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JPEG: Still Image Compression StandardStandard

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IntroductionTh JPEG L l C di Al i hThe JPEG Lossless Coding AlgorithmBaseline JPEG CompressionProgressive DCT-Based ModeHierarchical Mode

Multimedia Computing (CSIT 410) 2

I t d tiIntroduction

JPEG is the first image compression JPEG is the first image compression standard for continuous tone still imagesgAcronym for Joint Photographic Experts Groupp pOfficially referred to as

ISO/IEC IS (International Standard) 10918-1: Digital Compression and Coding of Continuous-tone Still ImagesITU T Recommendation T 81ITU-T Recommendation T.81


I t d tiIntroduction [2]

Goal of the standard is to support a variety of applications for compression of continuous-tone still images of most image sizes in any color space in order to achieve compression performance at or achieve compression performance at or near the state-of-the-art with user-adjustable compression ratios and with adjustable compression ratios and with very good to excellent reconstructed quality



JPEG d fi f d f iJPEG defines four modes of operation

1 Sequential Lossless Mode: Compress the image in a1. Sequential Lossless Mode: Compress the image in asingle scan and the decoded image is an exactreplica of the original image.

2. Sequential DCT-based Mode: Compress the imagein a single scan using DCT-based lossy compressiontechnique As a result the decoded image is not antechnique. As a result, the decoded image is not anexact replica, but an approximation of the originalimage.



3. Progressive DCT-based Mode: Compress theimage in multiple scans and alsod th i i lti l ithdecompress the image in multiple scans witheach successive scan producing a better-quality image.

4. Hierarchical Mode: Compress the image atmultiple resolutions for display on differentd idevices.



Modes 2 3 and 4 are lossyModes 2, 3 and 4 are lossyMode 1 uses predictive coding with no quantization hence losslessquantization, hence losslessSequential DCT-based JPEG algorithm

In it’s simplest form called baseline JPEGIn it s simplest form called baseline JPEGalgorithm, which is based on Huffman coding for entropy encoding (2)The other form is based on arithmetic coding for entropy encoding (3)


The JPEG Lossless Coding Algorithm

Based on the principle of predictiveBased on the principle of predictivecoding, a simple method for spatialredundancy reductionThe difference between the actual pixelvalue and the predicted value is called thedifferential or the prediction error value &is entropy encoded using a variable-length encoding techniquelength encoding techniqueDifferential Pulse Code Modulation (DPCM)


The JPEG Lossless Coding Algorithm [2]

The value of the pixel in location X is predicted using gone or more of the 3-neighbors as shown in fig-(a)g ( )Then the prediction error / prediction residualprediction residualis coded using Huffman coding / Arithmetic Coding Fig (a) : 3-pixel neighborhood for pixel XArithmetic Coding

Multimedia Computing (CSIT 410)

g ( ) p g p

Fig (b) : Encoder Diagram for Lossless mode


Eight possible options for predictionsOption-0 is available for Option Prediction Type Of Prediction

Table-1 : Prediction Functions for Lossless JPEG

Option-0 is available for only JPEG compression in hierarchical modeOptions 1-3 are 1-

Option Prediction Function

Type Of Prediction

0 No Prediction Differential coding

1 Xp=A 1-D horiz. PredictOptions 1-3 are 1-Dimensional PredictorsOptions 4-7 are 2-Dimensional Predictors

p

2 Xp=B 1-D Vert. Predict

3 Xp=C 1-D Diagonal Predict.

4 Xp=A+B-C 2-D PredictionDimensional PredictorsThe Chosen Predictor function is available at the header of the compressed

p

5 Xp=A+½ (B-C) 2-D Prediction

6 Xp=B+½ (A-C) 2-D Prediction

7 Xp=½ (A+B) 2 D Predictionheader of the compressed file


7 Xp=½ (A+B) 2-D Prediction

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P i i f th i b f 2 Precision of the source image can be from 2 to 16 bitsThe very first pixel is calculated as follows

2 P-Pt-1

P - Precision of the Source imagePt – Point Transform Parameter (default value =0)

For the pixels in the first row, except first pixel, use option 1 for predictionThe first pixel of second row to the last row The first pixel of second row to the last row are predicted using option 2Every other pixels are predicted using the chosen prediction functionchosen prediction function



Prediction residuals are calculated for modulo 216Prediction residuals are calculated for modulo 216

The Prediction residuals are first represented using (CATEGORY, MAGNITUDE) pair

CATEGORY Category of error ValueRepresents number of bits needed to represent the p perror

MAGNITUDE Variable length integer (VL1) to represent the errorg g ( ) p

Only the CATEGORY value in each pair is Huffman coded, not the other one



The 2-step pair formation process is as follows

1. Huffman code CATEGORY2. Append it to CATEGORY number of bits

to represent MAGNITUDEto represent MAGNITUDEa) If MAGNITUDE is positive, Append As Such

(hence starts with 1)b) If MAGNITUDE is negative, Append 1’s

complement



For prediction residual 25

The pair becomes The pair becomes (5,25)Assuming the Huffman

d f 5 i 011 th code for 5 is 011, the representation would be

01111001–25 is represented as,

01100110


Table 2: Categories of Prediction Error Values

14


So, Why not using Huffman code Just f th l t f di ti for the complete range of prediction residuals?

Huffman table with 216 entries for all the Huffman table with 216 entries for all the 216 possible symbols of prediction residuals would be almost impossible to work with.


Baseline JPEG Compression

D fi d f ti t i ith Defined for continuous tone images with 1 to 4 components

Grayscale image consists only one Grayscale image consists only one componentColor image may have up to 4 componentsO l 8 bit ll d f h tOnly 8 bits allowed for each component

Good compression relies on exploiting Good compression relies on exploiting the inter-component correlation between the R, G, B components


Baseline JPEG Compression [2]

I i R G B t i Image in R,G B components is converted into Luminance-Chrominance components (they are Chrominance components (they are more decorrelated than R,G,B components)

Ch i C f h Chrominance Components are further subsampled


Baseline JPEG Compression [3]Baseline JPEG Compression [3]COLOR SPACE CONVERSIONS

fConverting from RGB to YCBCR

CB & CR can result in negative To bring it CB & CR can result in negative. To bring it to positive & to representable in 8 bits


Baseline JPEG Compression [4]Baseline JPEG Compression [4]COLOR SPACE CONVERSIONS

The inverse color transformation is The inverse color transformation is

Baseline JPEG supports the subsampling of CB

d l& CR according to 4:2:0, 4:2:2 or 4:4:4 color formats

Choosing 4:2:2 would be the first lossy step in the g y pbaseline compression (4:2:0 will lose more)

The color space conversion is not applicable for Grayscale imagesfor Grayscale images


Baseline JPEG Compression [5]Baseline JPEG Compression [5]SOURCE IMAGE DATA ARRANGEMENT

Dimension of each component Y, Cb and CrDimension of each component Y, Cb and Crcould be different, due to subsamplingEach component is divided into 8 x 8 non ac co po e t s d ded to 8 8 ooverlapping blocksIn non interleaved scan, each data blocks ,are coded from left to right & top to bottomIn Interleaved scan, Minimum coded Unit(MCU) consists of data blocks from all the th tthree components


Baseline JPEG Compression [6]Baseline JPEG Compression [6]SOURCE IMAGE DATA ARRANGEMENT

(a) YCbCr 4:4:4, (b) YCbCr 4:2:2, ( )(c) YCbCr 4:2:0.

Different interleaved scans processing


p gorder

Baseline JPEG Compression [7]Baseline JPEG Compression [7]BASELINE COMPRESSION ALGORITHM


Baseline JPEG Compression [8]Baseline JPEG Compression [8]BASELINE COMPRESSION ALGORITHM

Level shift each pixel in the 8 x 8 block & e e s t eac p e t e 8 8 b oc &convert it to signed integer (subtract 128)Transform each pixel in the block into f d i i f d di frequency domain via forward discrete cosine transform (FDCT)The FDCT for 8 x 8 block is defined byThe FDCT for 8 x 8 block is defined by

For u = 0 7 & v = 0 7, where


Baseline JPEG Compression [9]Baseline JPEG Compression [9]CODING DCT COEFFICIENTS

Transformed 8 × 8 block Transformed 8 × 8 block now consists of 64 DCT coefficients

The first coefficient F(0, 0) is the DC component of the block

DC t i th DC components is the sum of all the 64 pixels in the input scaled by 1/8

Remaining 63 coefficients Remaining 63 coefficients are AC components AC(u,v)= F(u, v) of the block DC and AC components of the transformed block.


Transformation is done… next step in coding? QUANTIZATION

24


Each of the 64 coefficients are uniformly quantizedEach of the 64 coefficients are uniformly quantizedQuantization Matrix gives the 64 quantization step-size parameters for uniform quantization of the 64 DCT coefficients

Each element in the quantization matrix is an integer between 1 and 255. Each DCT coefficient F(u, v) is divided by the corresponding quantizer step-size parameter Q(u, v) in the quantization matrix and rounded to the nearest qinteger as



Luminance Quantization Matrix Chrominance Quantization Matrix



Quality of the reconstructed image and the Q y gachieved compression can be controlled by a user by selecting a quality factor Q_JPEG

Q JPEG ranges between 1 to 100Q_JPEG ranges between 1 to 100When Q_JPEG is used, the entries in tables in previous slide is scaled by the factor alpha (α), defined asdefined as

Q_JPEG is 100 for best reproductionQuantization is done… Proceeding to coding the quantized


Q g g qvalues…

27


Quantized DC coefficient is encoded by Quantized DC coefficient is encoded by differential encoding

DC coefficient DCi of the current block is subtracted by the DC coefficient Dc of the previous blockby the DC coefficient Dci-1 of the previous blockThe difference DIFF = DCi − DCi−1 is encoded

Encoding AC Componentsg pOnly the nonzero coefficients are encoded by an efficient manner such that the runs of zeros preceding a nonzero value are embedded into the p gencoding.Irregular ordering of the AC coefficients is called zig-zag orderingg g


Baseline JPEG Compression [14]Baseline JPEG Compression [14]CODING DCT COEFFICIENTS (Differential encoding)


(a) Zig-zag ordering of AC coefficients (b) differential coding of DC

29


h fThe zig-zag sequence of AC components is broken into a number of runs of zeros ending in a nonzero coefficientending in a nonzero coefficientFor 8-bit images in baseline JPEG, the DCT coefficients fall in the range DCT coefficients fall in the range [−1023, +1023]

Differential values of DC fall in the range e e t a a ues o C a t e a ge[−2047, +2047]



This sequence of AC coefficients is This sequence of AC coefficients is mapped into an intermediate sequence of a combination of two symbols, symbol1, symbol2symbol2

symbol1 is represented by a pair (RUNLENGTH, CATEGORY)

RUNLENGTH is the number of consecutive zeros RUNLENGTH is the number of consecutive zeros preceding the nonzero AC coefficient being encodedCATEGORY is the number of bits to represent the VLI code of this nonzero AC coefficient

symbol2 is a single piece of information designated (AMPLITUDE) that is encoded by the VLI code of the nonzero AC coefficient.



Assume the zigzag ordering results in the Assume the zigzag ordering results in the sequence as follows−6 6 −5 0 2 0 −1 0 0 0 0 0 −1 0 0 6 6 5 0 2 0 1 0 0 0 0 0 1 0 0 −1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 This can be represented as

(0, 3)(−6), (0, 3)(6), (0, 3)(−5), (1, 2)(2), (1, 1)(−1), (5, 1)(−1), (2, 1)(−1), (0 1)(1) (0 0) (0, 1)(1), (0,0).



Two special symbols in encoding the zig-zago spec a sy bo s e cod g t e g agsequence of AC coefficients

(0,0) referred to as EOB (end-of-block), to indicate that the remaining elements in the zig-zag block are that the remaining elements in the zig-zag block are zeros(15, 0) referred to as ZRL (zero-run-length) to indicate a run of 16 zerosindicate a run of 16 zeros

Maximum length of a run of zeros allowed in baseline JPEG is 16

Runs of more than 16 zeros should be broken into the number of runs of zeros of length 16.

Example : 57 zeros before a nonzero coefficient,−29.p ,Represented by (15, 0) (15, 0) (15, 0), (9, 5)(−29)


Baseline JPEG Compression [19]Baseline JPEG Compression [19]EXAMPLE

A Sample 8 × 8 Data Block After Level Shifting



DCT Coefficients of the Above 8 × 8 Block Results of DCT Coefficients Quantized by Luminance Quantization Matrix



h i b d d iThe ZigZag Sequence to be coded is−6 6 −5 0 2 0 −1 0 0 0 0 0 −1 0 0 −1 1 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

And the code is(0 3)( 6) (0 3)(6) (0 3)( 5) (1 2)(2) (0, 3)(−6), (0, 3)(6), (0, 3)(−5), (1, 2)(2),

(1, 1)(−1), (5, 1)(−1), (2, 1)(−1), (0, 1)(1), (0,0). (From Slide number 32)1)(1), (0,0). (From Slide number 32)



(a) Original Pepper image

(b) Compressed with baseline JPEG using quality factor 75 (1.57 bit/pixel)

(c) Compressed with baseline JPEG using quality factor 10 (0 24 i / i )(0.24 bit/pixel)

(d) Compressed with the new JPEG2000 standard using the same bit rate (0.24 bit/pixel).


Progressive DCT-Based ModeThe image is coded sequentially in multiple scang q y p

Need to wait till the decoding is over to view the image in sequential mode

Transmit a coarser version of the image in the first gscan and then progressively improve the reconstructed quality at the receiver by transmitting more compressed bits in successive scansp

Complete the computation of DCT coefficients before the start of entropy codingPerform selective encoding of the DCT coefficients & gtransmitTwo methods

spectral selection and successive approximation


Progressive DCT-Based Mode[2]Progressive DCT Based Mode[2]PROGRESSIVE CODING SUCESSIVE APPROXIMATION

Encode sets of DCT coefficients Start encoding with certain Encode sets of DCT coefficients starting from lower frequencies and moving progressively to higher frequencies.

For example

Start encoding with certain number of most significant bits (say N1) of all the DCT coefficients of all the blocks and transmit in the first scan

Encode all the DC coefficients of all the 8 × 8 DCT blocks in the first scanEncode and transmit the first three AC coefficients of the

transmit in the first scan. In the second scan, the following N2 most significant bits are encoded and transmitted and so onzig-zag sequence of all the

DCT blocks in the second scanTransmit the next 3 AC coefficients in the third scan, and so on

transmitted and so on.The scans continue until the least significant bit of all the coefficients is encoded. Usually

The last three AC coefficients can be transmitted in the 21st scanNumber of coefficients in each scan could be different

the successive approximation offers better reconstructed quality in the earlier scans compared to the spectral

and user selectable. selection method. Multimedia Computing

(CSIT 410) 39

Progressive DCT-Based Mode [3]

Progressive encoding:(a) spectral selection

(b) successive approximation.


Hierarchical ModeProgressive coding with increasing spatialresolution in a number of stagesresolution in a number of stagesOriginal image is filtered and down-sampled by required multiples of two forthe target resolution and the lower-resolution image is encoded using any ofresolution image is encoded using any ofthe other three JPEG modesThe compressed lower-resolution imageis then decoded and interpolated forupsampling by the same interpolationupsampling by the same interpolationmethod that will be used at the decoderInterpolated image is then subtractedfrom the next-higher-resolution image.The difference is then encoded by one of Hi hi l l i l i diThe difference is then encoded by one ofthe other three JPEG modes (lossless orlossy).This procedure of the hierarchicalencoding process is continued until it

Hierarchical multiresolution encoding.

encoding process is continued until itencodes all the resolutions.


Reference

1 Chapter 91. Chapter 92. Chapter 3 of JPEG2000 Standard for Image Compression: Concepts, Algorithms and VLSI Architectures by Tinku Acharya and Ping-Sing Tsai , John Wiley & Sons

See Blackboard, Course Materials


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