Institute of Medical Engineering | Image Processing

Image ProcessingFundamentals

Lecturer: Mandy Ahlborg

Institute of Medical EngineeringUniversity of Lübeck

Director: Prof. Dr. T. M. Buzug

Institute of Medical Engineering | Image Processing

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Image Representation – Continuous Model

𝑥1

𝑥2

𝜔 ❑12

❑❑

𝝏 𝜴

𝜴

𝜔 ❑11

❑❑𝜔 ❑2

1❑❑

𝜔 ❑22

❑❑

𝑥1

𝑥2

𝜔 ❑12

❑❑𝜔 ❑1

1❑❑𝜔 ❑2

1❑❑

𝜔 ❑22

❑❑

Institute of Medical Engineering | Image Processing

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Image Representation - Color Spaces

Institute of Medical Engineering | Image Processing

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Image Representation - Color Spaces

- Additive color model - Subtractive color model- For printing (with K)

- Cylindrical model

Institute of Medical Engineering | Image Processing

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Image Representation - RGB

Red Green Blue

Institute of Medical Engineering | Image Processing

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Image Representation - HSV

Hue Saturation Value

Institute of Medical Engineering | Image Processing

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Image Representation - Sampling

Continuous Discrete

Institute of Medical Engineering | Image Processing

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Image Representation - Sampling

512 x 512pixel

256 x 256pixel

128 x 128pixel

52 x 52pixel

Institute of Medical Engineering | Image Processing

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Image Representation - Quantization

256grey level

100grey level

10grey level

2grey level

Institute of Medical Engineering | Image Processing

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Image Representation - Discrete Model

𝑦 (𝑥)

𝑥

𝑦 (𝑥)

𝑥

𝑦 (𝑥)

𝑥

𝑦 (𝑥)

𝑥

continuous data

discrete data

sampled data

sampled and quantized data

Institute of Medical Engineering | Image Processing

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Image Representation - Sampling & Quantization

512 x 512 pixel256 grey level

256 x 256 pixel100 grey level

128 x 128 pixel10 grey level

52 x 52 pixel2 grey level

Institute of Medical Engineering | Image Processing

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Image Representation - Grid Types

𝑥1

𝑥2

𝜔 ❑12

❑❑

𝜴

𝜔 ❑11

❑❑𝜔 ❑2

1❑❑

𝜔 ❑22

❑❑

𝑥1

𝑥2

𝜔 ❑12

❑❑

𝜴

𝜔 ❑11

❑❑𝜔 ❑2

1❑❑

𝜔 ❑22

❑❑

Cell-centered grid Nodal grid

Institute of Medical Engineering | Image Processing

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Image Representation - Nyquist-Shannon-Theorem

𝑥1

𝑥2

𝑥1

𝑥2

Nyquist-Shannon-Theorem fulfilled Nyquist-Shannon-Theorem not fulfilled

Institute of Medical Engineering | Image Processing

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Image Representation – Patient Coordinate System

AXIAL: separates superior from inferior

CORONAL: separates anterior from posterior

SAGITTAL: separates anterior from posterior

Institute of Medical Engineering | Image Processing

15

Relationships of Pixels - Neighbors

neighbor of

4-neighbors Diagonal neighbors 8-neighbors

Institute of Medical Engineering | Image Processing

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Relationships of Pixels - Adjacency

Let and pixels and be given. Which adjacencies hold in the following examples?

4

9 5

1

�⃗� �⃗�

4-adjecent8-adjecentm-adjacent

8-adjecentm-adjacent

(with not adjacent

8

9

1

1

8-adjecent

8

9

9

4

Institute of Medical Engineering | Image Processing

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Relationships of Pixels - Path

1

0 10 1 0

0 01 1 1

0 0

0 00 1

0 00 0 0

0

00

no 4-path

1

0 10 1 0

0 01 1 1

0 0

0 00 1

0 00 0 0

0

00

8-path

1

0 10 1 0

0 01 1 1

0 0

0 00 1

0 00 0 0

0

00

8-path

1

0 10 1 0

0 01 1 1

0 0

0 00 1

0 00 0 0

0

00

m-path

Institute of Medical Engineering | Image Processing

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Relationships of Pixels - Distance Metrics

Euclidean distanceManhatten distanceChebychev distance

Institute of Medical Engineering | Image Processing

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Relationships of Pixels - Distance Metrics

𝑥1

𝑥2

𝑥1

𝑥2

𝑥1

𝑥2

Eucledean distance Manhatten distance Chebychev distance

Institute of Medical Engineering | Image Processing

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Relationships of Pixels - Distance Maps

3 2 1 1

2 1 1

1 11

1 21 1

31 2

3 12 1

1 41 2 3

1

1

2

3

4

2

5

4

3

2

2

1

4

2

2 1 1 1

1 1 1

1 11

1 11 1

21 2

2 12 1

1 31 1 2

1

1

1

2

2

1

3

2

2

2

1

1

3

1

Manhatten distance Chebyshev distance