ip_lecture02-funda

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Digital Image Processingigital Image Processing(UST 2007 FallUST 2007 Fall)

Sang Chul Ahn

[email protected]

Digital Image FundamentalsDigital Image Fundamentals


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Elements of Visual PerceptionElements of Visual Perception

Although the digital image processing field is built on afoundation of mathematical and probabilistic formulations,

human intuition and analysis play a central role in the choice oftechniques

Basic understanding of human visual perception is important

The mechanics and parameters related to how images areformed in the eye

The physical limitations of human vision in terms of factors thatalso are used in digital image processing

The factors how human and electronic imaging compare in

terms of resolution and ability to adapt to changes in illumination

Nearly a sphere with

an average diameter

of 2cm

3 membranes enclosethe eye

Cornea() &

Sclera()

Choroid()

ciliary body, iris

diaphragm

Retina ()

Structure of the Human EyeStructure of the Human Eye


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Cornea: transparent

sclera: opaque

Choroid

contains blood vessels

heavily pigmented and reduce the

amount of light entering the eye and

backscatter within the eye

At anterior, Ciliary body & iris diaphragm

Iris: control the amount of light, 2~8mm

Lens:

60~70% water, 6% fat, and protein,

slightly yellow,

absorbs approximately 8% of the visible light spectrum

Retina Image is focused on retina

Two classes of receptors: cones and rods

Cones

6~7million

Located primarily in the fovea

Color sense

One nerve for one cone: resolve fine detail

Cone vision called photopic or bright-light vision

Rods

75~105million

Distributed over the retinal surface

One nerve for several rods

Sensitive to low levels of illumination

Rod vision called scotopic or dim-light vision



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Blind spot

Receptor distribution

Fovea Circular indentation of about 1.5mm in diameter

Density of cones is approximately 150,000 cones/mm2

1.5mm x 1.5mm square 337,000 cones

Image FormationImage Formation

The shape of lens is controlled by tension of theciliary body

Lens flattened for distant objects

The distance between the center of the lens and theretina(focal length) varies 17mm~14mm


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Bright AdaptationBright Adaptation

Bright adaptation range is on the order of 1010

Subjective brightness is a logarithmic function of the light intensity

The range of photopic vision is about 106

The visual system cannot operate over the range simultaneously

It is done by changes in its overall sensitivity

Bright adaptation

DiscriminationDiscrimination

Weber ratio Ic/I, where Ic is the increment of illumination discriminable 50%

of the time

Small value represents good brightness discrimination

poor by rods

good by cones


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Perceived brightness is not a simple function of intensity

The visual system tends to undershoot or overshoot around theboundary of regions of different intensities

Mach bands

Although the intensity of the

stripes is constant, we actually

perceive a brightness pattern

that is strongly scalloped


A regions perceived brightness does not depend simply on itsintensity

simultaneous constrast

All the center squares have exactly the same intensity. However,

they appear to the eye to become darker as the background getslighter


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Optical illusionOptical illusion

The eye fills in nonexisting information or wronglyperceives geometrical properties of objects

Electromagnetic SpectrumElectromagnetic Spectrum

In 1666, Sir Isaac Newton discovered that when a beam of sunlight ispassed through a glass prism, the emerging beam of light is not whitebut consists instead of a continuous spectrum of colors ranging fromviolet to red


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Physics of Light and EM SpectrumPhysics of Light and EM Spectrum

Frequency( orf ) vs. wavelength()

f= c/ c: 2.998x108

m/s (the speed of light)Energy (unit: electron-volt)

E = h h: Plancks constant

Energy is proportional to frequency

Higher-frequency electromagnetic phenomena carry

more energy per photon

Gamma rays are dangerous to living organisms


Light that is void of color is called achromatic or monochromaticlight

The only attribute of such light is its intensity, or amount

Chromatic light spans the electomagnetic energy spectrum from

approximately 0.43 to 0.79um Three basic quantities are used to describe the quality of a

chromatic light source: radiance, luminance, and brightness

Radiance(unit: W) is the total amount of energy that flows from thelight source

Luminance(unit: lm, lumens) gives a measure of the amount ofenergy an observer perceives from a light source

ex) Light emitted from a source operating in the far infrared region of thespectrum could have high radiance, but an observer would hardly

perceive it(zero luminance) Brightness is a subjective descriptor of light perception that is

practically impossible to measure. It embodies the achromaticnotion of intensity


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Near-infrared: the part of the infrared band close to thevisible spectrum

Far-infrared: the part of the infrared band close to themicrowave band

It is important to note that the wavelength of anelectromagnetic wave required to see an object mustbe of the same size as or smaller than the object.

For example, a water molecule has a diameter on theorder of10-10m. Thus, to study molecules, we wouldneed a source capable of emitting in the far ultravioletor soft X-ray region

Image SensorsImage Sensors


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Image SensingImage Sensing

CCD vs. CMOSCCD vs. CMOS

A CCD is like a threedecker sandwich. The bottom layer

contains the photosites. Above them is a layer of colored

filters that determines which color each site records. Finally,

the top layer contains microlenses that gather light.Courtesy

of Fujifilm.

CCD (charge-coupled device) and CMOS (complimentary metal-oxide

semiconductor)


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In a CCD device, the charge is actually transported across the chip

and read at one corner of the array. An analog-to-digital converter

turns each pixel's value into a digital value. In most CMOS devices, there are several transistors at each pixel that

amplify and move the charge using more traditional wires. The CMOS

approach is more flexible because each pixel can be read individually.

CCDs use a special manufacturing process to create the ability to

transport charge across the chip without distortion. This process leads

to very high-quality sensors in terms of fidelity and light sensitivity.

CMOS chips, on the other hand, use traditional manufacturing

processes to create the chip. CMOS sensors, traditionally, are more

susceptible to noise. Because each pixel on a CMOS sensor has several transistors located

next to it, the light sensitivity of a CMOS chip tends to be lower. Many

of the photons hitting the chip hit the transistors instead of the

photodiode.


http://www.pictureline.com/newsletter/2004/september/pixels.html

http://www.axis.com/edu/axis/index.htm


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Simple Image ModelSimple Image Model

Monochrome(Gray) Image : f(x,y)f(x,y) = intensity value at coordinates (x,y)

0 < f(x,y) < ; f(x,y) is energy

Light TransportLight Transport

Simple image formationf(x,y) = i(x,y)r(x,y)

0 < i(x,y) < ; illumination

0 < r(x,y) < 1 ; reflectance

In real situationLmin l (=f(x,y)) Lmax


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Sampling & QuantizationSampling & Quantization

Image sampling Digitization of spatial coordinates (x,y)

Quantization Amplitude digitization

The quality of a digital image is determined to a largedegree by the number of samples and discrete graylevels used in sampling and quantization

f(x,y) f(0,0) f(1,0) f(M-1,0)

f(0,1) f(1,1) f(M-1,1)

:f(0,N-1) f(1,N-1) f(M-1,N-1)

Digital image

Continuousimage



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What isWhat is Digital Image?Digital Image?

x

y

Origin

(0,0)

Pixel

Digital image : x,y,f(x,y), three values are all

discretized

Pixel : Image elements, Picture elements, Pels


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Digital Color Image R(x,y), G(x,y), B(x,y), three values are assigned at

the same pixel location

HSI, YIQ, CMY representation

We can use more than 3 values for a pixel such asCMYK representation

Comparison f(x,y) : 2D still image

f(x,y,z) : 3D object

f(x,y,t) : Video or Image Sequence

f(x,y,z,t) : moving 3D object


Meaningbrightness(luminance) or color of an object

TV camera, scanner

absorption characteristics of objects(especially bodies) X-ray imaging, Ultrasonic imaging, CT

distance between objects and measuringinstrument sonar imaging, radar imaging, range camera

temperature of an object IR(infrared) camera


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Spatial Resolution (x,y)

Spatial resolution is the smallest discernible detail in an image

A line pair : a line and its adjacent space

A widely used definition of resolution is the smallest number of

discernible line pairs per unit distance

ex) 100 line pairs/mm

But, unit distance or unit area is omitted in most cases

Spatial ResolutionSpatial Resolution


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cf) Full HD

Screen resolution [wikipedia]

Spatial ResolutionSpatial Resolution


Gray-level Resolution

Gray-level resolution is the smallest discernible change in

gray level (but, highly subjective!)

Due to hardware considerations, we only considerquantization level

Usually an integer power of 2. The most common level is

28=256

However, we can find some systems that can digitize the

gray levels of an image with 10 to 12 bits of accuracy.


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GrayGray--level Resolutionlevel Resolution

Image displayed in 256, 128, 64, 32, 16, 8, 4, 2 gray-levels

StorageStorage

ForMxNimage with L(=2k) discrete gray level

The number, b, of bits required to store the image is

b = MNk

ex1) 1024x1024x8bit = 1Mbytes


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IsopreferenceIsopreference curvescurves

Relation between subjective image quality andresolution

Tested by images with low/medium/high detail

Result

A few gray levels may be needed for high

detailed image

Perceived quality in the other two image

categories remained the same in some intervals

in which the spatial resolution was increased,

but the number of gray levels actually decreased

AliasingAliasing

Shannon sampling theorem

if the function is sampled at a rate equal to or greater than twice its

highest frequency, it is possible to recover completely the original

function from its samples

if the function is undersampled, then a phenomenon called aliasingcorrupts the sampled image

The corruption is in the form of additional frequency components being

introduced into the sampled function. These are called aliased

frequencies

Nyquist freq. = 0.5 x sampling rate


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AliasingAliasing

Except for a special case, it is impossible to satisfy the sampling

theorem in practice

The principal approach for reducing the aliasing effects on an image

is to reduce its high-frequency components by blurring the image

prior to sampling

However, aliasing is always present in a sampled image

The effect of aliased frequencies can be seen under the right

conditions in the form of so-called Moir patterns

Aliasing in ImagesAliasing in Images When we view a digital photograph, the reconstruction (interpolation)

is performed by a display or printer device, and by our eyes and our

brain.

Typical aliasing in images can be seen in the form ofJaggies

The checkers should become smaller as the distance from theviewer increases. However, the checkers become larger or

irregularly shapedwhen their distance from the viewer becomes too

great

Anti-aliasing is the technique of minimizing the distortion artifacts

known as aliasing when representing a high-resolution signal at a

lower resolution

(a)Aliased (b),(c)Anti-aliasing is applied


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N4(p) : 4-neighbors of pixelp(y,x)

{ p(y+1,x), p(y-1,x), p(y,x+1), p(y,x-1)}

ND(p) : diagonal neighbors of pixelp(y,x){ p(y+1,x+1), p(y-1,x-1), p(y-1,x+1), p(y+1,x-1)}

N8(p) : 8-neighbors of pixelp(y,x)

N8(p) = N4(p) ND(p)

Some of the neighbors of pixel p lie outside the digital image ifthe pixel p is on the border of the image

p(x,y

)

N4

ND

N8

Neighbors of a PixelNeighbors of a Pixel

V : set of gray-level values to define adjacency

ex) V={1} ; binary image

V={32,33,,63,64} ; gray image

4-adjacency: Two pixels p, q with values from V are 4-adjacency if q is in the set N4(p)

8-adjacency: Two pixels p, q with values from V are 8-adjacency if q is in the set N8(p)

m-adjacency(mixed adjacency) : Two pixels p and q withvalues from V are m-adjacency if

i) q is in N4(p), or

ii) q is in ND(p) and the set N4(p) N4(q) has no pixels whose

values are from V

AdjacencyAdjacency


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m- adjacency

AdjacencyAdjacency

8-adjacency

PathPath

A (digital)path(or curve) from pixelp at (x,y) to pixel

q at (s,t) is a sequence of distinct pixels with

coordinates

(x0,y0), (x1,y1), ,, (xn,yn)where (x0,y0) =(x,y), (xn,yn)=(s,t), and pixel (xi,yi) and

(xi-1,yi-1) are adjacent for1in

n is the length of the path

If(x0,y0) =(xn,yn), the path is a closedpath

The path can be defined 4-,8-,m-paths depending on

adjacency type


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ConnectivityConnectivity

Let Sbe a subset of pixels in an image. Two pixelspand q are said to be connectedin Sif there exists a

path between them consisting entirely of pixels in S For any pixelp in S, the set of pixels that are

connected to it in Sis called a connected componentofS.

If it only has one connected component, then set Siscalled a connected set.

Let Rbe a subset of pixels in an image. We call Raregion of the image ifRis a connected set

The boundaryof a region Ris the set of pixels in theregion that have one or more neighbors that are notin R

Distance MeasuresDistance Measures

Let pixels be

p=p(x,y), q=q(s,t), z=z(u,v)

D() is a distance function ormetricif(a) D(p,q) 0 (D(p,q)=0 iff p=q)

(b) D(p,q) = D(q,p)

(c) D(p,z) D(p,q) + D(q,z)


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Euclidean distanceDe(p,q) = [(x-s)

2+ (y-t)2]1/2

D4 distance (city-block distance)D4(p,q) = |x-s| + |y-t|

2

2 1 2

2 1 0 1 22 1 2

2


D8distance (chessboard distance)D8(p,q) = max(|x-s|, |y-t|)

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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Arithmetic/Logic OperationsArithmetic/Logic Operations

Arithmetic operation

Addition: p+qSubtraction: p-q

Multiplication: pxq

Division: p q

Logic Operation

AND: p AND q (p. q)

OR: p OR q (p + q)COMPLEMENT: NOT q ( q )

Logic OperationsLogic Operations

A B

NOT(A) A AND B A OR B

A - B

A XOR B


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2D Image transformation

Translation

Scaling

Rotation

Order of application is important !!

x

y

x

y

tx

ty= +

x

y

Sx 0

0 Sy=

x

y

x

y

cos sin

-sin cos

=x

y

Original

Scaling(Sx=2, Sy=2)

2D Image transformation

30deg. rotation

y axis translation +100

Origin

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