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JPEG Still Image Data Compression Standard

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JPEGStill Image Data Compression Standard

- 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

- Ex) VGA(640x480) 640x480x8x3=7,372,800bits

- “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

entropy

encoder

compressed

image data

Source

image data

descriptors

symbols

encoder

statistical

model

Encoder

model

model

tables

entropy

coding tables

The basic parts of an JPEG encoder

statistical

model

entropy

encoder

quantizer

88 blocks

DCT-based encoder

compressed

image data

FDCT

Source

image data

table

specification

table

specification

The basic architecture of JPEG Baseline system

JPEG Baseline system is composed of:

- Sequential DCT-based mode
- Huffman coding

JPEG Baseline System

– Why does it work?

Frequency sensitivity of Human Visual System

- Lossy encoding
- HVS is generally more sensitive to low frequencies
- Natural images

The mathematical representation of FDCT (2-D):

Where

f(x,y): 2-D sample value

F(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.

An example of 1-D DCT decomposition

Before DCT (image data)

After DCT (coefficients)

The 8 basic functions for 1-D DCT

- 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

- 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”

F(u,v): original DCT coefficient

F’(u,v): DCT coefficient after quantization

Q(u,v): quantization value

JPEG Luminance quantization table

Original image pattern

After FDCT(DCT coefficients)

Digitized image

DCT coefficients

Quantized coefficients

DC difference

quantized DC

coefficients

DPCM

Differential pulse code modulation

- 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

Horizontal frequency

Vertical frequency

- AC coefficients are arranged into a zig-zag sequence:

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

- 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

- 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

- Bit plane shift
- Finer Quantization level used

- http://www.sfu.ca/~cjenning/toybox/hjpeg/index.html