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Performance Analysis of Discrete Cosine Transform based image compression S.VIJAYARAGHAVAN1, M.A.ARCHANA2, Dr.C.PARTHASARATHY3 1, 2 Research Scholars, 3 Assistant Professor-II, SCSVMV University. professorvijayece@gmail.com, maarchaname@gmail.com, drsarathy45@gmail.com ABSTRACT Image compression is one of the most important criteria in multimedia applications. Compression allows efficient utilization of channel bandwidth and storage size. Typical access speeds for storage mediums are inversely proportional to capacity. Through data compression, such tasks can be optimized. Image compression is a part of that data compression. The discrete cosine transform (DCT) is a technique for converting a signal into elementary frequency components. Here we develop some simple functions to compute the DCT and to compress images. Different images are taken for compression using DCT and the performance parameters are analyzed using Mat lab. Image Compression is studied using 2-D discrete Cosine Transform. The original image is transformed in different window sizes. The implementation of this work was successful on achieving significant PSNR values. Keywords: Discrete Cosine Transform, Pixels, Bit Rate, Mean Square Error, Signal to Noise Ratio, PSNR
information. The basic objective of image compression is to find an image representation in which pixels are less correlated. The two fundamental principles used in image compression are redundancy and irrelevancy. Redundancy removes redundancy from the signal source and irrelevancy omits pixel values which are not noticeable by human eye. JPEG and JPEG 2000 are two important techniques used for image compression. Work on international standards for image compression started in the late 1970s with the CCITT (currently ITU-T) need to standardize binary image compression algorithms for Group 3 facsimile communications. Since then, many other committees and standards have been formed to produce de jure standards (such as JPEG), while several commercially successful initiatives have effectively become de facto standards (such as GIF). Image compression standards bring about many benefits, such as: (1) easier exchange of image files between different devices and applications; (2) reuse of existing hardware and software for a wider array of products; (3) existence of benchmarks and reference data sets for new and alternative developments
INTRODUCTION Image compression is very important for efficient transmission and storage of images. Demand for communication of multimedia data through the telecommunications network and accessing the multimedia data through Internet is growing explosively. With the use of digital cameras, requirements for storage, manipulation, and transfer of digital images, has grown explosively. These image files can be very large and can occupy a lot of memory. A gray scale image that is 256 x 256 pixels has 65, 536 elements to store, and a a typical 640 x 480 color image has nearly a million. Downloading of these files from internet can be very time consuming task. Image data comprise of a significant portion of the multimedia data and they occupy the major portion of the communication bandwidth for multimedia communication. Therefore development of efficient techniques for image compression has become quite necessary. A common characteristic of most images is that the neighboring pixels are highly correlated and therefore contain highly redundant
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IMAGE COMPRESSION The need for image compression becomes apparent when number of bits per image is computed resulting from typical sampling rates and quantization methods. For example, the amount of storage required for given images is (i) a low resolution, TV quality, color video image which has 512 x 512 pixels/color,8 bits/pixel, and 3 colors approximately consists of 6 x 10⁶ bits;(ii) a 24 x 36 mm negative photograph scanned at 12 x 10⁻⁶mm:3000 x 2000 pixels/color, 8 bits/pixel, and 3 colors nearly contains 144 x 10⁶ bits; (3) a 14 x 17 inch radiograph scanned at 70 x 10⁻⁶mm: 5000 x 6000 pixels, 12 bits/pixel nearly contains 360 x 10⁶ bits. Thus storage of even a few images could cause a problem. As another example of the need for image compression, consider the transmission of low resolution 512 x 512 x 8 bits/pixel x 3-color video image over telephone lines. Using a 96000 bauds (bits/sec) modem, the transmission would take approximately 11 minutes for just a single image, which is unacceptable for most applications.
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Proceedings of International Conference on Advancements in Engineering and Technology
Figure 1 Block Diagram of Image Compression Principle Number of bits required to represent the information in an image can be minimized by removing the redundancy present in it. There are three types of redundancies: (i) Spatial redundancy, which is due to the correlation or dependence between neighboring pixel values. (ii) Spectral redundancy, which is due to the correlation between different color planes or spectral bands. (iii) Temporal redundancy, which is present because of correlation between different frames in images. Image compression research aims to reduce the number of bits required to represent an image by removing the spatial and spectral redundancies as much as possible. Data redundancy is of central issue in digital image compression. If n1 and n2 denote the number of information carrying units in original and compressed image respectively ,then the compression ratio CR can be defined as CR=n1/n2;And relative data redundancy RD of the original image can be defined as RD=1-1/CR; Three possibilities arise here: (1) If n1=n2, then CR=1 and hence RD=0 which implies that original image do not contain any redundancy between the pixels. (2) If n1>>n1, then CR→∞ and hence RD>1 which implies considerable amount of redundancy in the original image. (3) If n1<<n2, then CR>0 and hence RD→-∞ which indicates that the compressed image contains more data than original image. Types of compression Lossless versus Lossy compression: In lossless compression schemes, the reconstructed image, after compression, is numerically identical to the original image.
ISBN NO : 978 - 1502893314
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However lossless compression can only a achieve a modest amount of compression. Lossless compression is preferred for archival purposes and often medical imaging, technical drawings, clip art or comics. This is because lossy compression methods, especially when used at low bit rates, introduce compression artifacts. An image reconstructed following lossy compression contains degradation relative to the original. Often this is because the compression scheme completely discards redundant information. However, lossy schemes are capable of achieving much higher compression. Lossy methods are especially suitable for natural images such as photos in applications where minor (sometimes imperceptible) loss of fidelity is acceptable to achieve a substantial reduction in bit rate. The lossy compression that produces imperceptible differences can be called visually lossless. Predictive versus Transform coding: In predictive coding, information already sent or available is used to predict future values, and the difference is coded. Since this is done in the image or spatial domain, it is relatively simple to implement and is readily adapted to local image characteristics. Differential Pulse Code Modulation (DPCM) is one particular example of predictive coding. Transform coding, on the other hand, first transforms the image from its spatial domain representation to a different type of representation using some well-known transform and then codes the transformed values (coefficients). This method provides greater data compression compared to predictive methods, although at the expense of greater DISCRETE COSINE TRANSFORM BASED IMAGE COMPRESSION Discrete Cosine Transform (DCT) exploits cosine functions, it transform a signal from spatial representation into frequency domain. The DCT represents an image as a sum of sinusoids of varying magnitudes and frequencies. DCT has the property that, for a typical image most of the visually significant information about an image is concentrated in just few coefficients of DCT. After the computation of DCT coefficients, they are normalized according to a quantization table with different scales provided by the JPEG standard computed by psycho visual evidence. Selection of quantization table affects the entropy and compression ratio. The value of quantization is inversely proportional to quality of reconstructed image, better mean square error and better compression ratio. In a lossy compression technique, during a step called Quantization, the less important frequencies are discarded, then the most important frequencies that remain are used to retrieve the image in decomposition process. After quantization, quantized coefficients are rearranged in a zigzag order for further compressed by an efficient lossy coding algorithm.
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Proceedings of International Conference on Advancements in Engineering and Technology
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Let us present here briefly the computation technique for DCT’s of an image. The definition of DCT for a 2D images x (m,n) of size NxN is as follows:
C k , l m0 n0 4 xm, n cos 2 m2K1k cos 2 n2N1l N 1
N 1
Th
0 k, l N 1 e low-low sub band xLL (m,n) of the image be obtained as:
x LL ( m , n )
1 4
{ x ( 2 m , 2 n ) x ( 2 m 1, 2 n )
( 2 m , 2 n 1) x ( 2 m 1, 2 n 1 )}, 0 m,n
N 2
Figure 2 BUILDING- original image
1.
Let CLL (k,l), 0 < k,l < N/2-1 be the 2D DCT of xLL(m,n). Then the sub band approximation of DCT of x(m,n) is given by:
4cos(2Nk ) cos(2Nl )CLL (k, l), k, l 0,1,......,N2 1 C(k,l) 0, otherwise It may be noted that depending upon the definition of DCT, sub band DCT’s are multiplied by a factor (in this
k l cos ). The definition of inverse 2N 2N
case 4 cos
Figure 3 BUILDING- Gray scale image
DCT (IDCT) should also be modified accordingly. We refer this as sub band approximation of DCT as k , l 0 ,1 ,......, N2 1 4 C LL ( k , l ), C (k , l) 0, otherwise We refer this approximation as the low-pass truncated approximation of DCT. Interestingly, the multiplication factor 4 appears due to the definition of DCT used in this work. However, this factor does not have any effect in the final results obtained by them (PSNR values of downsized (halved) and then upsized. While halving an image, DCT coefficients for N/2-point DCT are obtained by dividing the N-point DCT coefficients.
Figure 4 BUILDING- DCT image
EXPERIMENTAL RESULTS Experimentations are carried out for studying the performances of the three different images compressed at different levels. In the context of the JPEG compression, the effect of quantization on the approximated coefficients during image-halving or image-doubling should be observed here. The PSNR values for different compression levels for the Building, BMW car, and Peacock images were plotted in Figures as shown below. The performance of Bit Rate, Mean Square Error, Signal to Noise Ratio, PSNR values for the images is also tabulated.
ISBN NO : 978 - 1502893314
Figure 5 BMW CAR- original image
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Proceedings of International Conference on Advancements in Engineering and Technology
Figure 6 BMW CAR- Gray scale image
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Figure 10 PEACOCKâ&#x20AC;&#x201D;DCT Image 200 150
PEACOCK
100
BMW CAR
50
BUILDING
0 0.5
0.75
1
2
4
Figure 7 BMW CAR - DCT image Figure 11 Bit rate (bps) vs. PSNR (dB) for DCT based image compression of Peacock, BMW car and Buildings images TABLE I - Performance Analysis
Image
Figure 8 PEACOCK- original image Building
BMW Car
Figure 9 PEACOCK- Gray scale image Peacock
ISBN NO : 978 - 1502893314
Bit Rate (bps)
Mean Square Error
Signal To Noise Ratio (db)
PSNR(db)
0.5 0.75 1 2 4 0.5 0.75 1 2 4 0.5 0.75 1 2 4
114.6 60.9 47.9 6.6 0.2 36.5 175.9 124.6 30.8 0.9 302.2 232.2 164.5 33.9 2.5
13.7 16.4 17.5 26.1 42.4 14.1 15.4 16.9 23.0 38.6 9.4 10.5 12.0 18.9 30.2
27.5 30.3 31.3 39.9 56.2 24.4 25.7 27.2 33.2 48.8 23.3 24.5 26.0 32.8 44.2
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Proceedings of International Conference on Advancements in Engineering and Technology
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CONCLUSION [9]
DCT based Image compression transform is an efficient technique for obtaining better quality of image in multimedia applications. The Performance analysis of three different images illustrates that the PSNR value varies for different bit rates and it also shows that there is a better performance of mean square error and for various bit rate. The outputs were obtained using MATLAB 8. The future of this is that it can be implemented using FPGA.
NageswaraRaoThota, Srinivasa Kumar Devireddy. “Image Compression Using Discrete Cosine Transform” Georgian Electronic Scientific Journal: Computer Science and Telecommunications 3 (2008). [10] Saraswathy, K., D. Vaithiyanathan, and R. Seshasayanan. “A DCT approximation with low complexity for image compression” Communications and Signal Processing (ICCSP), 2013 International Conference on. IEEE, 2013.
REFERENCES [1] A. M. Shams, a. Chidanandan, w. Pan, and m. A.Bayoumi, “NEDA: A LowPower High-PerformanceDCT rchitecture,” IEEE trans. Signal process. vol.54, no. 3, pp. 955–964, mar. 2006. [2] M. R. M. Rizk and m. Ammar, “Low Power Small Area High Performance 2D-Dct Architecture,” in proc. Int. Design test workshop, 2007, pp. 120–125. [3] C. Peng, X. Cao, D. Yu, and X. Zhang, “A 250 MHz Optimized D is tr i bu t ed A r c h i t e c t u r e O f 2 D 8 x 8 D C T ,” in Proc. Int. Conf. ASIC, 2007, pp. 189–192. [4] Shinsuke Kobayushi, Kenturo Mita Graduate S c h o o l of Engineering Science, “Rapid prototyping of jpeg encoder using the asip development systempeas-111” Osaka University 0-7803-7663. [5] L.V. Agostini, I.S. Silva, and S. Bampi. Pipelined fast 2d DCT architecture for JPEG image compression. In Integrated Circuits and Systems Design, 2001, 14th Symposium on, pages 226–231, Pireno polis, Brazil, 2001. [6] Yun-Lung Lee, Jun-Wei Yang, and Jer Min Jou Design of a Distributed “JPEG Encoder on a Scalable NoC Platform” Department of Electrical Engineering, National Cheng Kung University, No.1, University Road, Tainan, Taiwan, R.O.C. 978-14244-1617-2/08/S25.00 ©2008IEEE. [7] Telagarapu, Prabhakar, et al. “Image Compression Using DCT and Wavelet Transformations” International Journal of Signal Processing, Image Processing and Pattern Recognition 4.3 (2011). [8] Elamaran, V., and A. Praveen. “Comparison of DCT and wavelets in image coding” Computer Communication and Informatics (ICCCI), 2012 International Conference on. IEEE, 2012.
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