medical image processing & neural networks laboratory 1 medical image processing chapter 2...

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: [email protected]: MIPL.yuntech.edu.tw


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。


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


Image Formation in the Eye

Graphical representation of the eye looking at a palm tree


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


Image Formation in the Eye (cont.)


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


Optical illusion



Light and the Electromagnetic Spectrum


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

Light and the Electromagnetic Spectrum (cont.)


Chapter 2: Digital Image FundamentalsChapter 2: Digital Image Fundamentals


Chapter 2: Digital Image FundamentalsDigital Image Acquisition ProcessChapter 2: Digital Image FundamentalsDigital Image Acquisition Process


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


Chapter 2: Digital Image FundamentalsImage Sampling and QuantizationChapter 2: Digital Image FundamentalsImage Sampling and Quantization



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

Nfff

Nfff

yxf

1,11,10,1

1,11,10,1

1,01,00,0

...

:...::

...

...

NMMM

N

N

aaa

aaa

aaa

A


Chapter 2: Digital Image Fundamentals Spatial Resolution

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



Gray-Level Resolution The smallest discernible

change in gray level. The # of gray levels is

usually an integer power of 2.



False contouring


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.


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.


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.



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.


Zooming (cont.) Example 2.4

Using nearest neighbor gray-level / bilinear interpolation



Shrinking Shrinking may be views as undersampling.

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

row and column.


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


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.


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.



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.



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



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



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


medical image processing & neural networks laboratory 1 medical image processing chapter 2...

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