1. Image Compression
The still image and motion images can be compressed by lossless coding or lossy coding.
Principle of compression:
- reduce the redundant information, e.g.,
coding redundancy
interpixel redundancy
psychovisual redundancy
- knowledge-based image contents description and structure modeling

2. Image Compression Code length - fixed length - variable length
-- The average code-length is calculated as:
Pk(rk) is the probability of the occurrence of event rk,
l(rk) is the code length of event rk

3. Image Compression Entropy coding
- Use code-words with different lengths to losslessly represent symbols with different probabilities
- Why?
Use small number of bits to represent more frequent symbols and use large number of bits to represent less frequent symbols so that the length of overall symbols can be reduced.
- How:
- Huffman coding
- Arithmetic coding

4. Image Compression Example of variable length coding
r(k) p(r(k)) code L Code L2
r(0)=
r(1)=1/
r(2)=2/
r(3)=3/
r(4)=4/
r(5)=5/
r(6)=6/
r(7)=
L(avg)=2(0.19)+2(0.25)+2(0.21)+3(0.16)+4(0.08)+5(0.06)+6(0.03)+6(0.02) =2.7bits
Redundancy: R(D)=1-2.7/3 = 0.1 = 10%

5. Image Compression Inter-pixel correlation
- pixel values can be guessed (predicted) on the basis of the value of its neighbors
- The following redundancy can be reduced:
-- spatial redundancy
-- geometric redundancy
-- inter-frame redundancy
Human perception redundancy

6. Image Compression

7. Encoder and Decoder Example of image transmission
f(x,y)  source encoder channel encoder
f(x,y)’  source decoder  Channel decoder
Mapper quantizersymbol encoder
Inverse Mapper  symbol decoder

8. Information theory Information measurement Note:
Event E which occurs with probability P(E)
contains I(E) units of information
e.g., P(E) =1  I(E) =0 (which means there is no uncertainty
for event E, it always happens)
e.g., If we set the base as 2  -log2P(E)
if we flip a coin  P(E) = ½,
then I(E) = -log2(1/2) = 1 ( “bit”, unit of information) (e.g., flipping a coin)

9. Information theory (cont’d)
Entropy of the source (uncertainty):
H(Z) is the average amount of information;
H(Z)   uncertainty   information 
If the source symbols occur with equal probability,
the entropy is maximum
Theoretically, H(Z) is the minimum code length for each symbol,
which is the so-called Shannon’s first theorem for noiseless image coding

10. Information theory (cont’d)
Variable-length coding
-- Huffman coding generates the smallest possible number of code
-- example:
Symbol Probability (source reduction) code
A (code 0)
A (code 1) A A A A

11. Coding System Example Lossless predictive coding
Lossy predictive coding
Transform coding
-- Example of lossless predictive coding:
Compressed
image
Symbol encoder
Image
Encode:
Predictor
Compressed
image
Symbol decoder
Image
Decode:
Predictor

12. Coding System Example Transform coding Variable-length coding Image
block
DCT
Quantizer
Inverse
Quantizer
Inverse DCT
Motion estimator
Variable-length
coding

13. Image Compression Quantization
-- Map a large number of input amplitude levels to a small number of
amplitude levels with non-recoverable loss of quality
-- Why?
Reduce the amplitude levels can reduce the number of bits to
represent each pixel
-- How:
- scalar quantization (SQ)
- vector quantization (VQ)

14. Image Compression

15. Image Compression

16. Image Compression

17. Image Compression

18. Image Compression

19. Image Compression

20. Image Compression

21. Image Compression

22. Image Compression

23. Image Compression MPEG-4 TV/Film Computer MPEG4 Telecommunication
Interactive multimedia
GUI
Virtual environment
HDTV
Audio/Graphics/Video data
TV/Film
Computer
MPEG4
Telecommunication
Wireless, internet, WWW. ISDN, Cable, …

24. Image Compression
MPEG-4
-- video object plane (VOP):
VOP1
VOP2
VOP3

25. Image Compression MPEG-4
-- Structure of video object plane (VOP) encoder:
VOP0
coding
VOP1
Coding :
MUX
bitstream
Input
VOP definition
VOPn
coding