. Below fig.3 gives an idea how an image can be decomposed into four subimages. Fig. 3: Two Stage Decomposition The oriented wavelet sub-tree is a kind of structure with tree shape, it is composed by wavelet coefficients with different resolution same direction and same relative space position. The wavelet coefficients of image after wavelet transform can compose three kinds of oriented wavelet sub-trees: the horizontal direction wavelet sub-tree which has low frequency in horizontal direction and high frequency in vertical direction; the vertical direction wavelet sub-tree which has high frequency in horizontal direction and low frequency in vertical direction; the diagonal direction wavelet sub-tree which has both high frequency in horizontal and vertical direction, shown in Fig.3. 3.1. Wavelet based Fractal Image Coding Algorithm 3.1.1. Encoding Process 1. Take an image as input of size 512 x 512. 2. Calculate (DWT) Haar wavelet up to i = 1, 2,3.......N. levels. 3. For all N levels, divide the H,V,D components of the ith level in to domain blocks of size 2Bx2B and that of (i+1)th level in to range blocks of size BxB. 4. For domain block, find the best matching range block. 5. Save the mapping information i.e. scaling factor and position of the best matched block into a text file. 6. Also save the Nth level approximation component in to the same text file. 7. Transmit this text file as encoded as message. Fig.4 Wavelet Subtree 3.1.2. Decoding Process 1. Read the encoded message file. 2. Take a bitmap image of size 512x512. 3. For all N levels compute (DWT) Haar wavelet of the image and process the H,V,D components with the help of the data in the encoded message file. Performance Comparison of Image Compression Using Wavelets 99 4. Take Inverse Discrete Wavelet Transform (Haar) for all N levels and get the reconstructed image. Repeat the process for k iterations. 3.2. Fractal Image Compression Technique in Wavelet Domain using Threshold Encoding Process can be speeded up if a suitable threshold value for MSE is chosen. This speeds up the encoding process because after getting the suitable value it will stop finding the matches for range blocks and domain blocks. 3.2.1. Encoding Algorithm 1. Take an image as input of size 512x512. 2. Calculate (DWT) Haar wavelet up to i=1, 2, 3.......N. levels. 3. For all N levels, divide the H, V, D components of the ith level in to domain blocks of size 2Bx2B and that of (i+1)th level in to range blocks of size BxB. 4. Choose suitable value for threshold. 5. For every domain block find the matching of range block (depending on threshold value) 6. When the error value is less than the defined threshold value then save the mapping information i.e. scaling factor and position of the best matched block in to a text file. 7. Also save the N th level approximation component in to the same text file. 8. Transmit this text file encoded as message. 3.2.2. Decoding Algorithm The process for decoding the image is the same as that used for wavelet based Fractal Image Compression.