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Multimedia Systems

- Lecture - 9

Lecture Outline

- Compression Fundamentals
- Why is compression required
- Data Compression
- Compression Problems
- Information Theory Basics
- CODEC?
- Compression Model
- Compression Techniques
- Compression Algorithms types
- Compression Performance

Background Why Compression?

- Let us consider the general requirements imposed

on most multimedia systems - Storage
- multimedia elements require significant storage

space, e.g., A full screen true colour image is - 640 x 480 x 3 921600 bytes
- The storage of one second of uncompressed CD

quality stereo audio is - 44.1 kHz x (16/8) x 2 x 1 176400 bytes
- The raw video size of PAL (_at_ 25 frames/sec)

sampled at 352 x 288 with 16 bits per pixel, is - 352 x 288 x 16 x 25 40.55 Mbit/s 5 Mbyte/s

Background Why Compression?

- Throughput
- Continuous media require very large throughput.

For example, an uncompressed CD quality stereo

audio stream needs 176400 bytes/sec. - Interaction
- to support fast interaction, the end-to-end delay

should be small. A face-to-face application,

such as video conferencing, requires the delay to

be less than 50ms. Furthermore, multimedia

elements have to be accessed randomly. - It is challenging to transfer such files through

the available limited bandwidth network. - Hence concluded that multimedia content/data is

usually large and need to be reduced using

compression.

Data Compression

- Compression aims for efficient digital

representation of a source. - Data Compression is the representation of the

source in digital form with as few bits as

possible while maintain-ing an acceptable loss in

fidelity. - In simple words, compression is used to reduce

the amount of data with as little compromise to

source/data quality as possible for the given

application. - Source can be any data including still images,

speech, audio, video or whatever signal needs to

be stored transmitted.

Data Compression

- A compressed video (or other multimedia content)

requires lower bandwidth than uncompressed video.

In other words, the compressed video requires

lower data rates (bit rates) for transmission,

and takes up less storage space. - An image is compressed for recording/storage, and

decompressed for display. This process is also

referred to as encoding and decoding.

Synonyms for Data Compression

- Signal compression signal coding
- Source coding source coding with fidelity

criterion (in information theory) - Noiseless Noisy Source coding (lossless lossy

compression) - Bandwidth compression

Types of Data Compression Problem

- Distortion-rate Problem
- Given the constraint on transmitted data rate or

storage capacity, problem is to compress the

source at or below this rate but at the highest

fidelity possible - e.g. Voice mail, video conferencing, digital

cellular - Rate-distortion Problem
- Given the constraint on the fidelity, problem is

to achieve it with as few bits as possible - e.g. CD-Quality audio

Information Theory Basics

- The theoretical background of compression is

provided by Information theory and rate

distortion theory - Representation of data is the combination of

information and redundancy. - Data compression is essentially a redundancy

reduction technique. - Data compression scheme can be broadly divided

into two phases - Modeling
- Coding

Information Theory Basics

- In modeling phase information about redundancy is

analyzed represented as a model - This can be done via observing the empirical

distribution of the symbols the source generates - In the coding phase the difference between the

actual data and the model is coded

Discrete Memoryless Model

- Source is discrete memoryless if it generates

symbols statistically independent of one another - Described by
- the source alphabet Aa1,a2,a3an and
- associated probabilities P(p(a1), p(a2),

p(a3),. p(an)) - The amount of information content for a source

symbol I(ai) is - The base 2 logarithm indicates the information

content is represented in bits. Higher

probability symbols are coded with less bits.

Discrete Memoryless Model

- Averaging the information content over all

symbols, we get the entropy E as follows - Hence, entropy is the expected length of a binary

code over all the symbols. - Estimation of entropy depends on the observation

assumption on the structure of source symbols

Noiseless source coding theorem

- The Noiseless Source Coding Theorem states that
- any source can be losslessly encoded with a code

whose average number of bits per source symbol is

arbitrarily close to, but not less than, the

source entropy E in bits by coding infinitely

long extensions of the source.

Entropy Reduction

- Consider a discrete memoryless source, with
- source alphabet A1 a, ß, ?, d
- probability p(a) 0.65, p(ß) 0.20, p(?)

0.10, p(d) 0.05 - The entropy of this source is
- E -(0.65 log2 0.65 0.20 log2 0.20 0.10

log2 0.10 0.05 log2 0.05) - 1.42 bits per symbol
- A data source of 2000 symbols can be represented

using 2000 x 1.42 2840 bits

Entropy Reduction

- Now assume we know something about the structure

of the sequence - Alphabet A2 0, 1, 2, 3
- Sequence D 0 1 1 2 3 3 3 3 3 3 3 3 3 2 2 2 3 3

3 3 - p(0) 0.05, p(1) 0.10, p(2) 0.20, and p(3)

0.65 - E 1.42 bits per symbol
- Assume the correlation between consecutive bits

and we attempt to reduce it by ri si - si-1 for

each sample si

Entropy Reduction

- Now
- D 0 1 0 1 1 0 0 0 0 0 0 0 0 -1 0 0 1 0 0 0
- A2 -1, 1, 0
- P(-1) 0.05, p(1) 0.2, and p(0) 0.75
- E 0.992
- If appropriate entropy coding technique used

maximum compression can be achieved

Unique Decipherability

- Consider the following table
- Symbols are encoded with codes A, B and C.
- Consider the string S aa?aßad

Unique Decipherability

- Deciphering CA(S) and CB(S) are unambiguous and

we get the string S - CC(S) is ambiguous and not uniquely decipherable
- Fixed length codes are always uniquely

decipherable. - Not all variable length codes are uniquely

decipherable.

Unique Decipherability

- Uniquely decipherable codes maintain prefix

property, i.e. no codeword in the code-set forms

the prefix of another distinct codeword - Popular variable-length coding techniques
- Shannon-Fano Coding
- Huffman Coding
- Elias Coding
- Arithmetic Coding
- Fixed-length codes can be treated as a special

case of uniquely decipherable variable-length

code.

Compression and Decompression

CODEC

Compression and Decompression

- Data compression is a method that takes an input

data D and generates a shorter representation of

the data c(D) with a fewer number of bits

compared to that of D - The reverse process is called decompression,

which takes the compressed data c(D) and

generates or reconstructs the data D' - Sometimes the compression (coding) and

decompression (decoding) systems together are

called a "CODEC"

Classification of compression algorithms

- If the reconstructed data D' is an exact replica

of the original data D, we call the algorithm

applied to compress D and decompress c(D) to be

lossless. Otherwise the algorithms are lossy - Text, scientific data, medical images are some of

the applications which requires lossless

compression - Compression can be static or dynamic, depends on

the coding scheme used

Data compression model

- A data compression system mainly consists of

three major steps - removal or reduction in data redundancy
- reduction in entropy
- entropy encoding

Data compression modelREDUCTION IN DATA

REDUNDANCY

- Removal or reduction in data redundancy is

typically achieved by transforming the original

data from one form or representation to another - Popular transformation techniques are
- Discrete Cosine Transform (DCT)
- Discrete Wavelet Transformation (DWT) etc
- This step leads to the reduction of entropy
- For Lossless compression this transformation is

completely reversible

Data compression model REDUCTION IN ENTROPY

- Non reversible process
- Achieved by dropping insignificant information in

the transformed data (Lossy!!!) - Done by some quantization techniques
- Amount of quantization dictate the quality of the

reconstructed data - Entropy of the quantized data is less compared to

the original one, hence more compression.

Compression Techniques

- Entropy coding is lossless
- Source coding and Hybrid coding are lossy

Compression Performance

- The performance measures of data compression

algorithms can be looked at from different

perspectives depending on the application

requirements - amount of compression achieved
- objective and subjective quality of the

reconstructed data - relative complexity of the algorithm
- speed of execution, etc.

Compression Performance AMOUNT OF COMPRESSION

ACHIEVED

- Compression ratio
- the ratio of the number of bits to represent the

original data to the number of bits to represent

the compressed data - Achievable compression ratio using a lossless

compression scheme is totally input data

dependent. - Sources with less redundancy have more entropy

and hence are more difficult to achieve

compression

Compression Performance SUBJECTIVE QUALITY METRIC

- MOS mean observers score or mean opinion score

is a common measure - A statistically significant number of observers

are randomly chosen to evaluate visual quality of

the reconstructed images. - Each observer assigns a numeric score to each

reconstructed image based on his or her

perception of quality of the image, say within a

range 15 to describe the quality of the image5

being the highest quality and 1 being the worst

quality. - MOS is the average of these scores

Compression Performance OBJECTIVE QUALITY METRIC

- Common quality metrics are
- root-mean-squared error (RMSE)
- signal-to-noise ratio (SNR)
- peak signal-to-noise ratio (PSNR).
- If I is an M N image and I is the corresponding

reconstructed image after compression and

decompression, RMSE is calculated by - The SNR in decibel unit (dB) is expressed as

Compression Performance CODING DELAY AND

COMPLEXITY

- Coding delay
- a performance measure for compression algorithms

where interactive encoding and decoding is the

requirement (e.g., interactive video

teleconferencing, on-line image browsing,

real-time voice communication, etc.) - The complex the compression algorithm ? Increased

coding delay - Compression system designer often use a less

sophisticated algorithm for the compression

system.

Compression Performance CODING DELAY AND

COMPLEXITY

- Coding complexity
- a performance measure considered where the

computational requirement to implement the codec

is an important criteria - MOPS (millions of operations per second), MIPS

(millions of instructions per second) are often

used to measure the compression performance in a

specific computing engine's architecture.

JPEG Compression

- JPEG (stands for Joint Photographic Experts

Group) is a joint ISO and CCITT working group for

developing standards - for compressing still images
- The JPEG image compression standard became an

international standard in 1992 - JPEG can be applied to colour or grayscale images
- By changing appropriate parameters, the user can

select - the quality of the reproduced image
- compression processing time
- the size of the compressed image

JPEG Compression

- The JPEG standard have three levels of definition

as follows - Baseline system
- must reasonably decompress colour images,

maintain a high compression ratio, and handle

from 4bits/pixel to 16bits/pixel. - Extended system
- covers the various encoding aspects such as

variable length encoding, progressive encoding,

and hierarchical mode of encoding. - Special lossless function
- ensures that at the resolution at which the image

is compressed, decompression results in no loss

of any detail the was in the original image.

JPEG Compression Process

JPEG - Preparation

- A source image consists of at least one and at

most 255 planes. - Each plane Ci may have different number of pixels

in the horizontal (Xi) and vertical (Yi)

dimension. - The resolution of the individual plane may be

different. - Each pixel is represented by a number of bits p

where 2 p 12. - The meaning of the value in these planes is not

specified in the standard. - The image is divided into 8 x 8 blocks.

JPEG Discrete Cosine Transform

- DCT transforms the data from a spatial domain to

a frequency domain. - It removes redundancy in the data.
- It is proven to be the optimal transform for

large classes of images. - The DCT algorithm is symmetrical, and an inverse

DCT algorithm can be used to decompress an image. - The DCT coefficients of each 8x8 blocks are

calculated using the formula below.

JPEG Discrete Cosine Transform

- Here is an example. On the left is the 8 x 8

block of pixels, and on the right is the DCT

coefficients.

JPEG - Quantization

- The DCT output matrix is quantized to reduce the

precision of the coefficients. - This increases the compression DCT(0, 0) is

known as the DC coefficient which represents the

basic colour, i.e., wave-length, of the image

block - The other DCT coefficients are known as AC

coefficients which represent the frequency

components of the data block. - AC coefficients further away from the DC

coefficient can be dropped to reduce the data

size - JPEG baseline algorithm defines a set of

quantization tables - Each element q in the table, known as quantum is

used in the following formula to calculate the

quantized coefficients Q

JPEG - Quantization

On the left is quantum matrix for quality level

1, and on the right the result of quantizing the

example from slide.

JPEG Entropy Encoding

- The DC-coefficients are treated separately from

the AC-coefficients. - A DC-coefficient is encoded as the difference

between the current coefficient and the previous

one. - The AC-coefficients are encoded using Huffman

and/or arithmetic encoding. - They are put in a zig-zag order as shown in the

diagram below

Additional View of Zig-Zig Sequencing

References and further reading

- Chapter 1 of Digital Compression for Multimedia

Principles Standards by Jerry D.Gibson - Chapter 1 of JPEG200 Standard for Image

Compression Concepts, Algorithms and VLSI

Architecture by Tinku Acharya Ping-Sing Tsai - http//www.moviola.com/compression_fundamentals
- http//www.data-compression.com/theory.html