• The problem of reducing the amount of data required to represent a digital image.

• From a mathematical viewpoint: transforming a 2-

Image Compression?

• From a mathematical viewpoint: transforming a 2-D pixel array into a statistically uncorrelated data set.

• For data STORAGE and data TRANSMISSION

• DVD

• Remote Sensing

• Video conference

• FAX

Why do We Need Compression?

• FAX

• Control of remotely piloted vehicle

• The bit rate of uncompressed digital cinema data exceeds 1 Gbps

Information vs Data

� DATA = INFORMATION + REDUNDANT DATA

REDUNDANT DATA

INFORMATION

• Spatial redundancy

• Neighboring pixels are not independent but correlated

Why Can We Compress?

� Temporal redundancy

Image Compression Model.

Remove Input Redundancies

Increase the Noise

Immunity

Image Compression Model.

Reduce inter-pixel redundancy

(Reversible)

Reduce coding redundancy

(Reversible)

The source encoder and decoder

CLASSIFICATION

� Lossless compression

� lossless compression for legal and medical documents,

computer programs

� exploit only code and inter-pixel redundancy

� Lossy compression

� digital image and video where some errors or loss can be

tolerated

� exploit both code and inter-pixel redundancy and sycho-

visual perception properties

Error-Free Compression

Applications:

• Archive of medical or business documents

• Satellite imaging

• Digital radiography

� They provide: Compression ratio of 2 to 10.

Bit-plane coding

� Bit-plane coding has been widely used in lossless compression of

gray-scale images or color palette images.

� Progressive transmission can be used in bit-plane coding strategy.

• Process the image’s b i t p lanes individual ly.

Bit-plane coding

• Decompose the image in to a ser ies of b inary

images .

• Compress each binary image via a b inary

compress ion method.

Error-Free Compression

� Bit-plane coding

• Bit-plane coding is based on

decomposing a multilevel

a b c d e f

c

b

aa b c d e f

c

b

a

decomposing a multilevel

image into a series of binary

images and compressing each

binary image . f

e

d

f

e

d

Bit-plane coding

� The intensities of an m-bit monochrome image can be represented

in the form of base-2 polynomial:

� am-12m-1+am-22

m-2+…+a121+a02

0

� Therefore , to decompose an image into a set of binary images , � Therefore , to decompose an image into a set of binary images ,

we need to separate m coefficient of the polynomial into m 1-bit

plane.

� The lowest order bit-plane (corresponds to the least significant

bit) is generated by a0 bits of each pixel, while the highest order

bit-plane contains am-1 bits.

Bit-plane coding

� However, this approach leads to the situation, when small changes of

intensity can have significant impact on bit-planes. For instance, if a

pixel intensity 127 (01111111) is adjacent to a pixel intensity

128(10000000), every bit will contain a corresponding 0 to 1 (or 1 to 0)

transition.

� Alternatively, an image can be represented first by an m-bit Gray code.� Alternatively, an image can be represented first by an m-bit Gray code.

This code gm-1…g2 g1 g0 corresponding to the polynomial is

computed as

� gi=ai ai+1 0≤ i ≤ m-2

� gm-1=am-1

� The property of this code is that the successive code words differ in

only one bit position and small changes in intensity are less likely to

affect all m bit-planes.

+

BitBit--Plane Coding Plane Coding

Original image

Bit 7

Bit 6

…

Binary image compression

Binary image compression

Bit 0

Bit planeimages

Binary image compression

Example of binary image compression: Run length coding

Bit Planes

Bit 7

Bit 6

Bit 3

Bit 2

Original grayscale image

Bit 5

Bit 4

Bit 1

Bit 0

Gray-coded Bit Planes

a7

a6

g7

g6

Gray code:

60for

1

≤≤

⊗=+

i

aag iii

77 ag =

and

Original

bit planes

a5

a4

g5

g4

ai= Original bit planes

⊗ = XOR

GrayGray--coded Bit Planes (cont.) coded Bit Planes (cont.)

a3

a2

g3

g2

There are less 0-1 and 1-0

transitions in grayed code

bit planes.

Hence gray coded bit planes

are more efficient for coding.

a1

a0

g1

g0

Relative Address Coding (RAC) Relative Address Coding (RAC)

Concept: Tracking binary transitions that begin and end back

black and white run

Contour tracing and CodingContour tracing and Coding

Represent each contour by a set of boundary points and directional's .