International Journal of Scientific & Engineering Research, Volume 4, Issue 10, October-2013 710

ISSN 2229-5518

Compression Study Between ‘ezw’, spiht, stw, wdr, aswdr and spiht_3d

Tarun kumar1, Deepak Chaudhary2

1Ph.D scholar, Mahamaya Technical University, Noida, tarunkumar124@gmail.com

2Assistant Professor, IET-Alwar, Rajasthan, Deepak.se17@gmail.com

Abstract—six different Wavelet based Image Compression techniques are analyzed. The techniques involved in the comparison process are Embedded Zero tree Wavelet (ezw) , Set Partitioning In Hierarchical Trees (Spiht), Spatial- orientation Tree Wavelet (stw), Wavelet Difference Reduction (wdr), Adaptively Scanned Wavelet Difference Reduction (aswdr) and Spiht_3d. Here, there are six types of Wavelet transforms are applied on the images before compression, from the compressed image decompressed image can be retrieved and then the quality of the decompressed images is deliberate with six performance parameters i.e. Mean Square Error, Peak Signal to Noise Ratio, Normalized Cross- Correlation, Average Difference, Structural Content, Maximum Difference, Normalized Absolute Error and examine which technique is better for image compression.

Key Words: ezw, spiht,asdwr,wdr,stw

1. INTRODUCTION

Image compression has been the key technology for pass on huge amount of real-time image data via limited bandwidth channels. The data are in the form of audio, image, video and graphics. These types of data have to be compressed during the broadcast process. Some of the compression algorithms are used in the earlier days and it was one of the first to be comparison study using wavelet methods. Wavelet transforms have been widely studied over the last decade. For still images the widely used coding algorithms based on wavelet transform include the embedded zero-tree wavelet (EZW) algorithm, the set partitioning in hierarchical trees (SPIHT) algorithm and the wavelet difference reduction (WDR) algorithm. The SPIHT algorithm improves upon the EZW concept by replacing the raster scan with a number of sorted lists that contain sets of coefficients (i.e., zero-trees) and individual coefficients. Already the results are compared and it is identified that WDR provides better results.

Fig 1: image compression model using wavelets

Fig 2: image decompression model using wavelets

The relationship between the quantize and encode steps, shown in Fig 2, is the crucial aspect of wavelet transform compression. Each of the technique explained below takes a different approach to this relationship. The purpose served by the wavelet transform is that it produces a large number of values having zero, or near zero, magnitudes.

2. COMPRESSION TECHNIQUES

2.1.1 SPIHT

SPIHT is a fully embedded wavelet coding algorithm in the order of decreasing energy levels. It allocates the available bit budget between encoding the tree map and the significance information itself It permits for accurate rate control and reasonable computational complexity.

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The SPIHT quantize is reported to surpass other coding techniques such as DCT, EZT, etc.
The SPIHT algorithm is a highly refined version of the
EZW algorithm. It was introduced in Said and Pearlman [4, 5]. Some of the best results — highest PSNR values for given compression ratios — for a wide variety of images have been obtained with SPIHT. Consequently, it is probably the most widely used wavelet-based algorithm for image compression, providing a basic standard of comparison for all subsequent algorithms. SPIHT stands for set partitioning in hierarchical trees. Set partitioning refers to the way these quad trees partition the wavelet transform values at a given threshold. By a careful analysis of this partitioning of transform values, Said and Pearlman were able to greatly improve the EZW algorithm, significantly increasing its compressive power.

2.1.2 EZW

The embedded zerotree wavelet algorithm (EZW) [1] is a valuable image compression algorithm. This new method produces a fully embedded bit stream for image coding. Also, the compression performance of this algorithm is competitive with virtually all known techniques. Furthermore, this technique requires definitely no training, no pre-stored codebooks or tables and requires no preceding knowledge of the image source. The EZW algorithm is based on four principal concepts: a discrete wavelet transform or hierarchical sub-band decomposition, prediction of the absence of significant information across scales, entropy coded successive-approximation quantization and universal lossless data compression which is accomplished via adaptive arithmetic coding. The EZW algorithm includes: a discrete wavelet transform (DWT) [4], zerotree coding, successive approximation and a priorization protocol which helps us to determine the order of importance due to various characteristics. In
addition, adaptive arithmetic coding is used to achieve a
fast and efficient method for entropy coding. We want to call attention to the following sentence. ‘This algorithm runs consecutively and stops whenever a target bit rate or a target distortion is met. Certainly, one of the most significant parts of this algorithm is the encoding process.

2.1.3 Wavelet Difference Reduction:

The WDR algorithm is a very simple procedure. A wavelet transform is first applied to the image, and then the bit-plane based WDR encoding algorithm for the wavelet coefficients is carried out.

2.1.4 Adaptively Scanned Wavelet Difference

Reduction

The ASWDR method is a generalization of the WDR method of Tian and Wells ([1] and [2]), so we shall begin by briefly summarizing the WDR method. The WDR method has two principal advantages. First, it produces an embedded bit stream—thereby facilitating progressive transmission over small bandwidth channels and/or enabling multiresolution searching and processing algorithms. Second, it encodes the precise indices for significant transform values—thereby allowing for Region of Interest (ROI) capability and for image processing operations on compressed image files [4].

2.1.5 Spatial-orientation Tree Wavelet

STW is essentially the SPIHT algorithm, the only difference is that SPIHT is slightly more careful in its organization of coding output. Second, we shall describe

3d_spiht scheme extended from the 2 d spiht, having the

following three similar characteristics:

1) Partial ordering by magnitude of 3 d wavelets transformed video with a 3d set partitioning algorithm
2) Ordered bit plane transmission of refinement bits, and the SPIHT algorithm. It will be easier to explain SPIHT using the concepts underlying STW. Third, we shall see how well SPIHT compresses images. The only difference
between STW and EZW is that STW uses a different

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approach to encoding the zero tree information. STW uses a state transition model. From one threshold to the next, the locations of transform values undergo state transitions.[5]

2.1.6 SPIHT_3D

3) Exploitation of self similarity across spatial temporal orientation tress.in this way the compressed bit stream will be completely embedded, so that a single file for a video sequence can provide progressive video quality, that is, the algorithm can stooped at any compressed file size or let run until nearly lossless reconstruction is obtained, which is desirable in many application including HDTV.[5]

3 EXPERIMENTS

Images used in the Experiments The images tarun.bmp is used for the experiments. The original images are shown in Fig. 1. The results of experiments are used to find the compression ratio which is shown in table 1.PSNR (Peak Signal to Noise Ratio) values, MSE (Mean Square Error) and SNE (Sub-Norm Error) values from the reconstructed images.
Input image tarun.bmp size of 192 KB and dimension
256x256 has been compressed by using six different techniques and after compression size of the compressed image is shown in table 1.

Figure 1: Original Image

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Fig 5: decompressed with Spiht

Fig

6: decompressed with Spiht_3d Fig7 : decompressed with stw

Table 1:

After compressed the image do the decompression by using the compressed image as an input image and find the size and dimension of decompressed image, which is shown in table 2.

Table 2:

As discussed from the above table size and dimension are same as the original input image but the quality are not same as the original image as seems so the judgment
of quality of the image is calculated by performance parameter.

4 PERFORMANCE ANALYSES

The above six techniques are implemented and the results are shown in the above table. The PSNR, MSE and SNE values for the images compressed by the six techniques
by using different wavelet transforms are tabulated in Table 3. The PSNR and MSE values are calculated by using the following formula

4.1. Structural Content (SC)

The structural content measure used to compare two images in a number of small image patches the images have in common. The patches to be compared are chosen using 2D continuous wavelet which acts as a low level corner detector. The large value of structural content SC means that image is poor quality

4.2. Mean Square Error (MSE)

Mean square error is a measure of image quality index. The large value of mean square means that image is a poor quality. MSE means ‘Mean Square Error’. It

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represents the classical error estimate given by the equation:

where M and N are the image dimensions. It is a widely used criterion but is often not enough representative. JND and Hosaka Plots may be used as an alternative to MSE.

4.3. Peak Signal to Noise Ratio (PSNR in dB)

4.4. Normalized Cross-Correlation (NCC) Normalized cross correlation is the simplest but effective method as a similarity measure, which is invariant to linear brightness and contrast variations. Its easy hardware implementation makes it useful for real-time applications. Or normalized cross correlation is a measure of similarity of two waveforms as a function of the time lag applied to one of them. The cross correlation

is similar in nature to the convolution of two functions.
The PSNR can give an approximate index of image quality, but by itself it cannot make a comparison
between the quality of two different images. It is

Average Difference (AD)

4.5.

possible, indeed, that an image with a lower PSNR might be perceived as an image of better quality compared to one with a higher signal to noise ratio.

Peak Signal-to-Noise Ratio, often abbreviated PSNR, is an engineering term for the ratio between the maximum possible power of a signal and the power of corrupting noise that affects the fidelity of its representation. Because many signals have a very wide dynamic range, PSNR is usually expressed in terms of the logarithmic decibel scale.

5 COMPRESSION RATIOS

a) For aswdr:

Average difference is calculated by the given formula.

4.6. Maximum Difference (MD)

Difference between any two pixels such that the larger pixel appears after the smallest pixel. The large value of maximum difference means that image is poor in quality

4.7. Normalized Absolute Error (NAE)

The large value of normalized absolute error means that image is poor quality. NAE is defined as follows.

CR= (1 − 7.13/192) ∗ 100

=96.28%

b) For ezw

CR= (1 − 7.02/192) ∗ 100

=96.34%

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c) For spiht

CR= (1 − 4.97/192) ∗ 100

=97.414%

d) For stw

CR= (1 − 6.42/192) ∗ 100

=96.65%

e) For wdr

CR= (1 − 7.23/192) ∗ 100

=96.23%

f) For spiht_3d

CR= (1 − 4.37/192) ∗ 100

=97.7239%

Table 4: compression Ratio

CONCLUSIONS

In this paper, the results were compared for six different wavelet-based image compression techniques. compression ratio has been calculated for different six technique and analyzed . The results of the above six techniques ‘EZW’, SPHIT, STW, WDR, ASWDR and Spiht_3d were compared by using the parameters such
as SC, PSNR,MSE,NCC,AD and MD values from the
reconstructed image. These techniques are successfully tested in many images. The experimental results show that the spiht_3d technique performs
better than the rest wavelets based technique in terms of the performance parameters and coding time with acceptable image quality Finally, it is identified that spiht compression performs better when compare to WDR compression.

References

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