Sparse Transform Matrix at Low Complexity for Color Image Compression

Sparse Transform Matrix at Low Complexity for Color Image Compression Dr. K. Kuppusamy, M.Sc.,M.Phil.,M.C.A.,B.Ed.,Ph.D #1, R.Mehala, (M.Phil, Research Scholar) *2. # Department of Computer science and Engineering, Alagappa University, Karaikudi, INDIA Abstract- Image Processing is a powerful era of the Modern Digital Technology. Compression is a process of minimizing the size in bytes of a graphics file without degrading the quality of the image to an unacceptable level. In this paper, we have discusses about Digital Image Compression for the good performance complexity of still imagery and the comparative study of several algorithms. In future we are going to propose a new plan to provide a reduction in computation over the sparse matrix and using the various test images for the entropy coding and quality scalability is enabled by simply truncating the generated bit rate distortion performance. Keywords: image compression, sparse matrix, entropy coding, quality scalability, bit rate etc. I. INTRODUCTION A. Image An image is an essentially 2-D signal processed by the human visual system. The signals representing images are usually in analog form. An image is a processing, storage and transmission by computer applications, they are converted from analog to digital form. B. Digital Image A digital image is a representation of a two-dimensional image as a finite set of digital values, called picture elements or pixels. Pixel values are typically represented at gray levels, colors, heights, opacities etc. Digital Image Types 1. Binary Image 2. Color Image 3. Gray Scale Image 4. Indexed Image Digital image processing focuses on two major tasks 1. Improvement of pictorial information for human interpretation 2. Processing of image data for storage, transmission and representation for autonomous machine perception Some argument about where image processing ends and fields such as image analysis and computer vision start. C. Image Compression Compression is a process of reducing or eliminating redundant or irrelevant data. An Image compression is the addresses of the problem of reducing the amount of data required to represent a digital image. The Compressed image is not directly displayable. It must be decompressed before input to a Color Monitor. It also reduces the time required for images to be sent over the Internet or downloaded from Web pages. Basic data redundancies 1. Coding Redundancy 2. Interpixel Redundancy 3. Psychovisual Redundancy Coding redundancy is present when less than optimal code words are used. Interpixel ISSN: 2231-2803 http://www.ijcttjournal.org Page 1

redundancy results from correlations between the pixels of an image. Psychovisual redundancy is due to data that is ignored by the human visual system. Image compression techniques are reduced the number of bits required to represent an image by taking advantage of these redundancies. An inverse process called decompression (decoding) is applied to the compressed data to get the reconstructed image. f(x,y) Mapper Compressed Image Symbol Decoder Quantize r D. Basic Image Compressed Model Symbol Coder Inverse Mapper The JPEG compression process contains three primary parts as shown in JPEG Encoding flowchart. To prepare for processing, the matrix representing the image is converted from RGB color space to YCbCr and undergoes the subsampling process. Then the partition process divides the matrix into the size was dependent on the balance between image quality and the processing power of the time. This is formally called block and passes them through the encoding process in chunks. To reverse the compression and display a close approximation to the original image the compressed data is fed into the reverse process as shown in JPEG Encoding flow chart. These figures illustrate the special case of single-component (grayscale) image compression. Color image compression can then be approximately regarded as compression of multiple grayscale images, which are either compressed entirely one at a time, or are compressed by alternately interleaving 8x8 sample blocks from each in turn. JPEG encoding flow chart. JPEG decoding flow chart. II. TRANSFORMATION F(X,Y) A reversible process that reduces redundancy and/or provides an image representation that is more an enable to the efficient extraction and coding of relevant information. Examples 1. Block-based linear transformations, e.g. Discrete Cosine Transform (DCT) 2. Wavelet decompositions. 3. Prediction/residual formation, e.g. Differential Pulse Code Modulation (DPCM) 4. Color space transformations, e.g. RGB to YCrCb. 5. Model prediction/residual formation, e.g. Fractals A. Image Representation with DCT DCT coefficients can be viewed as weighting functions that, when applied to the 64 cosine basis functions of various spatial frequencies (8 x 8 templates), will reconstruct the Original block. Original image block = y(0,0) x + y(1,0) x + + y(7,7) x DC (flat) basis function ISSN: 2231-2803 http://www.ijcttjournal.org Page 1616

AC basis functions B. Differential Pulse Code Modulation Lossless JPEG and 4.3 DPCM are based on differential pulse code modulation (DPCM). A spatial transformation modifies the spatial relationship between pixels in an image, mapping pixel locations in an image to new locations in an output image. Toolbox Includes Functions: Resizing an Image In DPCM, a combination of previously encoded pixels (A, B, C) is used as a prediction (c) for the current pixel (X). Rotating an Image Cropping an Image 2-D Spatial Transformations The difference between the actual value and the prediction (c - X) is encoded using Huffman coding. The quantized difference is encoded in lossy DPCM Properties Low complexity High quality (limited compression) Low memory requirements N-D Spatial Transformations. E. Histogram Histogram consists of a graph indicating the number of times each levels occurs in the image. C. Color Space Transformation original output Color space conversion from RGB to YCbCr The process of compression starts from the conversion of color space. We use the transform matrix, to convert the three dimensions color matrix of the image from RGB to YCbCr pixel by pixel. Y 0.299 0.587 0.114 R 0 U 0.1687 0.3313 0.5 G 0.5 V 0.5 0.4187 0.0813 B 0.5 D. Spatial Transformation III. QUANTIZATION Quantization refers to the process of approximating the continuous set of values in the image data with a finite set of values. The input to a quantizer is the original data, and the output is always one among a finite number of levels. This is a process of approximation, and a good quantizer is one which represents the original signal with minimum loss or distortion. There are two types of quantization 1. Scalar Quantization 2. Vector Quantization. ISSN: 2231-2803 http://www.ijcttjournal.org Page 1617

In scalar quantization, each input symbol is treated separately in producing the output, while in vector quantization the input symbols are clubbed together in groups called vectors, and processed to give the output. This clubbing of data and treating them as a single unit increases the optimality of the vector quantizer, but at the cost of increased computational complexity. A quantizer can be specified by its input partitions and output levels. If the input range is divided into levels of equal spacing, then the quantizer is termed as a Uniform Quantizer, and if not, it is termed as a Non- Uniform Quantizer. A uniform quantizer can be easily specified by its lower bound and the step size. Also, implementing a uniform quantizer is easier than a non-uniform quantizer. Take a look at the uniform quantizer shown below. If the input falls between n*r and (n+1)*r, the quantizer outputs the symbol n. A uniform quantizer A many-to-one mapping that reduces the number of possible signal values at the cost of introducing errors. The simplest form of quantization (also used in all the compression standards) is scalar quantization (SQ), where each signal value is individually quantized. The joint quantization of a block of signal values is called vector quantization (VQ). It has been theoretically shown that the performance of VQ can get arbitrarily close to the rate-distortion (R-D) bound by increasing the block size. IV. IMAGE COMPRESSION TECHNIQUES The image compression techniques are broadly classified into two categories depending whether or not an exact replica of the original image could be reconstructed using the compressed image. These are: 1. Lossless technique 2. Lossy techniqhe A. Lossless compression technique In lossless compression techniques, the original image can be perfectly recovered from the compressed (encoded) image. These are also called noiseless since they do not add noise to the signal (image).it is also known as entropy coding since it use statistics/decomposition techniques to eliminate/minimize redundancy. Lossless compression is used only for a few applications with stringent requirements such as medical imaging. Following techniques are included in lossless compression: 1. Run length encoding 2. Huffman encoding 3. LZW coding 4. Area coding 1. Run Length Encoding This is a very simple compression method used for sequential data. This technique replaces sequences of identical symbols (pixels), called runs by shorter symbols. The run length code for a gray scale image is represented by a sequence {Vi, Ri} where Vi is the intensity of pixel and Ri refers to the number of consecutive pixels with the intensity Vi. If both Vi and Ri are represented by one byte, this span of 12 pixels is coded using eight bytes yielding a compression ratio of 1: 5. 82 82 82 82 82 89 89 89 89 90 90 {82,5} {89,4} {90,2} Run Length Encoding 2. Huffman Encoding This is a general technique for coding symbols based on their statistical occurrence ISSN: 2231-2803 http://www.ijcttjournal.org Page 1618

frequencies (probabilities). The pixels in the image are treated as symbols. The symbols that occur more frequently are assigned a smaller number of bits, while the symbols that occur less frequently are assigned a relatively larger number of bits. Huffman code is a prefix code. Most image coding standards use lossy techniques in the earlier stages of compression and use Huffman coding as the final step. 3. LZW Coding LZW (Lempel- Ziv Welch) is a dictionary based coding. Dictionary based coding can be static or dynamic. In static dictionary coding, dictionary is fixed during the encoding and decoding processes. In dynamic dictionary coding, the dictionary is updated on fly. LZW is widely used in computer industry and is implemented as compress command on UNIX. 4 Area Coding Area coding is an enhanced form of run length coding, reflecting the two dimensional character of images. This is a significant advance over the other lossless methods. The algorithms for area coding try to find rectangular regions with the same characteristics. These regions are coded in a descriptive form as an element with two points and a certain structure. This type of coding can be highly effective but it bears the problem of a nonlinear method, which cannot be implemented in hardware. Therefore, the performance in terms of compression time is not competitive, although the compression ratio is. B. Lossy compression technique Lossy schemes provide much higher compression ratios than lossless schemes. Lossy schemes are widely used since the quality of the reconstructed images is adequate for most applications.by this scheme, the decompressed image is not identical to the original image, but reasonably close to it. Major performance considerations of a lossy compression scheme include: 1. Compression ratio 2. Signal - to noise ratio 3. Speed of encoding & decoding. Lossy compression techniques includes following schemes: 1. Transformation coding 2. Vector quantization 3. Fractal coding 4. Block Truncation Coding 5. Sub band coding 1. Transformation Coding In this coding scheme, transforms such as DFT (Discrete Fourier Transform) and DCT (Discrete Cosine Transform) are used to change the pixels in the original image into frequency domain coefficients (called transform coefficients). The selected coefficients are considered for further quantization and entropy encoding. DCT coding has been the most common approach to transform coding. It is also adopted in the JPEG image compression standard. 2. Vector Quantization The basic idea in this technique is to develop a dictionary of fixed-size vectors, called code vectors. A vector is usually a block of pixel values. A given image is then partitioned into non-overlapping blocks (vectors) called image vectors. Then for each in the dictionary is determined and its index in the dictionary is used as the encoding of the original image vector. Thus, each image is represented by a sequence of indices that can be further entropy coded. 3. Fractal Coding The essential idea here is to decompose the image into segments by using standard image processing techniques such as color separation, edge detection, and spectrum and texture analysis. The library actually contains codes called iterated function system (IFS) codes, which are compact sets of numbers. This scheme is highly effective for compressing images that have good regularity and self-similarity. ISSN: 2231-2803 http://www.ijcttjournal.org Page 1619

4. Block truncation coding In this scheme, the image is divided into non overlapping blocks of pixels. For each block, threshold and reconstruction values are determined. The threshold is usually the mean of the pixel values in the block. Then a bitmap of the block is derived by replacing all pixels whose values are greater than or equal (less than) to the threshold by a 1 (0). Then for each segment (group of 1s and 0s) in the bitmap, the reconstruction value is determined. This is the average of the values of the corresponding pixels in the original block. 5. Sub band coding In this scheme, the image is analyzed to produce the components containing frequencies in well-defined bands, the sub bands. Subsequently, quantization and coding is applied to each of the bands. The advantage of this scheme is that the quantization and coding well suited for each of the sub bands can be designed separately. V. APPLICATION TO COLOR IMAGE COMPRESSION We will apply the above transform matrix in a standard JPEG baseline encoder. The quantization operation is applied after transformation using proposed matrix, the diagonal term of the matrix can be merge into the quantizer. VI.CONCLUSION In this paper, we proposed a sparse matrix transform for color image compression. A fast algorithm for computation is also developed. The basis of the proposed algorithm is based on integers, and made sufficiently sparse matrix. In future we are going to propose a new plan to provide a reduction in computation over the sparse matrix and using the various test images for the entropy coding and quality scalability is enabled by simply truncating the generated bit rate distortion performance. It can be suitable for fast VLSI implementation. REFERENCES 1. Subramanya A, Image Compression Technique, Potentials IEEE, Vol. 20, Issue 1, pp 19-23, Feb- March 2001, 2. Hong Zhang, Xiaofei Zhang & Shun Cao, Analysis & Evaluation of Some Image Compression Techniques, High Performance Computing in Asia Pacific Region, 2000 Proceedings, 4th Int. Conference, vol. 2, pp 799-803,14-17 May, 2000 3. Ming Yang & Nikolaos Bourbakis, An Overview of Lossless Digital Image Compression Techniques, Circuits & Systems, 2005 48th Midwest Symposium, vol. 2 IEEE, pp 1099-1102, 7 10 Aug, 2005 4.Milos Klima, Karel Fliegel, Image Compression Techniques in the field of securitytechnology: Examples and Discussion, Security Technology, 2004, 38th Annual 2004 Intn. Carnahan Conference, pp 278-284,11-14 Oct., 2004 5. Ismail Avcibas, Nasir Memon, Bulent Sankur, Khalid Sayood, A Progressive Lossless / Near Lossless Image Compression Algorithm, IEEE Signal Processing Letters, vol. 9, No. 10, pp 312-314, October 2002. 6. Dr. Charles F. Hall, A Hybrid Image Compression Technique, Acoustics Speech & Signal Processing, IEEE International Conference on ICASSP 85, Vol. 10, pp 149-152, Apr, 1985 7. Wen Shiung Chen, en- HuiYang & Zhen Zhang, A New Efficient Image Compression Technique with Index- Matching Vector Quantization, Consumer Electronics, IEEE Transactions, Vol. 43, Issue 2, pp 173-182, May 1997. 8. W.B.Pennebaker and J.L.Mitchell, JPEG Still Image Compression Standard, Chapman & Hall, New York, 1993. 9. David H. Kil and Fances Bongjoo Shin, Reduced Dimension Image Compression And its Applications, Image Processing, 1995, Proceedings, International Conference,Vol. 3, pp 500-503, 23-26 Oct.,1995 10. C.K. Li and H.Yuen, A High Performance Image Compression Technique For Multimedia Applications, IEEE Transactions on Consumer Electronics, Vol. 42, no. 2, pp 239-243, 2 May 1996. 11. Shi-Fei Ding, Zhong Zhi Shi,Yong Liang, Feng- Xiang Jin, Information Feature Analysis and Improved Algorithm of PCA, Proceedings of the 4 th International Conference on Machine Learning and Cybernetics, Guangzhou, pp 1756-1761, 18-21 August,2005 ISSN: 2231-2803 http://www.ijcttjournal.org Page 1620