JPEG Still Image Data Compression Standard

JPEGStill Image Data Compression

Standard

JPEG Introduction - The background JPEG stands for Joint Photographic Expert

Group A standard image compression method is

needed to enable interoperability of equipment from different manufacturer

It is the first international digital image compression standard for continuous-tone images (grayscale or color)

Why compression is needed? Ex) VGA(640x480) 640x480x8x3=7,372,800bits

with compression 200,000bits without any visual degradation

JPEG Introduction – what’s the objective?

“very good” or “excellent” compression rate, reconstructed image quality, transmission rate

be applicable to practically any kind of continuous-tone digital source image

good complexity have the following modes of operations:

sequential encoding Progressive encoding lossless encoding

JPEG Overview

encoderstatistical

model

entropyencoder

Encodermodel

Sourceimage data

compressedimage data

descriptors symbols

modeltables

entropycoding tables

The basic parts of an JPEG encoder

JPEG Baseline System

JPEG Baseline SystemJPEG Baseline system is composed of: Sequential DCT-based mode Huffman coding

The basic architecture of JPEG Baseline system

Sourceimage data

quantizer entropyencoder

compressedimage data

tablespecification

tablespecification

88 blocks DCT-based encoder

statisticalmodel

FDCT

Frequency sensitivity of Human Visual System

JPEG Baseline System– Why does it work?

Lossy encoding HVS is generally more sensitive to low

frequencies Natural images

The mathematical representation of FDCT (2-D):

7

0

7

0

)16/)1(2cos()16/)1(2cos(),()()(41),(

x y

vjuiyxfvCuCvuF

Where

otherwise

xxC1

02/1)(

f(x,y): 2-D sample valueF(u,v): 2-D DCT coefficient

The Baseline System – DCT

The Discrete Cosine Transform (DCT) separates the frequencies contained in an image.

The original data could be reconstructed by Inverse DCT.

Basis of DCT transform

7

0

7

0

)16/)1(2cos()16/)1(2cos(),()()(41),(

x y

vjuiyxfvCuCvuF

The Baseline System-DCT (cont.)

(b)

-150

-100

-50

0

50

100

150

1 2 3 4 5 6 7 8

x

f(x)

(c)

-150

-100

-50

0

50

100

150

1 2 3 4 5 6 7 8

u

S(u)

-1

0

1

1 2 3 4 5 6 7 8

U=7

Amplitude

-1

0

1

1 2 3 4 5 6 7 8

U=6

Amplitude

-1

0

1

1 2 3 4 5 6 7 8

U=5

Amplitude

-1

0

1

1 2 3 4 5 6 7 8

U=4

Amplitude

-1

0

1

1 2 3 4 5 6 7 8

U=3

Amplitude

-1

0

1

1 2 3 4 5 6 7 8

U=2

Amplitude

-1

0

1

1 2 3 4 5 6 7 8

U=1

Amplitude

-1

0

1

1 2 3 4 5 6 7 8

U=0

Amplitude

Before DCT (image data) After DCT (coefficients)

An example of 1-D DCT decomposition

The 8 basic functions for 1-D DCT

The Baseline System-DCT (cont.)

The DCT coefficient values can be regarded as the relative amounts of the 2-D spatial frequencies contained in the 88 block

the upper-left corner coefficient is called the DC coefficient, which is a measure of the average of the energy of the block

Other coefficients are called AC coefficients, coefficients correspond to high frequencies tend to be zero or near zero for most natural images

DC coefficient

The Baseline System – Quantization

Why quantization? . to achieve further compression by representing DCT coefficients

with no greater precision than is necessary to achieve the desired image quality

Generally, the “high frequency coefficients” has larger quantization values

Quantization makes most coefficients to be zero, it makes the compression system efficient, but it’s the main source that make the system “lossy”

)),(),((),('

vuQvuFRoundvuF

F(u,v): original DCT coefficientF’(u,v): DCT coefficient after quantizationQ(u,v): quantization value

16 11 10 16 24 40 51 61

12 12 14 19 26 58 60 5514 13 16 24 40 57 69 56

14 17 22 29 51 87 80 62

18 22 37 56 68 109 103 7724 35 55 64 81 104 113 92

49 64 78 87 103 121 120 101

72 92 95 98 112 100 103 99

JPEG Luminance quantization table

The Baseline System-Quantization (cont.)

A simple example

O O O X X O O OO X X X X X X OX X X X X X X XX X X X X X X XX X X X X X X XX X X X X X X XO X X X X X X OO O O X X O O O

-10 -10 -10 10 10 -10 -10 -10-10 10 10 10 10 10 10 -1010 10 10 10 10 10 10 1010 10 10 10 10 10 10 1010 10 10 10 10 10 10 1010 10 10 10 10 10 10 10

-10 10 10 10 10 10 10 -10-10 -10 -10 10 10 -10 -10 -10

40 0 -26 0 0 0 -11 00 0 0 0 0 0 0 0

-45 0 -24 0 8 0 -10 00 0 0 0 0 0 0 0

-20 0 0 0 20 0 0 00 0 0 0 0 0 0 0

-3 0 10 0 18 0 4 00 0 0 0 0 0 0 0

Original image pattern

Digitized image After FDCT(DCT coefficients)

A simple example(cont.)

40 0 -26 0 0 0 -11 00 0 0 0 0 0 0 0

-45 0 -24 0 8 0 -10 00 0 0 0 0 0 0 0

-20 0 0 0 20 0 0 00 0 0 0 0 0 0 0

-3 0 10 0 18 0 4 00 0 0 0 0 0 0 0

Quantized coefficientsDCT coefficients

16 11 10 16 24 40 51 6112 12 14 19 26 58 60 5514 13 16 24 40 57 69 56

14 17 22 29 51 87 80 6218 22 37 56 68 109 103 7724 35 55 64 81 104 113 92

49 64 78 87 103 121 120 10172 92 95 98 112 100 103 99

3 0 -3 0 0 0 0 00 0 0 0 0 0 0 0

-3 0 -2 0 0 0 0 00 0 0 0 0 0 0 0

-1 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0

Baseline System - DC coefficient coding Since most image samples have correlation and DC

coefficient is a measure of the average value of a 88 block, we make use of the “correlation” of DC coefficients

DPCMquantized DCcoefficients

DC difference

Differential pulse code modulation

Baseline System - AC coefficient coding AC coefficients are arranged into a zig-zag sequence:

0 1 5 6 14 15 27 28

2 4 7 13 16 26 29 42

3 8 12 17 25 30 41 43

9 11 18 24 31 40 44 53

10 19 23 32 39 45 52 54

20 22 33 38 46 51 55 60

21 34 37 47 50 56 59 61

35 36 49 48 57 58 62 63

Horizontal frequency

Ver

tical

freq

uenc

y

3 0 -3 0 0 0 0 00 0 0 0 0 0 0 0

-3 0 -2 0 0 0 0 00 0 0 0 0 0 0 0

-1 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0

3 0 0 -3 0 -3 0 0 0 0 -1 0 -2(EOB)

Baseline System - Statistical modeling Statistical modeling translate the inputs to a

sequence of “symbols” for Huffman coding to use

Statistical modeling on DC coefficients: symbol 1: different size (SSSS) symbol 2: amplitude of difference (additional bits)

Statistical modeling on AC coefficients: symbol 1: RUN-SIZE=16*RRRR+SSSS symbol 2: amplitude of difference (additional bits)

Additional bits for sign and magnitude

Huffman AC statistical model run-length/amplitude combinations Huffman coding of AC coefficients

An examples of statistical modeling

+8 +9 +8 -6 -8 -3 +3 +30 +1 -1 -14 -2 +5 +6 00 1 1 4 2 3 3 0-- 1 0 0001 00 101 110 --Additional bits

Example 1: Huffman symbol assignment to DC descriptorsquantized DC valueDPCM differenceSSSS

1 2 3 4 5 6 7 8 9 … 630 0 0 0 -14 0 0 +1 0 … 0

4 1RUN-SIZE 68 33

0001 1

Example 2: Huffman symbol assignment to AC descriptors

AC descriptorRRRRSSSS

0

zigzag index

Additional bits

4 2 EOB0

--

Other Operation Modes:JPEG2000 ROI coding

JPEG 2000 Allow efficient lossy and lossless compression

within a single unified coding framework Progressive transmission by quality,

resolution, component, or spatial locality Compressed domain processing Region of Interest coding JPEG2000 is NOT an extension of JPEG

Wavelet Transform An extremely flexible bitstream structure

DCT Transform vs. Space-Scale Transform

JPEG2000 ROI coding Bit plane shift Finer Quantization level used

Experiment http://

www.sfu.ca/~cjenning/toybox/hjpeg/index.html