Chapter 1 and 2 gonzalez and woods

Chapter-1 and 2

Subject: FIP (181102)Prof. Asodariya Bhavesh

ECD,SSASIT, Surat

Digital Image Processing, 3rd edition by Gonzalez and Woods

Optics and Human Vision

The physics of light

http://commons.wikimedia.org/wiki/File:Eye-diagram_bg.svg

Light Light

Particles known as photons Act as ‘waves’

Two fundamental properties Amplitude Wavelength

Frequency is the inverse of wavelength Relationship between wavelength (lambda) and

frequency (f)

fc /Where c = speed of light = 299,792,458 m / s

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What is Digital Image Processing?Digital image processing focuses on two major tasks

Improvement of pictorial information for human interpretation

Processing of image data for storage, transmission and representation for autonomous machine perception

Some argument about where image processing ends and fields such as image analysis and computer vision start

What is DIP? (cont…)The continuum from image processing to computer vision can be broken up into low-, mid- and high-level processes

Low Level ProcessInput: ImageOutput: ImageExamples: Noise removal, image sharpening

Mid Level ProcessInput: Image Output: AttributesExamples: Object recognition, segmentation

High Level ProcessInput: Attributes Output: UnderstandingExamples: Scene understanding, autonomous navigation

In this course we will stop here

History of Digital Image ProcessingEarly 1920s: One of the first applications of digital imaging was in the news-paper industry

The Bartlane cable picture transmission service

Images were transferred by submarine cable between London and New York

Pictures were coded for cable transfer and reconstructed at the receiving end on a telegraph printer

Early digital image

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History of DIP (cont…)Mid to late 1920s: Improvements to the Bartlane system resulted in higher quality images

New reproduction processes based on photographic techniques

Increased number of tones in reproduced images

Improved digital image

Early 15 tone digital image

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History of DIP (cont…)1960s: Improvements in computing technology and the onset of the space race led to a surge of work in digital image processing

1964: Computers used to improve the quality of images of the moon taken by the Ranger 7 probe

Such techniques were usedin other space missions including the Apollo landings

A picture of the moon taken by the Ranger 7 probe minutes before

landing

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History of DIP (cont…)1970s: Digital image processing begins to be used in medical applications

1979: Sir Godfrey N. Hounsfield & Prof. Allan M. Cormack share the Nobel Prize in medicine for the invention of tomography, the technology behind Computerised Axial Tomography (CAT) scans

Typical head slice CAT image

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Key Stages in Digital Image Processing

Image Acquisition

Image Restoration

Morphological Processing

Segmentation

Representation &

Description

Image Enhancemen

t

Object Recognition

Problem DomainColour Image

ProcessingImage

Compression

Key Stages in Digital Image Processing:Image Aquisition

Image Acquisition

Image Restoration


Segmentation

Representation &

Description

Image Enhancemen

t

Object Recognition


ProcessingImage

Compression

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Key Stages in Digital Image Processing:Image Enhancement

Image Acquisition

Image Restoration


Segmentation

Representation &

Description

Image Enhancemen

t

Object Recognition


ProcessingImage

Compression

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Key Stages in Digital Image Processing:Image Restoration

Image Acquisition

Image Restoration


Segmentation

Representation &

Description

Image Enhancemen

t

Object Recognition


ProcessingImage

Compression

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Key Stages in Digital Image Processing:Morphological Processing

Image Acquisition

Image Restoration


Segmentation

Representation &

Description

Image Enhancemen

t

Object Recognition


ProcessingImage

Compression

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Key Stages in Digital Image Processing:Segmentation

Image Acquisition

Image Restoration


Segmentation

Representation &

Description

Image Enhancemen

t

Object Recognition


ProcessingImage

Compression

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Key Stages in Digital Image Processing:Object Recognition

Image Acquisition

Image Restoration


Segmentation

Representation &

Description

Image Enhancemen

t

Object Recognition


ProcessingImage

Compression

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Key Stages in Digital Image Processing:Representation & Description

Image Acquisition

Image Restoration


Segmentation

Representation &

Description

Image Enhancemen

t

Object Recognition


ProcessingImage

Compression

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Key Stages in Digital Image Processing:Image Compression

Image Acquisition

Image Restoration


Segmentation

Representation &

Description

Image Enhancemen

t

Object Recognition


ProcessingImage

Compression

Key Stages in Digital Image Processing:Colour Image Processing

Image Acquisition

Image Restoration


Segmentation

Representation &

Description

Image Enhancemen

t

Object Recognition


ProcessingImage

Compression

Visible Spectrum

(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

Light

Diagram of a light wave.

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Conventional Coordinate for Image Representation


Digital Image Types : Intensity Image

Intensity image or monochrome image each pixel corresponds to light intensitynormally represented in gray scale (gray level).

398715322213251537266928161010

Gray scale values

398715322213251537266928161010

39656554424754216796543243567065

99876532924385856796906078567099

Digital Image Types : RGB Image

Color image or RGB image:each pixel contains a vectorrepresenting red, green andblue components.

RGB components

Image Types : Binary Image

Binary image or black and white imageEach pixel contains one bit :

1 represent white0 represents black

1111111100000000

Binary data

Image Types : Index Image

Index imageEach pixel contains index numberpointing to a color in a color table

256746941

Index value

Index No.

Redcomponent

Greencomponent

Bluecomponent

1 0.1 0.5 0.32 1.0 0.0 0.03 0.0 1.0 0.04 0.5 0.5 0.55 0.2 0.8 0.9

… … … …

Color Table

Cross Section of the Human Eye


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Human Eye

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Anatomy of the Human Eye

Source: http://webvision.med.utah.edu/

Human Visual System Human vision

Cornea acts as a protective lens that roughly focuses incoming light

Iris controls the amount of light that enters the eye

The lens sharply focuses incoming light onto the retina Absorbs both infra-red and ultra-violet light which can

damage the lens The retina is covered by photoreceptors (light

sensors) which measure light

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Photoreceptors Rods

Approximately 100-150 million rods Non-uniform distribution across the retina Sensitive to low-light levels (scotopic vision) Lower resolution

Cones Approximately 6-7 million cones Sensitive to higher-light levels (photopic vision) High resolution Detect color by the use of 3 different kinds of cones each

of which is sensitive to red, green, or blue frequencies Red (L cone) : 564-580 nm wavelengths (65% of all cones) Green (M cone) : 534-545 nm wavelengths (30% of all cones) Blue (S cone) : 420-440 nm wavelengths (5% of all cones)

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Cone (LMS) and Rod (R) responses

http://en.wikipedia.org/wiki/File:Cone-response.svg34

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Photoreceptor density across retina

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Comparison between rods and cones

Rods ConesUsed for night vision Used for day visionLoss causes night blindness Loss causes legal blindnessLow spatial resolution with higher noise

High spatial resolution with lower noise

Not present in fovea Concentrated in foveaSlower time response to light Quicker time response to lightOne type of photosensitive pigment

Three types of photosensitive pigment

Emphasis on motion detection Emphasis on detecting fine detail

Color and Human Perception Chromatic light

has a color component

Achromatic light has no color component has only one property – intensity

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Image Formation in the Human Eye

(Picture from Microsoft Encarta 2000)


Brightness AdaptationActual light intensity is (basically) log-compressed for perception.

Human vision can see light between the glare limit and scotopic threshold but not all levels at the same time.

The eye adjusts to an average value (the red dot) and can simultaneously see all light in a smaller range surrounding the adaptation level.

Light appears black at the bottom of the instantaneous range and white at the top of that range.39

Weber Ratio ∆I/I

Weber Ratio

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Human Visual Perception Light intensity:

The lowest (darkest) perceptible intensity is the scotopic threshold The highest (brightest) perceptible intensity is the glare limit The difference between these two levels is on the order of 1010

We can’t discriminate all these intensities at the same time! We adjust to an average value of light intensities and then discriminate around the average.

Log compression. Experimental results show that the relationship between the

perceived amount of light and the actual amount of light in a scene are generally related logarithmically. The human visual system perceives brightness as the logarithm of the actual

light intensity and interprets the image accordingly. Consider, for example, a bright light source that is approximately 6times

brighter than another. The eye will perceive the brighter light as approximately twice the brightness of the darker.

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Brightness Adaptation and Mach Banding When viewing any scene:

The eye rapidly scans across the field of view while coming to momentary rest at each point of particular interest.

At each of these points the eye adapts to the average brightness of the local region surrounding the point of interest.

This phenomena is known as local brightness adaptation. Mach banding is a visual effect that results, in part, from local

brightness adaptation. The eye over-shoots/under-shoots at edges where the

brightness changes rapidly. This causes ‘false perception’ of the intensities

Examples follow….

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Brightness Adaptation and Mach Banding

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Brightness Adaptation(Hermann Grid)

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Optical illusion


Simultaneous Contrast Simultaneous contrast refers to the way in which

two adjacent intensities (or colors) affect each other. Example: Note that a blank sheet of paper may

appear white when placed on a desktop but may appear black when used to shield the eyes against the sun.

Figure 2.9 is a common way of illustrating that the perceived intensity of a region is dependent upon the contrast of the region with its local background. The four inner squares are of identical intensity but are

contextualized by the four surrounding squares The perceived intensity of the inner squares varies from

bright on the left to dark on the right.

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Simultaneous Contrast

Image Sensing and acquisition

Single sensor

Line sensor

Array sensor


Image Sensors : Single Sensor


Image Sensors : Line Sensor

Fingerprint sweep sensorComputerized Axial Tomography


CCD KAF-3200E from Kodak.(2184 x 1472 pixels,

Pixel size 6.8 microns2)

Charge-Coupled Device (CCD)

w Used for convert a continuous image into a digital image

w Contains an array of light sensors

w Converts photon into electric chargesaccumulated in each sensor unit

Image Sensors : Array Sensor

Horizontal Transportation RegisterOutput Gate

Ampl

ifier

Verti

cal T

rans

port

Regi

ster

Gate

Verti

cal T

rans

port

Regi

ster

Gate

Verti

cal T

rans

port

Regi

ster

Gate

Photosites Output

Image Sensor: Inside Charge-Coupled Device

Image Sensor: How CCD works

abc

ghi

def

abc

ghi

def

abc

ghi

def

Vertical shift

Horizontal shift

Image pixel

Horizontal transportregister

Output

Digital Image Acquisition Process


Generating a Digital Image


Image Sampling and Quantization

Image sampling: discretize an image in the spatial domainSpatial resolution / image resolution: pixel size or number of pixels


How to choose the spatial resolution

= Sampling locationsOr

igin

al im

age

Sam

pled

imag

e

Under sampling, we lost some image details!

Spatial resolution

How to choose the spatial resolution : Nyquist Rate

Orig

inal

imag

e

= Sampling locations

MinimumPeriod Spatial resolution

(sampling rate)

Sampled image

No detail is lost!Nyquist Rate: Spatial resolution must be less or equalhalf of the minimum period of the imageor sampling frequency must be greater orEqual twice of the maximum frequency.

2mm 1mm

0 0.5 1 1.5 2-1

-0.5

0

0.5

1

0 0.5 1 1.5 2-1

-0.5

0

0.5

1

1 ),2sin()(1 fttx

6 ),12sin()(2 fttx

Sampling rate: 5 samples/sec

Aliased Frequency

Two different frequencies but the same results !

Effect of Spatial Resolution

256x256 pixels

64x64 pixels

128x128 pixels

32x32 pixels

Spatial Resolution It is a measure of the smallest discernible

detail in an image Can be stated in line pairs per unit distance,

and dots(pixels) per unit distance Dots per unit distance commonly used in

printing and publishing industry (dots per inch)

Newspaper are printed with a resolution of 75 dpi, magazines at 133 dpi, and glossy brochures at175 dpi

examples





Can we increase spatial resolution by interpolation ?

Down sampling is an irreversible process.(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

Image Quantization

Image quantization: discretize continuous pixel values into discrete numbers

Color resolution/ color depth/ levels: - No. of colors or gray levels or- No. of bits representing each pixel value- No. of colors or gray levels Nc is given by

bcN 2

where b = no. of bits

Quantization function

Light intensity

Quan

tizat

ion

leve

l

012

Nc-1Nc-2

Darkest Brightest

Intensity Resolution It refers to the smallest discernible change in

intensity level Number of intensity levels usually is an

integer power of two Also refers to Number of bits used to quantize

intensity as the intensity resolution Which intensity resolution is good for human

perception 8 bit, 16 bit, or 32 bit

Effect of Quantization Levels or Intensity resolution

256 levels 128 levels

32 levels64 levels

Effect of Quantization Levels (cont.)

16 levels 8 levels

2 levels4 levels

In this image,it is easy to seefalse contour.

Effect of Quantization Levels or Intensity resolution

How to select the suitable size and pixel depth of images

Low detail image Medium detail image High detail imageLena image Cameraman image

To satisfy human mind1. For images of the same size, the low detail image may need more pixel depth.2. As an image size increase, fewer gray levels may be needed.

The word “suitable” is subjective: depending on “subject”.


Isopreference Curve Curves tend to become more vertical as the

detail in the image increases Image with a large amount of detail only a few

intensity levels may be needed

Image Interpolation Used in image resizing (zooming and shrinking),

rotating, and geometric corrections Interpolation is the process of using known data to

estimate values at unknown locations Nearest Neighbor interpolation

It assigns to each new location the intensity of its nearest neighbor in the original image

Produce undesirable artifacts, such as severe distortion of straight edges

Bilinear Interpolation We use the four nearest neighbors to estimate the

intensity V(x, y) = ax + by + cxy + d

Image Interpolation Need to solve four equations Better results than nearest neighbor interpolation,

with a modest increase in computational burden Bicubic Interpolation

Involves sixteen neighbors to estimate intensity

V(x, y) = ∑∑aij xi yj ( i, j = 0 to 3) Need to solve sixteen equations Gives better results than other methods More complex Used in Adobe Photoshop, and Corel Photopaint

Basic Relationship of Pixels

x

y

(0,0)

Conventional indexing method

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

(x,y-1)

(x,y+1)

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

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

Neighbors of a Pixel

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

(x,y-1)

(x,y+1)

4-neighbors of p:

N4(p) =

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

Neighborhood relation is used to tell adjacent pixels. It is useful for analyzing regions.

Note: q Î N4(p) implies p Î N4(q)

4-neighborhood relation considers only vertical and horizontal neighbors.

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

(x,y-1)

(x,y+1)

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

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

Neighbors of a Pixel (cont.)

8-neighbors of p:

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

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

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

(x+1,y+1)

N8(p) =

8-neighborhood relation considers all neighbor pixels.

p

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

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

Diagonal neighbors of p:

ND(p) =

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

(x+1,y+1)

Neighbors of a Pixel (cont.)

Diagonal -neighborhood relation considers only diagonalneighbor pixels.

Connectivity

Connectivity is adapted from neighborhood relation. Two pixels are connected if they are in the same class (i.e. the same color or the same range of intensity) and they are neighbors of one another.

For p and q from the same classw 4-connectivity: p and q are 4-connected if q Î N4(p)w 8-connectivity: p and q are 8-connected if q Î N8(p)w mixed-connectivity (m-connectivity): p and q are m-connected if q Î N4(p) or q Î ND(p) and N4(p) Ç N4(q) = Æ

Adjacency

A pixel p is adjacent to pixel q is they are connected.Two image subsets S1 and S2 are adjacent if some pixelin S1 is adjacent to some pixel in S2

S1

S2

We can define type of adjacency: 4-adjacency, 8-adjacencyor m-adjacency depending on type of connectivity.

Path

A path from pixel p at (x,y) to pixel q at (s,t) is a sequenceof distinct pixels:

(x0,y0), (x1,y1), (x2,y2),…, (xn,yn)such that

(x0,y0) = (x,y) and (xn,yn) = (s,t)and (xi,yi) is adjacent to (xi-1,yi-1), i = 1,…,n

pq

We can define type of path: 4-path, 8-path or m-pathdepending on type of adjacency.

Path (cont.)

p

q

p

q

p

q

8-path from p to qresults in some ambiguity

m-path from p to qsolves this ambiguity

8-path m-path

Distance

For pixel p, q, and z with coordinates (x,y), (s,t) and (u,v),D is a distance function or metric if

w D(p,q) ³ 0 (D(p,q) = 0 if and only if p = q)

w D(p,q) = D(q,p)

w D(p,z) £ D(p,q) + D(q,z)

Example: Euclidean distance

22 )()(),( tysxqpDe -+-

Distance (cont.)

D4-distance (city-block distance) is defined as

tysxqpD -+-),(4

1 210

1 212

2

2

2

2

2

Pixels with D4(p) = 1 is 4-neighbors of p.

Distance (cont.)

D8-distance (chessboard distance) is defined as

),max(),(8 tysxqpD --

12

101

2

12

2

2

2

2

2

Pixels with D8(p) = 1 is 8-neighbors of p.

22

2

2

2222

1

1

1

1

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Boundary (Border or Contour)of a region R is the set of points that are adjacent to points in the complement of R.of a region is the set of pixels in the region that have at least one background neighbor.Inner BorderOuter Border

Moire Pattern Effect : Special Case of Sampling

Moire patterns occur when frequencies of two superimposed periodic patterns are close to each other.


Human vision: Spatial Frequency vs Contrast

Human vision: Distinguish ability for Difference in brightness

Regions with 5% brightness difference

Chapter 1 and 2 gonzalez and woods

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