DIP-Module1

8/3/2019 DIP-Module1

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MODULE 1:IMAGE REPRESENTATION AND MODELING

Jeevan K M

Asst. Professor

Department of Electronics & Communication

Sree Narayana Gurukulam College of EngineeringKadayiruppu


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What is an image?

Two dimensional function that represents a measure of some

characteristic such as brightness or coloure of a viewed scene

Projection of a 3D scene into a 2D projection plane

A two variable function f(x,y) where each position (x,y) in the projectionplane f(x,y) defines the light intensity at this point.

An image is two dimensional function, f(x,y), where x and y are

spatial coordinates, and the amplitude of f at any pair of

coordinates (x,y) is called the intensity or grey level of the image atthat point.


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Image

1. Analog Image

Type of images that we, as humans, look at.

They include such things as photographs, paintings etc.

What we see in an analog image is various levels of brightness (or film

density) and colours.

It is generally continuous and not broken into many small individual

pieces.

Can be mathematically represented as a continuous range of

values representing position and intensity. It is characterized by

a physical magnitude varying continuously in space. Eg: image

produced on the screen of a CRT


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Images

2. Digital image

A digital image is composed of picture element calledpixelsPixels are the smallest sample of an image

A digital image is a matrix of many small elements, or pixels.

Each pixel is represented by a numerical value.

The pixel value is related to the brightness or color that we will see when

the digital image is converted into an analog image for display and viewing.

.

AnalogImage

Sampling Quantisation DigitalImage


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Advantage of Digital Images

The processing of image is faster and cost effective

Digital image can be effectively stored and efficiently transmitted from

one place to another

Copying of digital image easy, The quality of digital image will not be

degraded even if it is copied for several time.

Whenever the image is in digital format, the reproduction of image is both

faster and cheaper

Drawbacks of Digital images

Misuse of copyright has become easier because image can be copied from

internet just by clicking the mouse

A digital image cannot be enlarged beyond a certain size with outcompromising the quality.

The memory required to store and process good quality image is very

high.


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Fundamental steps in image processing:

1. Image acquisition:

To acquire a digital image

Image Acquisition Tools

Human Eye

Ordinary Camera

X-Ray Machine

Infrared Imaging

Geophysical Imaging

Digital Image Processing

The processing of an image by means of a computer is termed as digital

image processing.


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2. Image preprocessing:

To improve the image in ways that increase the chances

for success of the other processes.

3. Image segmentation:To partitions an input image into its constituent parts or

objects.

4. Image representation:

To convert the input data to a form suitable for computer

processing.

5. Image description:To extract features that result in some quantitative information

of interest or features that are basic for differentiating one class

of objects from another.

6. Image recognition:To assign a label to an object based on the information

provided by its descriptors.

7. Image interpretation:

To assign meaning to an ensemble of recognized objects.

Knowledge about a problem domain is coded into an imageprocessing system in the form of a knowledge database.


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Fundamental Steps in image Processing


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Elements of Digital Image Processing


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1. Image Sensing

Two elements are required to acquire digital images

The first is a physical device that is sensitive to the energy radiated bythe object we wish to image

The second is a digitizera device for converting the output of the

physical sensing device into digital form

Eg. Digital Camera: the sensors produce a electrical output proportional

to light intensity and the digitizer convert this output to digital data

2. Specialized image processing hardware

Consist of the digitizer plus hardware that performs some operation

ALU-which performs arithmetic and logic operations in parallel on

entire images.

ALU-used in averaging images as quickly as they are digitized, for

the purpose of noise reduction.


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3. Computer

is a general purpose computer can range from a PC tosupercomputer

4. Software

for image processing consists of specialized modules that performspecific tasks.

A well designed package includes the capability for the user to write

minimum codes by utilizing the specialized modules

Eg: Matlab


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5.Mass Storage

is a must in image processingDigital storage for image processing applications -3 categories

Short term storage- use during processing eg: frame buffers-store one or

many images and can be accessed rapidly, usually at video rates

On-line storage-Frequentaccess data is stored Eg: magnetic disks

,optical disks.

Archival storage-characterized by infrequent access eg: magnetic tapes

and optical disks

An image size of 1024X102 pixels in which the intensity of each pixel is

an 8 bit quantity required one megabyte of storage space.

6.Image Displayscolor tv monitors

7.Hard copy devices

for recording images include laser printers, film cameras, inkjet units etc.


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Elements of Visual Perception

Structure of the human eye

Image formation in the human eye

Brightness adaptation and discrimination


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Elements of visual perception

In presenting the output of an imaging system to a human observer

it is essential to consider how it is transformed into information by

the viewerperception

Anyone who use devices for digital image processing should take into

account the principle of perception

Human will find an object in an image only if they may be

distinguished effortlessly from the background

Some parameters considered (Human Perception)

1. Brightness and Contrast

Brightness is the psychological concept or sensation associated with

the amount of light stimulus. Light source intensity depends upon the total light emitted from the

source.

Two source of equal intensity do not appear equally bright.


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Contrast

Is used to emphasize the difference in grey level of the object.

Depend on the brightness of the backgroundsimultaneous contrast

Illustration of simultaneous contrast


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2. Acuity

Is the ability to detect the details in the image

Less sensitive to slow and fast changes in brightness in the image plane

More sensitive to intermediate changes

3. Resolution

Degree of distinguishable details

There is know sense in representing visual information with higherresolution than that of the viewer

Best resolutionat a distance of about 250mm from an eye under

illumination of about 500lux

This illumination is provided by a 60W bulb from a distance of 400mm

The distance between two distinguishable point is approx. 0.16mm


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4.Object border

Boundaries of objects and simple patterns such as blobs or lines

enable some effect similar to conditional contrast

Eg: Ebbinghans illusion


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Optical illusions: Examples of human perception phenomenon


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Human eye structure

Shape nearly a sphere with an average diameter of 20mm

The front of the eye is covered by a transparent surfacecornea

-Tough& Transparent

The outer cover is composed of a fibrous coatsclera-Opaque membrane

Inner to the sclera a layer containing blood capillarieschoroid

-Heavily pigmented and help to reduce the amount of

extraneous light entering the eye

-Ciliary body and iris

The innermost membraneretina

when the eye is properly focused , light from the object is

imaged in the retina


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Lens

Made up of concentric layers of fibrous cell

Suspended by the fibers attached to the ciliary body60-70% water and 6% fat and more protein

It is coloured by slightly yellow pigmentation

Absorb approx 8% of the visible light spectrum

Higher absorption at lower wavelength.

RetinaIn details

Light receptors are distributed over the retina

Two type of receptors Cones and rods


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Cones

They are located in central portion of the retinafoveaThe muscles controlling the eye, rotate the eye ball until the

image falls on the fovea

They are highly sensitive to colour

They are around 6-7 million in number

Each cones are connected to fovea using its own nerve hence human

can resolve fine details using cones

Cones help us to see the objects in bright light and the cone vision iscalledphotopicor bright-lightvision


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Rods

They are distributed over the retinal surface

The number is much greater than cones :75150 millions

Several roads are connected to fovea using a single nervethis reduce

the amount of details discernible by these receptors.

Not involved in colour vision

It is sensitive to low level of illumination

Rods help us to see the objects in dim light (low level illumination) and

the road vision is called scotopic or dim lightvision


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Density of cones and rods

Blind spot : absence of receptors

Receptors density is measured in degree from the fovea

Cones: more dens in the centre of the retina (in the centre area of the

fovea)Rods: increase its densit from the centre to a rx 20 d then decrease


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Image formation in the eye

The distance between the lens and imaging plane (retina) is fixed

The focal length is adjusted by varying the shape of the lens and this is

achieved by the fibers in the ciliary body.

Near object : lens is thicker and the refractive power is maximum

Distant object: lens is flattened and the refractive power is minimum

LightReceptor

BrainRadiantEnergy


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The distance between the centre of the lens and the retina along

the visual axis is approx

The range of focal length is approx 14mm to 17m

[15/100 = h/17]

Perception takes place by excitation of receptors which transform

radiant energy into electrical impulses that are decoded by the

brain.

Image formation in the eye..


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Brightness adaptation and Discrimination

Digital images are displayed as a discrete set of intensities.

The dynamic range of light intensity to which eye can adapt is in the

order of from the scotopic to photopic (Glare) limit

Light intensity versus subjective brightness

Subjective brightness (intensity as perceived

by the human visual system) : logarithmic

function of light intensity.

Solid curve : the range of intensities to whichthe visual system can adapt [ photopic vision

]

The transition from scotopic to photopic vision

is gradual (-3 to -1 in the log scale)

The human visual system can not operate all

the range shown in the figure simultaneously.

It accomplishes this large variation by

changing its overall sensitivityknown as

brightness adaptation


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When compared with the total adaptation range , the total range of distinct

intensity levels the eye can discriminate simultaneously is rather small

For any given set of condition, the current sensitivity level of the visual

system is called the brightness adaptation level

The short curve representing BbBa the range of subjective brightness that

the eye can perceive when adapted to the level Ba. (it is restricted to the levelBb)

Consider a flat uniformly illuminated area which is large

enough to occupy the entire field of viewIt is illuminated from behind by a light source of intensity I

Then add an increment of illumination in the form of a

short duration flash that appears as a circle in the centre.

If is not bright enough : no perceivable change

When gets stronger: perceived change

Webber Ratio: the quantity where is the increment of

illumination distrainable 50% of the time with background

illumination I


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Small value of : small percentage change in intensity is distrainable.

This represent good brightness discrimination

Large value of : large percentage change in intensity required. This

represent poor bright discrimination.

Webber ratio ( ) as a

function of intensity

Brightness discrimination is poor

(large Weber ratio) at low level of

illuminationBrightness discrimination improves

as background illumination

increases

Rods : Poor discrimination

Cones: Better discrimination


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Image Sampling and quantization

1. Image formation model

2. Uniform Sampling & Quantization

3. Digital image representation

4. Relationships between pixels

5. Arithmetic & Logical operations


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Image Formation Model

The image refers to a two-dimensional light intensity function f(x,y)

The value or amplitude of f is determined by the source of the image.

In an image , its intensity values are proportional to energy radiated by thesource

Image function values f(x,y) at each point are positive and finite

The basic nature of f(x,y) may be characterised by two components

1. The amount of source illumination (Light) incident on the scene being viewed: Illumination, i(x,y).

2. The amount of illumination reflected by objects in the scene

: Reflectance, r(x,y)

Two function combine as a product to form f(x, y) = i(x, y)r(x, y)0 < i(x, y) < : determined by the nature of the light source

0 < r(x, y)


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Typical values of the illumination and reflectance:

Illumination: sun on earth: 90,000 lm/m2 on a sunny day; 10,000lm/m2 on a cloud day; moon on clear evening: 0.1 lm/m2; in a

commercial office is about 1000 lm/m2

Reflectance: 0.01 for black velvet, 0.65 for stainless steel, 0.80 for

flat-white wall paint, 0.90 for silver-plated metal, and 0.93 for snow

Monochrome image

Intensity of monochrome image at any coordinate is called the gray

level l of the image at that point

l= f(x0,y0)

The range of l is given byLmin


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Image Sampling and Quantization

Two process involved in converting continuous image to discrete/ digital

image

1. Sampling 2. Quantization

Image continuous with respect to x and y coordinates as well as

amplitude

Sampling: Digitizing the coordinate values

Quantization: Digitizing the amplitude values

Example

Figure a: Continuous image Figure b: one dimensional representation. It is a plot of amplitude

(intensity level) values of the continuous image along the line AB

Figure c: Equally spaced samples along the line AB - Sampling

Vertical tick markthe spatial location of each samples

Small white squarethe samples

To get a digital function intensity values also converted to discretequantityQuantization

The intensity scale divided into 8 discrete levels, ranging from black to

white The continuous intensity levels are quantized by assigning one of the

eight value to each sample,

Figure d: the digital samples obtained after both sampling anduantization.


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Sampling and Quantization.

1. Continuous image 2. Image after sampling

and quantization


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Digital Image Representation

F(s,t) represent a continuous image

Sampling and quantizationDigital Image

Sampling the image into a 2-D array f(x,y) containing M rows and Ncolumn

(x,y) are integer values.X = 0,1,2M-1 ; y = 0,1,2.N-1

The value of the digital image at origin f(0,0).

Some other values: f(0,1), f(2,1)f(M-1,N-1)The section of the real plane spanned by the coordinate of an image

is called the spatial domain and x and y the spatial variable or

coordinates

A digital image can be considered a matrix whose row and columnindices identify a point in the image and the corresponding matrix

element value identifies the gray level at that point.

We can represent an M X N digital


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image in the following compact

matrix form

Each element of this matrix is called

an image element, picture element or

pixel

Some times the digital image is

represented with following notation

Size of a Digital Image


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Size of a Digital Image

Z : Set of integers R : Set of real numbers

Sampling process

: partitioning the xy plane into grids

: Coordinates of the center of each cell in the gridpair of elements

from the Cartesian products Z(2), (zi.zj); Zi and Zj are integers from Z

: if the intensity levels also are integers , we can replace R as Z. That

is digital image becomes a 2-D function whose co-ordinate and

intensity values are integers.The values of M and N are positive. Due to processing, storage, and sampling

hardware considerations, the number of gray levels typically is an integer

power of 2:

L = 2(K) Where k is number of bits require to represent a grey value

The discrete levels should be equally spaced and that they are integers in theinterval [0, L-1].

The range of values spanned by the gray scale is called the dynamic range ofan image

Define the dynamic range of an imaging system as the ratio of the maximumintensity to the minimum detectable intensity level in the system


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Dynamic range establishes the lowest and highest intensity that a system

can represent.

The upper limit is determined bysaturationand the lower limit bynoise

Contrast : the difference in intensity between the highest and lowest intensitylevel in the image.

More number of pixels in an image have a high dynamic range: high contrast

Image with a low dynamic range: dull or washed out gray look

The number, b, of bits required to store a digitized image isb=M*N*k. if M=N, b = N(2)k


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Resolution

Resolution (how much you can see the details of the image ) depends onsampling and gray level.

The bigger the sampling rate and the gray scale, the better the approximationof the digitized image from the original.

The more the quantization scale becomes, the bigger the size of the image.

Spatial Resolution: Spatial resolution is the smallest detectable detail in an

image.Grey level Resolution: Gray-level resolutionsimilarly refers to the smallestdetectable change in gray level.


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B i R l ti Shi b t Pi l


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Neighbors of a pixel

1. 4-neighbors

A pixel p at coordinates (x,y) has two

horizontal and two vertical neighbors

Coordinates are (x+1,y), (x-1,y),(x,y+1)

and (x,y-1) : Denoted by ; N4(p)

2. Diagonal-neighbors

A pixel p have 4 diagonal neighbor withcoordintes (x+1,y+1), (x+1,y-1),(x-1,y+1)

and (x-1,y-1) : Denoted by Nd(p)

3. 8-neighbors4-neighbors & diagonal-neighbors

together consist of 8-neighbours of p:

Denoted by N8(p).

(x-1,y-1) (x-1,y) (x-1,y+1)

(x,,y-1) (x,y) (x,y+1)

(x+1,y-1) (x+1,y) (x+1,y+1)

Basic Relation Ships between Pixels

B i R l ti Shi b t Pi l


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Basic Relation Ships between Pixels.

Adjacency

Let V be a set of intensity values

In a gray scale image with intensity values from 0-255, V could be asub set of these 256 values

1. 4-adjacency

Two pixels p & q with values from V are 4-adjucent if q is in

the set N4(p)

2. 8-adjacency

Two pixels p & q with values from V are 8-adjucent if q is inthe set N8(p)

3. M-adjacency

Two pixels p & q with values from V are M-adjucent if*q is in the set N4(p) or

*q is in the set Nd(p) and the set N4(p) N4(q) has no pixels

whose values are from V


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Arithmetic & Logical operations

1. Arithmetic operations

Addition

Subtraction

Multiplication

Division

2. Logical operations

AND

OR

Complement (NOT)

XOR

END

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