SSIM based image quality assessment for vector quantization based lossy image compression using LZW coding

Transcription

1 Available online at University Journal of Research ISSN (Online) , ISSN (Print) SSIM based image quality assessment for vector quantization based lossy image compression using LZW coding Amrutbhai N. Patel a, D. J. Shah b a Ph. D. Scholar, Faculty of Engineering and Technology, Ganpat University, Gujarat, India b Director,Shruj LED Technologies, Ahmedabad, Gujarat, India. Abstract The recent development in the digital electronics and computer engineering has resulted in generation of large amount of data in the digital form. High resolution images are required in many fields such as remote sensing, criminal investigation, medical imaging etc. This motivates the need of compression of the size of the data. The main objective of the present study is to obtain better quality of decompressed images even at very low bit rates and to reduce the size of the data as well as processing and transmission time. Considerable efforts have been made to design image compression methods. There are various lossy image compression techniques existing in digital domain, among them vector quantization (VQ) based image compression technique provides good picture quality and higher compression ratio. Vector quantization is an effective technique for still image compression which gives higher quality of reconstructed image at low bit rate.this paper presents a lossy image compression technique which combines Vector Quantization (VQ) and LZW (Lempel- Ziv Welch) coding. In the proposed method, image is vector quantized and later VQ indices are coded using LZW coding to increase the compression ratio but, the reduction of processing time is the major issue in VQ. Experimental 16

2 Patel A. and Shah D/ University Journal of Research Vol. 01, Issue 01 (2015) ISSN: results are measured in terms of Compression Ratio (CR), Peak Signal to Noise Ratio (PSNR), Mean Square Error (MSE) and Structural Similarity Index Measurement (SSIM) for image quality The proposed method of lossy image compression shows better image quality in terms of PSNR at the same compression ratio as compared to other VQ based image compression techniques. Keywords: Discrete wavelet transform; Vector quantization; Peak signal to noise ratio; Mean square error; Structural similarity index measurement. 1. Introduction Multimedia applications like text, image, audio and video are represented in digital form. As the huge amount of multimedia data occupies the large amount of space of memory, it is required to compress the size of the multimedia data. According to Patel et al. (2014), the image compression is a significant research area for many years due to continuously increasing demand on transfer and storage of data. The aim of image compression is to reduce the amount of data required to represent digital image. Thus image compression is very important necessity. There are two types of image compression; (1) lossless compression and (2) lossy compression. When the exact reconstruction of an image is not expected, the lossy image compression algorithms are applicable. These algorithms are usually based on transform methods. In recent years, considerable efforts have been made to design image compression method in which the main goal is to obtain good quality of decompressed images even at very low bit rates. The basic aim of image compression is to reduce the storage requirement while maintaining acceptable image quality. According to Patel et al. (2014), Vector quantization (VQ) is one of the popular lossy image compression techniques for its simpler decoding structure and it can achieve high compression ratio while maintaining acceptable value of SSIM, FSIM and PSNR. 17

3 Patel A. and Shah D/ University Journal of Research Vol. 01, Issue 01 (2015) ISSN: Thepade et al. (2015), presented different methods for Codebook generation in Vector quantization which is the soul of Vector Quantization. Among several methods to generate Codebook Thepade s Cosine Error Vector Rotation (TCEVR) gives better performance than others like KEVR. Meng et al. (2010), presented Discrete Cosine Transform (DCT) and VQ coding based new image compression technique. They have also introduced new algorithm that merges DCT and wavelet transform to obtain very high compression ratio and visual quality in texture regions of images. Zhang et al., (2011), presented new technique. A Feature Similarity Index Measurement (FSIM) for subjective image quality assessment uses computational models to measure the image quality consistently. This algorithm uses the phase congruency (PC), a dimensionless measure of the significance of a local structure as the primary feature and the image gradient magnitude (GM) is employed as the secondary feature in FSIM. PC and GM play complementary roles in characterizing the image local quality. Selvakumarasam et al.(2012) presented different methods in terms of PSNR and MSE which can be used to better understand the relationship between various methods like EZW, SPIHTT, SPECK,LZW, Huffman coding and Arithmetic coding and their features. Kalaivani et al. (2013) presented SOM based vector quantization and Discrete Wavelet Transform based new technique for the still image compression which gives high reconstruction quality at low coding rates and rapid decoding, but it has high encoding time complexity. The performance can be further improved by using linear vector quantization. Ma et al., (2015) proposed ESMVQ introduced the concept of CSC which gives good visual quality compared to the VQ technique with a low BR close to the SMVQ technique. Nandi et al. (2012), presented dictionary based image compression technique based on the optimality of LZW code in which compression process is started with empty dictionary and if the next symbol to be encoded is already in dictionary. In this paper, lossy compression technique is used. A combined approach of image compression, VQ as per Meng et al. (2010) and LZW coding is presented. VQ, which is a powerful tool for digital image compression and is classical quantization technique from signal processing and 18

4 Patel A. and Shah D/ University Journal of Research Vol. 01, Issue 01 (2015) ISSN: image compression which allows the modeling of probability density functions by the distribution of prototype vectors. After Vector quantization, the discrete values are entropy encoded using LZW coding. We map the set of quantized coefficients to a set of symbols so that the total number of bits per symbol gets minimized. The encoding process works with the probabilities of the quantized coefficients. The proposed lossy image compression technique gives superior result, which are in general applicable to any images. This proposed method of image compression is applicable to those areas of digital images, where higher compression ratio with better image reconstruction is required like criminal investigations, medical imaging, etc. This method is tested on gray scale test images, but it can be easily extended to colored image. 2. Proposed Approach This paper proposes an effective way to reduce the size of an image with the combination of vector quantization and LZW coding. Steps followed are: An image is divided into nonoverlapping smaller blocks. Vector quantization is applied to each of these blocks. LZW coding is applied to the resultant weight vector. The resultant image obtained has better compression ratio with better SSIM value as subjective image quality measure. 2.1 Vector quantization It is a powerful tool for digital image compression. The vector quantization is a classical quantization technique from signal processing and image compression, which allows the modelling of probability density functions by the distribution of prototype vectors. It was originally used for data compression. It works by dividing a large set of points (vectors) into groups having approximately the same number of points closest to them. Each group is represented by its centred point, similar to k-means and some other algorithms of Kalaivani, et al. (2013). It is a generalization of scalar quantization technique, where the number of possible 19

5 pixel is reduced. Patel A. and Shah D/ University Journal of Research Vol. 01, Issue 01 (2015) ISSN: Original image is Cameraman image with size of 256x256 pixels as per JiShen et al. (2011). The primary process of VQ compression is to divide the image into a number of non-overlapping sub-blocks. For example, an image with pixels (block size is 4 4 pixels) can be divided into ( ) / (4 4) = 4096 blocks. After this, we take each pixel value within the block from left to right, top to bottom to construct a vector. This vector calculates the Euclidean distance with all code words in the codebook. The calculation of Euclidean distance is shown in Eq. (1) as follows, where d is Euclidean distance, B is block s vector, C i is the i th index codeword in the codebook, k is the dimension of vectors. Then we can find the closest or the shortest codeword, and use the index value of this codeword to represent this block, finally obtain an index table including indices. In the decompression phase, we can then use this index table to find out the codeword from the codebook, restore block vectors, and reconstruct the image according to equation (1). (1) 2.2 Algorithm of vector quantization Step 1: Input the given image of size M M pixels. M is dimension of image. Step 2: Divide it into 4 4 blocks. Step 3: Generate N training vectors. Step 4: Fix the codebook size to n. Step 5: Compute p = N/n. Step 6: Select every p th training vector as a code vector till the codebook of desired size is obtained. 20

6 Patel A. and Shah D/ University Journal of Research Vol. 01, Issue 01 (2015) ISSN: Compression of an image is done by taking every training vector and finding a closest match in the codebook by computing the minimum distortion d (i, j). Such that, p = N/n, where, n is the size of the codebook. 2.3 LZW (Lempel- Ziv Welch) It is a dictionary based coding. Dictionary based coding can be static or dynamic. In static dictionary based coding, dictionary is fixed during the encoding and decoding processes. In dynamic dictionary based coding, the dictionary is updated on fly. The LZW coding is widely used in computer applications. Optimality of LZW codes can be achieved by starting the encoding process with empty dictionary. First phrase to be entered into the dictionary should have code values 1 which can be represented using only single bit. The 2 nd and3 rd phrases to be entered into the dictionary should have code values 2 and 3 and can be represented by 2 bits. Similarly 3 bits are required for 4 th to 7 th phrases to be entered into the dictionary and so on. This is in contrast to LZW coding, where first 256 phrases entered initially into the dictionary are represented by 8 bits per phrase. Therefore, significant reduction of number of bits can be done by optimization of LZW codes in Nandi et al. (2012). 2.4 SSIM(Structural similarity index measurement) According to Patel et al. (2014), Digital images and videos are prone to different kinds of distortions during different phases like acquisition, processing, compression, storage, transmission, and reproduction. This degradation results in poor visual quality. There are several metrics, which are widely used to quantify the image quality like FSIM, SSIM, bit rate, PSNR and MSE. This work is primarily focussed on metrics like SSIM and bit rate. The other conventional metrics like PSNR and MSE will not be measured, as they are directly dependent on the intensity of an image and do not correlate with the subjective fidelity ratings. MSE cannot model the human visual system very accurately according to Wang et al., (2004). 21

7 Patel A. and Shah D/ University Journal of Research Vol. 01, Issue 01 (2015) ISSN: SSIM is the quality assessment of an image based on the degradation of structural information. The SSIM takes an approach that the human visual system is adapted to extract structural information from images. Thus, it is important to retain the structural signal for image fidelity measurement in Wang et al., (2004). 3. Evaluation of image compression technique Essential criteria: The obtained compression ratio CR and the quality of the reconstructed image, PSNR. 3.1 Compression ratio The compression ratio (CR) is the ratio between the size of the original image (n1) and the size of the compressed image (n2). 4. Distance Measure Mean Square Error (MSE) is used to measure the rate of distortion in the reconstructed image. (2)... (3) Where, f(x,y), f (x,y) are, respectively, the original and recovered pixel values at the m th row and n th column for the image of size MxN. 4.1 Peak signal to noise ratio It is used as an approximation to human perception of reconstruction quality. PSNR has been accepted as a widely used quality measurement in the field of image compression. PSNR is normally quoted in decibels (db), which measure the ratio of the peak signal and the difference between two images (error image). Logically, a higher value of PSNR is good because it means that the ratio of Signal to Noise is higher. So, if we find a compression scheme having a high 22

8 Patel A. and Shah D/ University Journal of Research Vol. 01, Issue 01 (2015) ISSN: PSNR, we can organize that it is a better one. As per Patel et al. (2014), For an 8-bit gray scale image, the peak signal value is 255. Therefore, the PSNR of 8-bit gray scale image and its reconstructed image is calculated. A high PSNR would normally indicate less distortion and high reconstruction quality.... (4) 4.2 Structural Similarity Index Measurement Where C 1 and C 2 are constant and equal to unity.... (5) When both images are same, SSIM is 1 so a Value nearer to 1 would normally indicate high reconstruction quality in Wang et al., (2004). 5. Results and discussion In this paper we have shown the result of proposed work based on vector quantization for the evaluation of the test image cameraman (256 X 256) with LZW coding. The results are shown in Table 1 and 2, and the parameters are PSNR and CR, RMSE and SSIM for different size of cluster and codebook of Vector Quantization. Table 1. Result of proposed work [Cameraman test image] P1 -Shenyang,.China JPEG - Khalifa (2010) (2005) P2- Khalifa (2005) Proposed work CR PSNR(db) CR PSNR(db) CR PSNR(db) CR PSNR(db)

9 Patel A. and Shah D/ University Journal of Research Vol. 01, Issue 01 (2015) ISSN: Table 2. Result of comparison of proposed work with different techniques for Compression Ratio vs. PSNR for different techniques] [Cameraman test image] Parameter Cluster size (2x2) Codebook size Cluster size (4x4) Codebook size CR PSNR(db) MSE SSIM Figure 1. Comparison of proposed work with existing techniques for Compression Ratio vs PSNR Table 1, 2 and Figure 1 show result of proposed work complied with JPEG techniques. It shows for compression ratio of 64 at PSNR is 16.9 but proposed work gives the compression ratio at PSNR of 29.9, which is better than standard technique. The study done by Mitra et al. 24

10 Patel A. and Shah D/ University Journal of Research Vol. 01, Issue 01 (2015) ISSN: (1998) provides Compression ratio of 20 and PSNR 24.83, where proposed work gives the result of higher compassion ratio at PSNR The study done by Khalifa (2005) provides compression ratio 31.6 at PSNR 26.78, where proposed work gives the result of higher compassion ratio and PSNR Figure 2. Cameraman Test Image CR= , PSNR=32.91, MSE= , SSIM= Figure 3. Cameraman Test Image CR= , PSNR=24.07, MSE=254.38, SSIM= By comparing Figure 2 and Figure 3 it can be concluded that Figure 3 have higher compression ratio than Figure 2 but SSIM value of Figure 3 is which indicates that the quality of image is poor than Figure 2 with SSIM value of Table 3. Comparison of the proposed method with the methods available in the literature [Cameraman test image] Work PSNR (db) CR Leu et al., (2004) Sudhakar R. et al., (2007) Joshi et al., (2008) Kalaivani et al., (2013) Proposed work From Table 3 it is seen that while comparing the proposed method with the existing works done by above mentioned scholars, our proposed method gives better performance for PSNR and CR. 25

11 Patel A. and Shah D/ University Journal of Research Vol. 01, Issue 01 (2015) ISSN: Table 4. Comparison of the proposed method with the advance image compression techniques in the literature [Brain MRI gray scale image (256x256)] Work PSNR(dB) CR Padmashree et al. (2015) Proposed work From Table 4 it is seen that while comparing the proposed method with the existing works done by Padmashree et al. (2015), our proposed method gives better performance for PSNR and CR. 6. Conclusion In proposed work the various parameters have been measured such as compression ratio, PSNR, MSE, SSIM and it is compared with the already existing methods. It puts emphasis to develop a simulation that implements the algorithms for the lossy compression of the two dimensional images. This simulation has achieved reasonable performance in general. However, there are still some components that do not perform very well. If cluster size in Vector Quantization is increased, the compression performance improves but the quality of image deteriorates. Proposed work gives great improvement on the overall image compression process. It increases the compression ratio drastically, but the PSNR is reduced a little bit, which ultimately assures the purpose of the method for that area of image compression which requires high quality image. SSIM is the best parameter than MSE for analyzing the quality of reconstructed image. The proposed method of Vector Quantization (VQ) with combination of LZW coding provides better quality with high compression ratio compared to existing techniques. 7. Future Work This lossy Image Compression field may include the upcoming standard which incorporates many of the research works in vector quantization and will address many important aspects in image compression for the coming years. Future work determines to enhance the wavelet based 26

12 Patel A. and Shah D/ University Journal of Research Vol. 01, Issue 01 (2015) ISSN: vector quantization algorithm that performs well for any format of the image. By implementing an effective codebook and the wavelet based tree structure the computation complexity can be reduced more. Also, compression algorithm can be improved by analysis of wavelet based vector quantization analysed using image denoising and compressive sensing technique. 8. References JiShen J., Lo Y., (2011). A New Approach of Image Compression Based on Difference Vector Quantization, Seventh International Conference on Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP), Joshi M. S.; Manthalkar R. R.; Joshi Y. V. (2008). Image compression using curvelet, ridgelet and wavelet transform, a comparative study, ICGST-GVIP, 2(3), Kalaivani, K., Thirumaraiselvi, C., Sudhakar, R., (2013). An effective way of image compression using DWT and SOM based vector quantisation. IEEE International Conference on Computational Intelligence and Computing Research, 1-5. Khalifa O., (2005). Wavelet coding design for image data compression. International Arab Journal of Information Technology, 2(1), Leu Sanche;, Perez Meana Hector M.; Miyatake Mariko Nakana (2004). Wavelet image compression using universal coefficients matrix detail estimation. Proceedings 14 th International Conference on Electronics, Communications and Computers, IEEE, 3(1),

13 Patel A. and Shah D/ University Journal of Research Vol. 01, Issue 01 (2015) ISSN: Ma X., Pan Z., Hu S., Wang L., (2015). Enhanced side match vector quantisation based on constructing complementary state codebook. Image Processing, IE, 9(4), Meng, M., Zong, M., (2010). A new zero tree structure for color image compression based on DWT and VQ. Information Management and Engineering, 2(4), Mitra S., Yang S., Kustov V., (1998). Wavelet-Based Vector Quantization for High-Fidelity Compression and Fast Transmission of Medical Images. Journal of Digital Imaging, 11(4), Nandi, U.; Mandal, J. K. (2012). A Compression Technique Based on Optimality of LZW Code (OLZW). Third International Conference on Computer and Communication Technology, Padmashree, S.; Nagapadma, R., (2015). Images using Embedded Block Coding Optimization Truncation(EBCOT). International Conference on Advance Computing. IEEE, Patel, A. N., Shah D. J. (2014). Structural Similarity Index Measurement (SSIM) Based Performance Analysis of Wavelet Families For Image Compression. International Journal of Emerging Technologies and Applications in Engineering, Technology and Sciences, 1(2), Selvakumarasamy, K.; Poornachandra, S. (2012). Wavelet based image compression methods State of the art. Third International Conference on Computing Communication & Networking Technologies,

14 Patel A. and Shah D/ University Journal of Research Vol. 01, Issue 01 (2015) ISSN: Shenyang A; China P. R. (2010). Research on image compression algorithm based on SPIHT. International Conference on Intelligent Networks and Intelligent Systems, IEEE, An Overview of the JPEG 2000 Still Image Compression Standard, Sudhakar R.; Karthiga R.; Jayaraman S. (2007). Image compression using coding of wavelet coefficients a survey, GVIP Special Issue on Image Compression, ICGST 7: 2(2), Thepade, S.D.; Katore, L.S. (2015). Image compression using improvised column based Thepade's Cosine Error Vector Rotation (TCEVR) Codebook generation in Vector Quantization. International Conference on Communication, Information & Computing Technology, 2(5), 1-5. Wang, Z.; Bovik, A. C., Sheikh H. R., (2004). Image Quality Assessment: From Error Visibility to Structural Similarity. IEEE Transactions on Image Processing, 13(4), Zhang L.; Mou X., Zhang D. (2011). FSIM: A feature similarity index for image quality assessment. IEEE Transactions on Image Processing, 20(8),