JPEGStill Image Data Compression Standard

JPEG Introduction - The background

JPEG stands for Joint Photographic Expert GroupA standard image compression method is needed to enable interoperability of equipment from different manufacturerIt is the first international digital image compression standard for continuous-tone images (grayscale or color)Why compression is needed?

Ex) VGA(640x480) 640x480x8x3=7,372,800bitswith compression 200,000bits without any visual degradation

JPEG Introduction – what’s the objective?

“very good” or “excellent” compression rate, reconstructed image quality, transmission ratebe applicable to practically any kind of continuous-tone digital source imagegood complexityhave the following modes of operations:

sequential encodingProgressive encodinglossless 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 modeHuffman coding

The basic architecture of JPEG Baseline system

Sourceimage data

quantizer entropyencoder

compressedimage data

tablespecification

tablespecification

8×8 blocks DCT-based encoder

statisticalmodel

FDCT

JPEG Baseline System– Why does it work?

Frequency sensitivity of Human Visual Systemfreq u en cy0

sen sitivity

Lossy encodingHVS is generally more sensitive to low frequenciesNatural images

The Baseline System – DCT

The mathematical representation of FDCT (2-D):

∑∑= =

++=7

0

7

0

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

x y

vjuiyxfvCuCvuF ππ

Where

⎩⎨⎧ =

=otherwise

xxC1

02/1)(

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

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 yvjuiyxfvCuCvuF ππ

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

Am

plitu

de

-1

0

1

1 2 3 4 5 6 7 8

U=6

Am

plitu

de

-1

0

1

1 2 3 4 5 6 7 8

U=5

Am

plitu

de

-1

0

1

1 2 3 4 5 6 7 8

U=4

Am

plitu

de

-1

0

1

1 2 3 4 5 6 7 8

U=3

Am

plitu

de

-1

0

1

1 2 3 4 5 6 7 8

U=2

Am

plitu

de-1

0

1

1 2 3 4 5 6 7 8

U=1

Am

plitu

de

-1

0

1

1 2 3 4 5 6 7 8

U=0

Am

plitu

de

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.) DC coefficient

The DCT coefficient values can be regarded as the relative amounts of the 2-D spatial frequencies contained in the 8×8 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

The Baseline System – Quantization

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

vuQvuFRoundvuF =

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

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”

The Baseline System-Quantization (cont.)

16 11 10 16 24 40 51 6112 12 14 19 26 58 60 5514 13 16 24 40 57 69 5614 17 22 29 51 87 80 6218 22 37 56 68 109 103 7724 35 55 64 81 104 113 9249 64 78 87 103 121 120 10172 92 95 98 112 100 103 99

JPEG Luminance quantization table

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

16 11 10 16 24 40 51 6112 12 14 19 26 58 60 5514 13 16 24 40 57 69 5614 17 22 29 51 87 80 6218 22 37 56 68 109 103 7724 35 55 64 81 104 113 9249 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

DCT coefficients Quantized coefficients

Baseline System - DC coefficient coding

Since most image samples have correlation and DC coefficient is a measure of the average value of a 8×8 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 useStatistical 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+SSSSsymbol 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 frameworkProgressive transmission by quality, resolution, component, or spatial localityCompressed domain processingRegion of Interest codingJPEG2000 is NOT an extension of JPEG

Wavelet TransformAn 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