NOVEL TECHNIQUE FOR IMPROVING THE METRICS OF JPEG ... · portion of the communication bandwidth for multimedia communication. Therefore development of efficient techniques for image

International Journal of Emerging Trends & Technology in Computer Science (IJETTCS) Web Site: www.ijettcs.org Email: [email protected], [email protected]

Volume 2, Issue 2, March – April 2013 ISSN 2278-6856

Volume 2, Issue 2 March – April 2013 Page 165

Abstract: JPEG (Joint Photographic Experts Group) is an international compression standard for continuous-tone still image, both grayscale and color. JPEG standard supports two basic compression methods. The DCT-based-Lossy compression method, and the predictive based- Lossless compression method. The DCT-based-Lossy compression method is widely used today for a large number of applications. This technique converts a signal into elementary frequency components. This work involves the design and implementation of JPEG Encoder and Decoder for the compression of gray scale images and color images as well, the process involves the application of Discrete Cosine Transformation and quantization followed by Zigzag scan and Run Length Encoding techniques as a part of compressing the input image, while the decompression involves the same operations in a reverse order. Keywords: Discrete Cosine Transform(DCT), JPEG Image Compression, Quantization, Run Length Coding(RLC), Zigzag Scan.

1. INTRODUCTION Image compression basically deals with the application of various data compression techniques on digital images. Digital representation of analog signals requires huge storage, It had always been a great challenge to transfer such files within the available limited bandwidth and storage requirement constraints. Unlike all of the other compression methods, JPEG is not a single algorithm. Instead, it may be thought of as a toolkit of image compression methods that may be altered to fit the needs of the user. JPEG may be adjusted to produce very small, compressed images that are of relatively poor quality in appearance but still suitable for many applications. Conversely, JPEG is capable of producing very high-quality compressed images that are still far smaller than the original uncompressed data.

2. IMAGE COMPRESSION FUNDAMENTALS The need for image compression becomes apparent when number of bits per image is computed resulting from typical sampling rates and quantization methods. 2.1 PRINCIPLES BEHIND COMPRESSION

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>>n2, 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. 2.2 IMAGE COMPRESSION 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 have 65, 536 elements to store and a typical 640 x 480 color image have 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

NOVEL TECHNIQUE FOR IMPROVING THE METRICS OF JPEG COMPRESSION SYSTEM

N. Baby Anusha1, K.Deepika2 and S.Sridhar3

JNTUK, Lendi Institute Of Engineering & Technology, Dept.of Electronics and communication, India




that the neighboring pixels are highly correlated and therefore contain highly redundant 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. 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. As our use of and reliance of computers continues to grow, so too does our need for efficient ways of storing large amounts of data. For example someone with a web page or online catalog-that uses dozens or perhaps hundreds of images-will more than likely need to use some form of image compression to store those images. This is because the amount of space required to hold unadulterated images can be prohibitively large in terms of cost. Fortunately, there are several methods of image compression available today. These fall into two general categories: lossless and lossy image compression. The JPEG standard is a collaboration among the International Telecommunication Union (ITU), International Organization for Standardization (ISO), and International Electro technical Commission (IEC). Its official name is "ISO/IEC 10918-1 Digital compression and coding of continuous-tone still image", and "ITU-T Recommendation T.81".The JPEG process is a widely used form of lossy image compression that centers around the Discrete Cosine Transform. JPEG have the following modes of operations : (a) Lossless mode: The image is encoded to guarantee

exact recovery of every pixel of original image even though the compression ratio is lower than the lossy modes.

(b) Sequential mode: It compresses the image in a single left-to-right, top-to-bottom scan.

(c) Progressive mode: It compresses the image in multiple scans. When transmission time is long, the image will display from indistinct to clear appearance.

(d) Hierarchical mode: Compress the image at multiple resolutions so that the lower resolution of the image can be accessed first without decompressing the whole resolution of the image.

The last three DCT-based modes (b, c, and d) are lossy compression because precision limitation to compute

DCT and the quantization process introduce distortion in the reconstructed image. The lossless mode uses predictive method and does not have quantization process. The hierarchical mode can use DCT-based coding or predictive coding optionally. The most widely used mode in practice is called the baseline JPEG system, which is based on sequential mode, DCT-based coding and Huffman coding for entropy encoding. 2.3 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. They are: 1. Lossy Image Compression 2. Lossless Image Compression 2.3.1 LOSSY IMAGE COMPRESSION 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. The transformation is applied to the original image. The quantization process results in loss of information. The entropy coding after the quantization step, however, is lossless. The decoding is a reverse process. Firstly, entropy decoding is applied to compressed data to get the quantized data. Secondly, reverse quantization is applied to it & finally the inverse transformation to get the reconstructed image. Major performance considerations of a lossy compression scheme include:

Compression ratio Signal - to – noise ratio 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 2.3.1.1 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. 2.3.2 LOSSLESS IMAGE COMPRESSION 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. Lossless compression techniques includes following schemes: 1. Run length encoding 2. Huffman encoding 3. LZW coding 4. Area coding 2.3.2.1 RUN LENGTH ENCODING This is a very simple compression method used for sequential data. It is very useful in case of repetitive 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. 3. PROPOSED ARCHITECTURE The prescribed architecture of JPEG Image Compression using DCT for Grayscale images is shown below

Fig.3.1: Prescribed Architecture of JPEG Image Compression using DCT for Grayscale Images

We will discuss in detail about each block in the above block diagram:

DCT (Discrete cosine transform) Quantization Zigzag Scan RLC (Run length coding) Inverse RLC Inverse Zigzag Reverse Quantization IDCT (Inverse Discrete Cosine Transform)

3.1 DISCRETE COSINE TRANSFORM 1. ONE-DIMENSIONAL DCT The most common DCT definition of a 1-D sequence of length N is

In both equations as above, α(k) is defined as:

The basis sequences of the 1D DCT are real, discrete-time sinusoids are defined by:

Each element of the transformed list X[k] in equation of Forward DCT is the inner dot product of the input list x[n] and a basis vector. Constant factors are chosen so the basis vectors are orthogonal and normalized. The DCT can be written as the product of a vector (the input list) and the N x N orthogonal matrix whose rows are the basis vectors. 2. TWO-DIMENSIONAL DCT The two-dimensional discrete cosine transform (2D-DCT) is used for processing signals such as images. The 2D DCT resembles the 1D DCT transform since it is a separable linear transformation; that is if the two-dimensional transform is equivalent to a one-dimensional DCT performed along a single dimension followed by a one-dimensional DCT in the other dimension. For example, in an n x m matrix, S, the 2D DCT is computed by applying it to each row of S and then to each column of the result. Since the 2D DCT can be computed by applying 1D transforms separately to the rows and columns, hence the 2D DCT is separable in the two dimensions. The 2-D DCT is similar to a Fourier transform but uses purely real math. It has purely real transform domain coefficients and incorporates strictly positive frequencies. The 2D DCT is equivalent to a DFT of roughly twice the length, operating on real data with even symmetry, where in some variants the input and/or output data are shifted by half a sample. As the 2D DCT is simpler to evaluate than the Fourier transform, it has become the transform of choice in image compression standards such as JPEG. The 2D DCT represents an image as a sum of sinusoids of varying magnitudes and frequencies. It has the property that, for a typical image, most of the visually significant information about the image is concentrated in just a few coefficients of the DCT. The mathematical definition of DCT is :




The above equation is called the analysis formula or the ‘forward transform’ Because the DCT uses cosine functions, the resulting matrix depends on the horizontal, diagonal, and vertical frequencies. Therefore am image black with a lot of change in frequency has a very random looking resulting matrix , while an image matrix of just one color, has a resulting matrix of a large value for the first element and zeros for the other elements. Mathematically, the DCT is perfectly reversible and there is no loss of image definition until coefficients are quantized. The pixels in the DCT image describe the proportion of each two-dimensional basis function present in the image. Each basis matrix is characterized by a horizontal and vertical spatial frequency. The matrices arranged from left to right and top to bottom in order of decreasing frequencies. The top-left function (brightest pixel) is the basis function of the "DC" coefficient, with frequency {0,0} and represents zero spatial frequency. It is the average of the pixels in the input, and is typically the largest coefficient in the DCT of "natural" images. Along the top row the basis functions have increasing horizontal spatial frequency content. Down the left column the functions have increasing vertical spatial frequency content. 3.2 QUANTIZATION The block of 8 x 8 DCT coefficients are divided by an 8 x 8 quantization table. In quantization the low DCT coefficients of the high frequencies are discarded. Thus, quantization is applied to allow further compression of entropy encoding by neglecting insignificant low coefficients. The DCT implies that many of the higher frequencies of an image can be discarded without any perceived degradation of image quality. In lossy compression, quantization exploits both facts by scaling the DCT coefficients to levels that will result in the zeroing of most of the higher frequencies, but maintaining most of the image’s energy. The 8 x 8 block of DCT coefficients is now ready for compression by quantization. A remarkable and highly useful feature of the JPEG process is that in this step, varying levels of image compression and quality are obtainable through selection of specific quantization matrices. This enables the user to decide on quality levels ranging from 1 to 100, where 1 gives the poorest image quality and highest compression, while 100 gives the best quality and lowest compression. As a result, the quality/compression ratio can be tailored to suit different needs. Subjective experiments involving the human visual system have resulted in the JPEG standard quantization matrix. With a quality level of 50, this matrix renders both high compression and excellent decompressed image quality. If, however, another level of quality and compression is desired, scalar multiplies of the JPEG standard quantization matrix may be used. For a quality level

greater than 50 (less compression, higher image quality), the standard quantization matrix is multiplied by (100-quality level)/50. For a quality level less than 50 (more compression, lower image quality), the standard quantization matrix is multiplied by 50/quality level. The scaled quantization matrix is then rounded and clipped to have positive integer values ranging from 1 to 255. Quantization is achieved by dividing each element in the transformed image matrix D by the corresponding element in the quantization matrix, and then rounding to the nearest integer value.

3.3 ZIGZAG SCAN After doing 8x8 DCT and quantization over a block we have new 8x8 blocks which denotes the value in frequency domain of the original blocks. Then we have to reorder the values into one dimensional form in order to encode them. the AC terms are scanned in a Zigzag manner. The reason for this zigzag traversing is that we traverse the 8x8 DCT coefficients in the order of increasing the spatial frequencies. So, we get a vector sorted by the criteria of the spatial frequency. After we are done with traversing in zigzag the 88 matrix we have now a vector with 64 coefficients (0, 1... 63).

Fig 3.1: Zigzag Scan

3.4 RUN-LENGTH CODING Run-length encoding (RLE) is a very simple form of data compression in which runs of data (that is, sequences in which the same data value occurs in many consecutive data elements) are stored as a single data value and count, rather than as the original run. This is most useful on data that contains many such runs: for example, simple graphic images such as icons, line drawings, and animations. It is not useful with files that don't have many runs as it could greatly increase the file size. Now we have the one dimensional quantized vector with a lot of consecutive zeroes. We can process this by run length coding of the consecutive zeroes. Let's consider the 63 AC coefficients in the original 64 quantized vectors first. For example, we have: 57, 45, 0, 0, 0, 0, 23, 0, -30, -16, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,

..., 0 We encode for each value which is not 0, than add the number of consecutive zeroes preceding that value in front of it. The RLC (run length coding) is:

(0,57) ; (0,45) ; (4,23) ; (1,-30) ; (0,-16) ; (2,1) ; EOB




The EOB (End of Block) is a special coded value. If we have reached in a position in the vector from which we have till the end of the vector only zeroes, we'll mark that position with EOB and finish the RLC of the quantized vector. Note that if the quantized vector does not finishes with zeroes (the last element is not 0), we do not add the EOB marker. Actually, EOB is equivalent to (0,0), so we have : (0,57) ; (0,45) ; (4,23) ; (1,-30) ; (0,-16) ; (2,1) ; (0,0) 3.5 RUN-LENGTH DECODER The 4-bit run-length is a count of the number of zero data values occurred between the last non-zero data value and the current one. The 4-bit data-length is the number of bits following this 8-bit word that make up the actual non-zero data point. A data-length of 0 signifies either the end of a data block or if the run-length is 15 then the event of 16 consecutive zero data values. 3.6 INVERSE ZIGZAG The frequency matrix is ordered in a zigzag fashion as described in the following Figure 3.2

Fig 3.2: After Inverse Zigzag

3.7 REVERSE QUANTIZATION

The Reverse Quantization requests data values from its input. It multiplies these data values by the corresponding value in the Quantization table and then places them in the appropriate location in the 8x8 JPEG data block. During JPEG encoding the frequency components of the data block are ordered so that the low frequency components are at the beginning and higher frequency components follow. This data block is then passed on to the Inverse Discrete Cosine Transform unit. Since the Reverse Quantization block is in the middle of the JPEG decoder pipeline and is relatively simple. It requests the Huffman Decoder to give it data and with that data it assembles a data block and requests the Inverse Discrete Cosine Transform unit to decode it. This allows almost all of the operations of the Quantization Unit to be done while the Huffman decoder,

which takes a long time since it has to make decisions at every bit, is running. Reconstruction of our image begins by decoding the bit stream representing the quantized matrix C. Each element of C is then multiplied by the corresponding element of the quantization matrix originally used.

The IDCT is next applied to matrix R, which is rounded to the nearest integer. 3.9 INVERSE DISCRETE COSINE TRANSFORM The Inverse Discrete Cosine Transform unit is definitely the most complex unit in the JPEG decoder. The IDCT requires many multiplications and additions of irrational values and is computationally intensive. Since a floating point ALU is very difficult to design, very large, and very slow floating point arithmetic is generally never done in custom hardware designs except for the data-path of a microprocessor where it can be properly shared among many different uses.

Here are the equations for the 2-Dimensional 8x8 Inverse Discrete Cosine Transform

0102

11612cos

1612cos

41,:IDCT

7

0

7

0,,

nnC

vyuxSCCyxs

n

u vvuvuyx

4. DESIGN METRICS

4.1 MEAN SQUARE ERROR

The MSE is the second moment (about the origin) of the error, and thus incorporates both the variance of the estimator and its bias. For an unbiased estimator, the MSE is the variance of the estimator. Like the variance, MSE has the same units of measurement as the square of the quantity being estimated. In an analogy to standard deviation, taking the square root of MSE yields the root mean square error or root mean square deviation (RMSE or RMSD), which has the same units as the quantity being estimated; for an unbiased estimator, the RMSE is the square root of the variance, known as the standard deviation.

If is a vector of n predictions, and is the vector of the true values, then the MSE of the predictor is:

4.2 PEAK 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.

PSNR is most easily defined via the mean squared error (MSE). Given a noise-free m×n monochrome image I and its noisy approximation K, MSE is defined as:

The PSNR is defined as:

4.3 COMPRESSION RATIO

The size of the compressed image divided by the size of the original image and this value will be subtracted from 1 and the final value gives the compression ratio. This ratio gives an indication of how much compression is achieved for a particular image. Most algorithms have a typical range of compression ratios that they can achieve over a variety of images. Because of this, it is usually more useful to look at an average compression ratio for a particular method.

The compression ratio typically affects the picture quality. Generally, the higher the compression ratio, the poorer the quality of the resulting image. The tradeoff between compression ratio and picture quality is an important one to consider when compressing images.

Compression ratio = 1- (Compressed image size / Original image size) x 100%

4.4 BITS PER PIXEL The number of bits of information stored per pixel of an image or displayed by a graphics adapter. The more bits there are, the more colors can be represented, but the more memory is required to store or display the image.

Bpp = numbers of bits/number of pixels 5. EXPERIMENTAL ANALYSIS RESULTS FOR GRAY SCALE IMAGES For Baboongray image

Fig 5.1: Quality level vs Design metrics for Baboongray

image For Lenagray image

Qua

lity

Level

Size

of the

image

PSN

R

MSE CR

10 256 x

256

22.31

39

381.6

680

94.8

%

40 256 x

256

26.08

83

160.0

485

67.9

%

60 256 x

256

27.92

75

104.7

921

49.9

%

80 256 x

256

31.72

55

43.70

46

15.0

%




Qual

ity

Level

Size of

the

image

PSNR MSE CR

10 256 x

256

23.03

88

322.9

979

95.8%

40 256 x

256

27.96

38

103.9

202

78.5%

60 256 x

256

29.88

06

66.83

77

66.6%

80 256 x

256

33.49

60

29.07

24

40.5%

Fig 5.2: Quality level vs Design metrics for Lenagray image

For Rosesgray image

Qual

ity

Level

Size of

the

image

PSN

R

MSE CR

10 256 x

256

24.31

35

240.8

423

96.7%

40 256 x

256

29.17

67

78.59

70

83.8%

60 256 x

256

31.16

42

49.73

44

74.2%

80 256 x

256

34.52

13

22.95

87

53.2%

Fig 5.3: Quality level vs Design metrics for Rosesgray

image 6. CONCLUSION

For the gray scale images, different objective fidelity quality metrics like Peak Signal to Noise




Ratio(PSNR), Mean Square Error(MSE) and Compression Ratio(CR) have been arrived.

The findings for gray scale images are

For Rosesgray image, the PSNR value is 34.5213 and it is more compared to other input gray scale images.

For Rosesgray image, the CR value is 96.7% and it is more compared to other input gray scale images.

For Rosesgray image, the MSE value is 22.9587 and it is less compared to other input gray scale images.

Finally the proposed JPEG algorithm can be extended for Region Of Interest(ROI) segmentation based image compression technique which involves dividing the image into two images namely front portion of the image and back portion of the image.

The back portion of the image comes under redundant data and so it can be compressed to the maximum extent.

This doesn't effect the front portion of the image and so the compression can be done better only to our desired area.

REFERENCES [1] Z. Lin, J. He, X. Tang, and C. -K. Tang, “Fast,

automatic and fine grained tampered JPEG image detection via DCT coefficient analysis,” Pattern Recognit., vol. 42, pp. 2492–2501, 2009.

[2] G. K. Wallace, “The JPEG still picture compression standard,” IEEE Trans. Consumer Electron., vol. 38, no. 1, pp. XVIII–XXXIV, Feb. 1992.

[3] Kesavan, Hareesh. Choosing a DCT Quantization Matrix for JPEG Encoding. Web page. http://www.ise.Stanford.EDU/class/ee392c/demos/kesavan/

[4] McGowan, John. The Discrete Cosine Transform. Web page. http://www.rahul.net/jfm/dct.html

[5] Wallace, Gregory K. The JPEG Still Picture Compression Standard. Paper submitted in December1991 for publication in IEEE Transactions on Consumer Electronics.

[6] Wolfgang, Ray. JPEG Tutorial. Web page. [7] Nelson, Mark, The Data Compression Book:

Featuring Fast, Efficient, Data Compression Techniques in C, M&T Books, Redwood City, CA, 1992.

[8] Ramstad, Tor A. Still Image Compression, New York: CRC Press, 1998.

[9] Data Compression Book (The Complete Reference) by David Salomon

[10] Digital Image Processing, 2/E by Gonzalez www.prenhall.com/gonzalezwoods

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NOVEL TECHNIQUE FOR IMPROVING THE METRICS OF JPEG ... · portion of the communication bandwidth for multimedia communication. Therefore development of efficient techniques for image