Chapter 2 Digital Image Fundamentals

Medical Image Processing & Neural Networks Laboratory 1

Medical Image Processing

Chapter 2Digital Image Fundamentals

國立雲林科技大學 資訊工程研究所張傳育 (Chuan-Yu Chang ) 博士Office: EB 212TEL: 05-5342601 ext. 4337E-mail: chuanyu@yuntech.edu.twWebsite: MIPL.yuntech.edu.tw

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Structure of the Human Eye角膜虹膜

視網膜鞏膜脈絡膜

盲點 中央凹玻璃體

水晶體睫狀體

睫狀肌

光受體有兩種：1. 錐狀體 (cones)600-700 萬 , 對色彩很靈敏，白晝視覺。2. 桿狀體 (rods)7500-1500 萬 , 對低亮度很靈敏，夜視視覺。

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Structure of the Human Eye (cont.) Distribution of rods and cones in the retina

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Image Formation in the Eye

Graphical representation of the eye looking at a palm tree

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Image Formation in the Eye (cont.) Brightness adaptation and Discrimination

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Image Formation in the Eye (cont.)

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Image Formation in the Eye (cont.) Typical Weber ratio as a function of intensity

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Image Formation in the Eye (cont.)

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Image Formation in the Eye (cont.)

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Optical illusion

Image Formation in the Eye (cont.)

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Light and the Electromagnetic Spectrum

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=c/v: wavelengthv: frequencyc: speed of light (2.998*108 m/s)

Light and the Electromagnetic Spectrum (cont.)

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Chapter 2: Digital Image Fundamentals

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Chapter 2: Digital Image Fundamentals

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Chapter 2: Digital Image Fundamentals

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Chapter 2: Digital Image FundamentalsDigital Image Acquisition Process

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Chapter 2: Digital Image Fundamentals

Image Sampling and Quantization To create a digital image, we need to convert the

continuous sensed data into digital form. This involves two processes: Sampling

Digitizing the coordinate values Quantization

Digitizing the amplitude values

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Chapter 2: Digital Image FundamentalsImage Sampling and Quantization

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Chapter 2: Digital Image Fundamentals

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Chapter 2: Digital Image Fundamentals

Representing Digital Images The result of sampling and quantization is a matrix of real

numbers.

)1,1(...)1,1()0,1(::::

)1,1(...)1,1()0,1()1,0(...)1,0()0,0(

),(

NMfMfMf

NfffNfff

yxf

1,11,10,1

1,11,10,1

1,01,00,0

...:...::

...

...

NMMM

N

N

aaa

aaaaaa

A

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Chapter 2: Digital Image Fundamentals

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Chapter 2: Digital Image Fundamentals Spatial Resolution

The smallest discernible detail in an image. Line pair Size: 1024*1024

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Chapter 2: Digital Image Fundamentals

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Chapter 2: Digital Image Fundamentals

Gray-Level Resolution The smallest discernible

change in gray level. The # of gray levels is

usually an integer power of 2.

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Chapter 2: Digital Image Fundamentals

False contouring

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Chapter 2: Digital Image Fundamentals Isopreference curves (Huang, 1965)

Quantify experimentally the effects on image quality produced by varying N and k simultaneously.

Points lying on an isopreference curves correspond to images of equal subjective quality

Isopreference curves tend to become more vertical as the detail in the image increase. For image with a large amount of detail only a few gray levels may

be needed.

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Chapter 2: Digital Image Fundamentals Aliasing and Moire Patterns

Functions whose area under the curve is finite can be represented in terms of sine and cosines of various frequencies.

Suppose that this highest frequency is finite and that the function is of unlimited duration.

The Shannon sampling theorem tells us, 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 aliasing corrupted the sampled image.

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Chapter 2: Digital Image Fundamentals In practice, it is impossible to satisfy the sampling theorem.

We can only work with sampled data that are finite in duration. Multiplying the unlimited function by a “gating function” that is

valued 1 for some interval and 0 elsewhere. The gating function itself has frequency components that

extend to infinity. 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.

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Chapter 2: Digital Image Fundamentals

Zooming Zooming may be views as oversampling. Zooming requires two steps:

Step 1: the creation of new pixel location. Step 2: the assignment of gray level to those new locations.

Nearest neighbor interpolation Look for the closest pixel in the original image and assign its

gray level to the new pixel in the grid. Pixel replication

To double the size of an image, we can duplicate each column/ row

Biliner interpolation Using the four nearest neighbors of a point.

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Zooming (cont.) Example 2.4

Using nearest neighbor gray-level / bilinear interpolation

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Chapter 2: Digital Image Fundamentals

Shrinking Shrinking may be views as undersampling.

Row-column deletion To shrink an image by one-half, we delete every other

row and column.

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Some basic relationships between pixels Neighbors of a pixel

4-neighbors of p: N4(p) (x+1, y), (x-1, y), (x, y+1), (x, y-1)

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

8-neighbors of p: N8(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)

p

p

p

Some basic relationships between pixels

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Some basic relationships between pixels (cont.) If two pixels are connected, it must be

determined If they are neighbors and If their gray levels satisfy a specified criterion of

similarity.

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Adjacency: two pixels p and q with value from V are 4-adjacency: if q is in the set N4(p). 8-adjacency : if q is in the set N8(p). 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. To eliminate the ambiguities arise when 8-adjacency is used.

Some basic relationships between pixels (cont.)

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Digital path (or curve) Path is a sequence of distinct pixels with coordinates

(x0, y0), (x1, y1),…,(xn, yn) n is the length of the path If (x0, y0)=(xn, yn), the path is closed path.

Connectivity Connected component

Regions If R is a connected set.

Boundary (border, contour) The boundary of a region R is the set of pixels in the region that have

one or more neighbors that are not in R. The boundary of a finite region forms a closed path

Edge The edges are formed from pixels with derivative values that exceed

a preset threshold.

Some basic relationships between pixels (cont.)

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Distance measure Pixels:

p=(x,y), q=(s,t), z=(v, w) Euclidean distance between p and q is defined as

D4 distance (city-block distance) between p and q is defined as

22),( tysxqpDe

tysxqpD ),(421012

212

212

22

Some basic relationships between pixels (cont.)

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D8 distance (chessboard distance) between p and q is defined as

Example: D8 distance<=2

tysxqpD ,max),(8

2 2 2 2 22 1 1 1 22 1 0 1 22 1 1 1 22 2 2 2 2

Some basic relationships between pixels (cont.)

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Dm distance between p and q is defined as the shortest m-path between the points. Assume that p, p2, and p4 are 1.

p3 p4

p1 p2

p

0 p4

0 p2

p

0 p4

1 p2

p

1 p4

0 p2

p

1 p4

1 p2

pm-path=2

m-path=3

m-path=3

m-path=4

Some basic relationships between pixels (cont.)