Digital Image Processing Of Images

Application Oriented Image Analysis

Lecture 2 - Digitization Maria Axelsson, [email protected]

Reading instructions „

Chapters for this lecture …

2.2 – 2.6 in Gonzalez-Woods

2007-10-17

Maria Axelsson, [email protected]

1

Questions „ „

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What is a digital image? How are resolution, sampling and quantization related? What is connectivity in a digital image? How can we measure distances in a digital image? ...

2007-10-17

Maria Axelsson, [email protected]

2007-10-17

Maria Axelsson, [email protected]

2

Signals for digital imaging „

Visible light … … …

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IR and UV light X-ray

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Radio waves

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Gamma rays Microwaves

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…

…

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…

Tomography Magnetic Resonance Imaging

Electrons

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Ultrasound ...

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Not based on EM waves

Radar

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…

2007-10-17

Digital camera Light microscope Confocal microscope

Scanning electron microscopy

Maria Axelsson, [email protected]

Digital image - f(x,y) pixel - picture element x

y

⎛ ⎜ ⎜ ⎜ ⎜ ⎝

f ( 0,0)

f ( 0,1)

f ( 0,2 )

f (1,0)

f (1,1)

f (1,2 )

f ( 2 ,0) f ( 3,0)

f ( 2 ,1) f ( 3,1)

f ( 2 ,2 ) f ( 3,2 )

2007-10-17

f ( 0,3) ⎞ ⎟ f (1,3) ⎟ f ( 2 ,3)⎟ ⎟ f ( 3,3) ⎠

2 3 0 1 0 3

1 1 2 2 1 1

2 3

2 2

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Sensors for digital imaging „

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To image something we need sensors that can capture the energy of the signal. There are specific types of sensors for all different signals that can be imaged Some important categories are

Single sensor

2007-10-17

Sensor strips

Sensor arrays

Maria Axelsson, [email protected]

Sensors for digital imaging (cont) „

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The output from each sensor is a positive finite value proportional to the recieved energy The continious value needs to be possible to represent in a computer, it needs to be digitized.

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Digitizing the coordinate values is called sampling

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Digitizing the amplitude values is called quantization

2007-10-17

Maria Axelsson, [email protected]

4

Resolution „

Spatial resolution - sampling

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Grey level resolution – quantization

2007-10-17

Maria Axelsson, [email protected]

Sampling „

Uniform sampling …

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Non-uniform sampling …

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Closer where it is necessary, eye.

Image size …

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Square grid, Rectangular grid, Hexagonal grid

128 x 128, 256 x 256, 512 x 512, 1024 x 1024

The sampling is normally determined by the sensor arrangement 2007-10-17

Maria Axelsson, [email protected]

5

Spatial grids

Square Rectangular Hexagonal (Common) (z-direction in medical) (Theory)

2007-10-17

Maria Axelsson, [email protected]

Sampling example

512

128

256

64

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32

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Grey level resolution „ „ „

Min = 0 Max = 2n – 1 Levels = 2n n

Levels

Comments

1

2

Binary

5

32

Eye

8

256

Common

16

65536

Medical

2007-10-17

2007-10-17

Maria Axelsson, [email protected]

256

128

64

32

16

8

4

2

Maria Axelsson, [email protected]

7

Dimensions „

Image, 5-dimensions, f(x,y,z,t,b)

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x, y, z – spatial

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t – time b – spectral

2007-10-17

Maria Axelsson, [email protected]

Volume – f(x,y,z)

HIV volume

Slice 40 2007-10-17

Slice 50

Slice 60

Maria Axelsson, [email protected]

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Spectral image – f(x,y,b)

Color image

Red

Blue

Green

2007-10-17

Maria Axelsson, [email protected]

Neighbours Pixel p with coordinate (x,y)

N4(p): 4-neighbour ( x , y − 1) ( x − 1, y )

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

2007-10-17

N8(p): 8-neighbour ( 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) Maria Axelsson, [email protected]

9

Connectivity, adjacency „ „

Connection between pixels. 4- or 8-connectivity. …

…

p and q 4-connected if q is in N4(p) with similar grey level. p and q 8-connected if q is in N8(p) with similar grey level

2007-10-17

Maria Axelsson, [email protected]

Connectivity, examples

4-connectivity

2007-10-17

8-connectivity

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Path „ „

Sequence of adjacent pixels between A and B. A path can be 4- or 8-connected.

2007-10-17

Maria Axelsson, [email protected]

Connected components „

Object

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Path between every pixel pair.

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4- or 8-connectivity.

2007-10-17

Maria Axelsson, [email protected]

11

Labeling „ „

Giving each object a label. 4- or 8-connectivity.

Binary image 2007-10-17

Labeled image Maria Axelsson, [email protected]

Algorithm

A – pixel of interest Pass 1

Pass 2

If A = 1 Give equivalent labels If B=0 AND C=0 one label. new label If B=1 (or C=1), let A=label of the B (C) If B=1 AND C=1 with same label let A= label of B If B=1 AND C=1 with different label let A=label of B, update equivalence table 2007-10-17

Maria Axelsson, [email protected]

12

Exampel

Pass 1 2007-10-17

Pass 2 Maria Axelsson, [email protected]

Measuring distance „

Euclidean, square root of two

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City-block, infinity (2 steps req. gives dist. 2)

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Chessboard, one

2007-10-17

Maria Axelsson, [email protected]

13

Reading instructions „

Chapters for next lecture Point processes … 3.1 – 3.4 in Gonzalez-Woods

2007-10-17

Maria Axelsson, [email protected]

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