Chapter 02 Digital Image Fundamentals 6spp

7/27/2019 Chapter 02 Digital Image Fundamentals 6spp

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University of Ioannina - Department of Computer Science

Digital Imaging Fundamentals

Christophoros Nikou

[email protected]

Digital Image Processing

Images taken from:

R. Gonzalez and R. Woods. Digital Image Processing, Prentice Hall, 2008.

Digital Image Processing course by Brian Mac Namee, Dublin Institute of Technology.

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C. Nikou Digital Image Processing (E12)

Digital Image Fundamentals

Those who wish to succeed must ask the

right preliminary questions

Aristotle

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Contents

This lecture will cover:

The human visual system

Light and the electromagnetic spectrum

Image representation

Image sensing and acquisition

Sampling, quantisation and resolution

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Human Visual System

The best vision model we have!

Knowledge of how images form in the eye

can help us with processing digital images

We will take just a whirlwind tour of the

human visual system

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Structure Of The Human Eye

The lens focuses light from objects onto theretina

The retina is covered withlight receptors calledcones (6-7 million) androds (75-150 million)

Cones are concentratedaround the fovea and arevery sensitive to colour

Rods are more spread outand are sensitive to low levels

of illuminationImagestakenfromGonzalez&Woods,

DigitalImageProcessing(2002)

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Structure Of The Human Eye (cont.)

ImagestakenfromGonzalez&Woods,


Density of cones and rods across a section of the right eye


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Structure Of The Human Eye (cont.)

Each cone is connectedto each own nerve end. They can resolve fine

details.

Sensitive to color (photopicvision)

Many rods are connectedto a single nerve end

Limited resolution withrespect to cones

Not sensitive to color

Sensitive to low levelillumination (scotopicvision)Im

agestakenfromGonzalez&Woods,

DigitalImageProcessing

(2002)

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Blind-Spot Experiment

Draw an image similar to that below on a pieceof paper (the dot and cross are about 6 inches

apart)

Close your right eye and focus on the cross withyour left eye

Hold the image about 20 inches away from yourface and move it slowly towards you

The dot should disappear!

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Image Formation In The Eye

Muscles within the eye can be used to changethe shape of the lens allowing us focus onobjects that are near or far away (in contrast witha camera where the distance between the lensand the focal plane varies)

An image is focused onto the retina causing rods

and cones to become excited which ultimatelysend signals to the brain

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Brightness Adaptation & Discrimination

The human visual system can perceiveapproximately 1010 different light intensitylevels.

At any time instance, we can onlydiscriminate between a much smaller

number brightness adaptation. Similarly, the perceived intensity of a

region is related to the light intensities ofthe regions surrounding it.

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Brightness Adaptation & Discrimination(cont)


DigitalImageProcessing(2002) Weber ratio

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Brightness Adaptation & Discrimination(cont)

An example of Mach bands




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(cont)



(2002)

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(cont)

An example ofsimultaneous contrast



(2002)

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Optical Illusions

Our visual systemplays manyinteresting trickson us

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Optical Illusions (cont)

Stare at the cross

in the middle of

the image and

think circles

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Optical Illusions (cont) 18


Light And The ElectromagneticSpectrum

Light is just a particular part of theelectromagnetic spectrum that can besensed by the human eye

The electromagnetic spectrum is split upaccording to the wavelengths of differentforms of energy


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Reflected Light

The colours that weperceive are

determined by thenature of the lightreflected from anobject

For example, if whitelight is shone onto agreen object mostwavelengths areabsorbed, while greenlight is reflected fromthe object

ColoursAbsorbed

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Image Acquisition

Images are typically generated by

illuminatinga scene and absorbing theenergy reflected by the objects in that scene

Typical notions of

illumination and

scene can be way off:

X-rays of a skeleton

Ultrasound of an

unborn baby

Electro-microscopic

images of molecules



(2002)

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Image Sensing and Acquisition

Sensors transform the incoming energyinto voltage and the output of the sensor isdigitized.

Imaging Sensor

Line of Image Sensors Array of Image Sensors

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Image Sensing

ImagestakenfromGonzalez&Woods

,DigitalImageProcessing(2002)

Using Sensor Strips and Rings

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Image Representation

col

row

f (row, col)

A digital image iscomposed ofMrowsandNcolumns of pixelseach storing a value

Pixel values are in therange 0-255 (black-white)

Images can easilybe represented asmatrices



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Colour images




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Colour images



(2002)

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Image Sampling And Quantisation

A digital sensor can only measure a limited

number ofsamples at a discrete set ofenergy levels

Quantisation is the process of converting acontinuous analogue signal into a digitalrepresentation of this signal



(2002)

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Image Sampling And Quantisation

(cont)

Remember that a digital image is alwaysonly an approximation of a real worldscene



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Image Representation



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Saturation & Noise



Dynamic range: Theratio of the maximum(saturation) to theminimum (noise)detectable intensity ofthe imaging system.

Noise generally appearas a grainy texturepattern in the darkerregions and masks thelowest detectable true

intensity level

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Spatial Resolution

The spatial resolution of an image isdetermined by how sampling was carried out

Spatial resolution simply refers to thesmallest discernable detail in an image Vision specialists will

often talk about pixelsize

Graphic designers willtalk about dots perinch (DPI)


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Spatial Resolution (cont)



(2002)

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1024 * 1024 512 * 512 256 * 256

128 * 128 64 * 64 32 * 32



(2002)

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Intensity Level Resolution

Intensity level resolution refers to the number ofintensity levels used to represent the image The more intensity levels used, the finer the level of

detail discernable in an image

Intensity level resolution is usually given in terms of thenumber of bits used to store each intensity level

Number of BitsNumber of Intensity

LevelsExamples

1 2 0, 1

2 4 00, 01, 10, 11

4 16 0000, 0101, 1111

8 256 00110011, 01010101

16 65,536 1010101010101010

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Intensity Level Resolution (cont)

128 grey levels (7 bpp) 64 grey levels (6 bpp) 32 grey levels (5 bpp)

16 grey levels (4 bpp) 8 grey levels (3 bpp) 4 grey levels (2 bpp) 2 grey levels (1 bpp)

256 grey levels (8 bits per pixel)



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Low Detail Medium Detail High Detail


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(2002)

Isopreference curvesrepresent the dependence

between intensity andspatial resolutions. Points lying on a curve

represent images of equalquality as described byobservers.

The curves become morevertical as the degree ofdetail increases (a lot ofdetail need less intensitylevels).

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Resolution: How Much Is Enough?

The big question with resolution is always

how much is enough? This all depends on what is in the image and

what you would like to do with it

Key questions include

Does the image look aesthetically pleasing?

Can you see what you need to see within the

image?

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Resolution: How Much Is Enough?

(cont)

The picture on the right is fine for counting

the number of cars, but not for reading the

number plate

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Interpolation

The process of using known data to estimatevalues at unknown locations

Basic operation for shrinking, zooming, rotationand translation e.g. a 500x500 image has to be enlarged by 1.5 to

750x750 pixels

Create an imaginary 750x750 grid with the same pixelspacing as the original and then shrink it to 500x500

The 750x750 shrunk pixel spacing will be less thanthe spacing in the original image.

Pixel values have to be determined in between theoriginal pixel locations

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Interpolation (cont.)

How to determine pixel values

Nearest neighbour

Bilinear

Bicubic

2D sinc

Ya 1-a

b

1-b

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Interpolation (cont...)




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Distances between pixels



(2002) For pixelsp(x,y), q(s,t) andz(v,w),D is a

distance function or metric if:) ( , ) 0 ( ( , ) 0 ),

) ( , ) ( , ),

) ( , ) ( , ) ( , ).

a D p q D p q iff p q

b D p q D q p

c D p z D p q D q z

The Euclidean distance betweenp and q is

defined as:

12 2 2( , ) ( ) ( )eD p q x s y t

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Distances between pixels (cont.)



(2002)

The city-block orD4 distance between p and q is

defined as:4 ( , ) | | | |D p q x s y t

Pixels having the city-block distance from a pixel

(x,y) less than or equal to some value T form a

diamond centered at (x,y) . For example, forT=2:

2

2 1 2

2 1 0 1 2

2 1 2

2

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Distances between pixels (cont.)



The chessboard orD8 distance betweenp and q isdefined as:

8 ( , ) max(| |,| |)D p q x s y t

Pixels having the city-block distance from a pixel

(x,y) less than or equal to some value T form asquare centered at (x,y). For example, forT=2:

2 2 2 2 2

2 1 1 1 2

2 1 0 1 2

2 1 1 1 2

2 2 2 2 2

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Mathematical operations used in

digital image processing


,DigitalImageProcessing(2002) Arithmetic operations (e.g image subtraction pixel

by pixel)

Matrix and vector operations

Linear (e.g. sum) and nonlinear operations (e.g.

min and max)

Set and logical operations

Spatial and neighbourhood operations (e.g. local

average)

Geometric spatial transformations (e.g. rotation)

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Image subtraction



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Image multiplication




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Image multiplication (cont.)



(2002)

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Logical operator



(2002)

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Neighbourhood operation



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A note on arithmetic operations


,DigitalImageProcessing(2002) Most images are displayed at 8 bits (0-255).

When images are saved in standard formats

like TIFF or JPEG the conversion to this range

is automatic.

However, the approach used for the conversion

depends on the software package. The difference of two images is in the range [-255,

255] and the sum is in the range [0, 510].

Many packages simply set all negative values to 0and all values exceeding 255 to 255 which isundesirable.

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A note on arithmetic operations(cont.)


DigitalImageProcessing(2002) An approach that guarantees that the full range

is captured into a fixed number of bits is the

following:

At first, make the minimum value of the image

equal to zero:

Then perform intensity scaling to [0,K]

minmf f f

maxm

s

m

f

f Kf

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Geometric spatial transformations



11 11

21 12

31 13

0

1 1 1 0

1

t t

x y u v u v t t

t t

T

A common geometric transformation is the affine

transform

It may translate, rotate, scale and sheer an image

depending on the value of the elements ofT

To avoid empty pixels we implement the inverse

mapping Interpolation is essential


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(cont.)



(2002)

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(cont.)



(2002) The effects and importance of interpolation in

image transformations

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Image Registration


,DigitalImageProcessing(2002) Estimate the transformation parameters

between two images.

Very important application of digital image

processing.

Single and multimodal

Temporal evolution and quantitative analysis(medicine, satellite images)

A basic approach is to use control points (user

defined or automatically detected) and estimate

the elements of the transformation matrix by

solving a linear system.

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Image Registration (cont.)



Manually selected

landmarks

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Chapter 02 Digital Image Fundamentals 6spp