Digital Image Processing Introduction

Digital Image Processing 

Introduction 

Image compression 

Digital Image Processing 1

Image compression 

 

 

Data redundancy is a central issue in digital image 

compression. 

If n1 and n2 denote the number of information-carrying units 

in two data sets that represent the same information, the 

relative data redundancy RD of the first data set (the one 

characterized by n1) can be defined as 

 

 

 

Rd = 1 - 1/Cr 

where CR: - compression ratio, is 

CR = n1/n2 


Three basic data redundancies: 

 

 

 

Coding redundancy 

Interpixel redundancy 

Psychovisual redundancy 

Data compression is achieved when one or 

more of these redundancies are reduced or 

eliminated. 


Coding redundancy 

 

Variable-length coding. 

 

 

assigning fewer bits to the more probable gray levels 

than to the less probable ones achieves data 

compression. 

If the gray levels of an image are coded in a way that 

uses more code symbols than absolutely necessary to 

represent each gray level, the resulting image is said to 

contain coding redundancy. 

.... 


Interpixel redundancy 

 

spatial redundancy, geometric redundancy, and interframe 

redundancy, have been coined to refer to these interpixel 

redundancy. 

Illustration of run-length coding: 

(a) original image. 

(b) Binary image with line 100 

marked, 

(c) Line profile and binarization 

threshold. 

(d) Run-length code. 

Line 100: (1,63) (0,87) (1,37) (0,5) (1,4) (0,556) (1,62) (0,210) 


Psychovisual redundancy 

 

 

Human perception of the information in an image 

normally does not involve quantitative analysis of 

every pixel value in the image. 

In general, an observer searches for distinguishing 

features such as edges or textural regions and 

mentally combines them into recognizable groupings. 

The brain then correlates these groupings with prior 

knowledge in order to complete the image 

interpretation process. 

 

Example - TV 


Image Compression Models 

 

 

 

The Source Encoder and Decoder 

The source encoder is responsible for reducing or 

eliminating any coding, interpixel, or psychovisual 

redundancies in the input image. 

General compression system model: 


Error-Free Compression 

 

 

 

 

 

 

Variable-Length Coding 

 

Huffman coding 

Arithmetic coding 

 

Unlike the variable-length codes described previously, arithmetic 

coding generates nonblock codes. 

Bit-Plane Coding 

 

the concept of decomposing a multilevel (monochrome or color) 

image into a series of binary images and compressing each binary 

image via one of several well-known binary compression methods. 

Constant area coding 

One/two -dimensional run-length coding 

Contour tracing and coding 


Lossless Predictive Coding 

 

The approach, commonly referred to as lossless predictive coding, 

is based on eliminating the interpixel redundancies of closely 

spaced pixels by extracting and coding only the new information in 

each pixel. 

 

The new 

information of a 

pixel is defined as 

the difference 

between the 

actual and 

predicted value of 

that pixel. 


Lossy Compression 

 

Unlike the error-free approaches outlined in the previous section, lossy 

encoding is based on the concept of compromising the accuracy of the 

reconstructed image in exchange for increased compression. If the 

resulting distortion (which may or may not be visually apparent) can be 

tolerated, the increase in compression can be significant 

Delta modulation (DM) :. 


Transform Coding 

 

A transform coding system: 

Encoder + decoder. 


Transform selection 

 

Walsh-Hadamard 

basis functions for 

N = 4.The origin of 

each block is at its 

top left. 


Transform selection 

 

Discrete-cosine 

basis functions for 

N — 4. The origin 

of each block is at 

its top left. 


Wavelet Coding 

 

the transform's basis functions—in this case wavelets—pack most of the 

important visual information into a small number of coefficients, the remaining 

coefficients can be quantized coarsely or truncated to zero with little image 

distortion. 


JPEG standard 

It defines three different coding systems: 

 

A) a lossy baseline coding system, which is based on the DCT and is 

adequate for most compression applications; 

B) an extended coding system for greater compression, higher precision, 

or progressive reconstruction applications; and 

 

C) a lossless independent coding system for reversible compression. To 

be JPEG compatible, a product or system must include support for the 

baseline system. 


JPEG 2000 

 

Although not yet formally adopted, JPEG 2000 extends the 

initial JPEG standard to provide increased flexibility in both 

the compression of continuous tone still images and access 

to the compressed data. 

For example, portions of a JPEG 2000 compressed image 

can be extracted for retransmission, storage, display, and/or 

editing. 

The standard is based on the wavelet coding techniques . 

Coefficient quantization is adapted to individual scales and 

subbands and the quantized coefficients are arithmetically 

coded on a bit-plane basis.

Digital Image Processing Introduction

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