1. JPEG Still Image Data Compression Standard
School of Computer Science,
University of Central Florida,
VLSI and M-5 Research Group
May, 1999

2. 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)
The history of JPEG – the selection process
--The “joint” in JPEG refers to collaboration between CCITT and ISO.
--many continuous-tone image applications require a compression standard in order to develop significantly beyond their present state. JPEG has undertaken the ambitious task for developing a general-purpose compression standard to meet the needs of almost all continuous-tome still-image application.
--From June 1987, JPEG conducted a selection process based on a blind assessment of subjective picture quality, and narrowed 12 proposed methods to three, in 1988 the a second, more rigorous selection process reveals that “ADCT” proposal produced the best quality. Later JPEG developed the “ADCT” and formalized it, so is the first
international still-image compression standard.

3. 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
hierarchical encoding
--JPEG encoder and decoder makes the user to be able to change the parameters so they can control the compression/quality tradeoff. When we say a “very good” image quality, the compression rate must be in a acceptable level.
Sequential encoding: each image component is encoded in a single left-to-right, top-to-bottom scan.
Progressive encoding: the image is encoded in a multiple scans for applications in which transmission time is long, and the viewer prefers to watch the image built up in multiple coarse-to-clear passes.
Loss-less encoding: the image is encoded to guarantee exact recovery of every source image sample value (even through the compression rate is low compared to the lossy modes)
Hierarchical encoding: the image is encoded at multiple resolutions, so that lower-resolution versions may be accessed without first having to decompress the image at its full
resolution. – A kind of Progressive encoding.

4. The basic parts of an JPEG encoder
JPEG Overview
encoder
statistical
model
entropy
Encoder
Source
image data
compressed
descriptors
symbols
tables
coding tables
The basic parts of an JPEG encoder
In this presentation, I will only talk about how JPEG encoder works. The decoding process is simply the inverse procedure of encoding.

5. JPEG Overview (cont.) JPEG has the following Operation Modes:
Sequential DCT-based mode
Progressive DCT-based mode
Sequential lossless mode
Hierarchical mode
JPEG entropy coding supports:
Huffman encoding
Arithmetic encoding

6. JPEG Baseline System

7. JPEG Baseline System JPEG Baseline system is composed of:
Sequential DCT-based mode
Huffman coding
The basic architecture of JPEG Baseline system
Source
image data
quantizer
entropy
encoder
compressed
table
specification
88 blocks
DCT-based encoder
statistical
model
FDCT

8. 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
Frequency sensitivity of Human Visual System

9. 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.
The mathematical representation of FDCT (2-D):
Where
f(x,y): 2-D sample value
F(u,v): 2-D DCT coefficient

10. The Baseline System-DCT (cont.)
Before DCT (image data)
After DCT (coefficients)
An example of 1-D DCT decomposition
The 8 basic functions for 1-D DCT

11. 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 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

12. The Baseline System – Quantization
F(u,v): original DCT coefficient
F’(u,v): DCT coefficient after quantization
Q(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”

13. The Baseline System-Quantization (cont.)
JPEG Luminance quantization table

14. A simple example Original image pattern After FDCT(DCT coefficients)
Digitized image
After FDCT(DCT coefficients)

15. A simple example(cont.)
DCT coefficients
Quantized coefficients

16. 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
DPCM
quantized DC
coefficients
DC difference
Differential pulse code modulation

17. Baseline System - AC coefficient coding
AC coefficients are arranged into a zig-zag sequence:
Horizontal frequency
Vertical frequency

18. 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

19. Additional bits for sign and magnitude
Huffman AC statistical model
run-length/amplitude combinations
Huffman coding of AC coefficients

20. An examples of statistical modeling

21. Other Operation Modes

22. JPEG Progressive Model
Why progressive model?
Quick transmission
Image built up in a coarse-to-fine passes
First stage: encode a rough but recognizable version of the image
Later stage(s): the image refined by successive scans till get the final image
Two ways to do this:
Spectral selection – send DC, AC coefficients separately
Successive approximation – send the most significant bits first and then the least significant bits

23. JPEG Lossless Model DPCM Sample values Descriptors
Differential pulse code modulation C B A X

24. JPEG Hierarchical Model
Hierarchical model is an alternative of progressive model (pyramid)
Steps:
filter and down-sample the original images by the desired number of multiplies of 2 in each dimension
Encode the reduced-size image using one of the above coding model
Use the up-sampled image as a prediction of the origin at this resolution, encode the difference
Repeat till the full resolution image has been encode