Chapter 2 Digital Image Fundamentals
description
Transcript of Chapter 2 Digital Image Fundamentals
![Page 1: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/1.jpg)
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
![Page 2: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/2.jpg)
Medical Image Processing & Neural Networks Laboratory 2
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。
![Page 3: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/3.jpg)
Medical Image Processing & Neural Networks Laboratory 3
Structure of the Human Eye (cont.) Distribution of rods and cones in the retina
![Page 4: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/4.jpg)
Medical Image Processing & Neural Networks Laboratory 4
Image Formation in the Eye
Graphical representation of the eye looking at a palm tree
![Page 5: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/5.jpg)
Medical Image Processing & Neural Networks Laboratory 5
Image Formation in the Eye (cont.) Brightness adaptation and Discrimination
![Page 6: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/6.jpg)
Medical Image Processing & Neural Networks Laboratory 6
Image Formation in the Eye (cont.)
![Page 7: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/7.jpg)
Medical Image Processing & Neural Networks Laboratory 7
Image Formation in the Eye (cont.) Typical Weber ratio as a function of intensity
![Page 8: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/8.jpg)
Medical Image Processing & Neural Networks Laboratory 8
Image Formation in the Eye (cont.)
![Page 9: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/9.jpg)
Medical Image Processing & Neural Networks Laboratory 9
Image Formation in the Eye (cont.)
![Page 10: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/10.jpg)
Medical Image Processing & Neural Networks Laboratory 10
Optical illusion
Image Formation in the Eye (cont.)
![Page 11: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/11.jpg)
Medical Image Processing & Neural Networks Laboratory 11
Light and the Electromagnetic Spectrum
![Page 12: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/12.jpg)
Medical Image Processing & Neural Networks Laboratory 12
=c/v: wavelengthv: frequencyc: speed of light (2.998*108 m/s)
Light and the Electromagnetic Spectrum (cont.)
![Page 13: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/13.jpg)
Medical Image Processing & Neural Networks Laboratory 13
Chapter 2: Digital Image Fundamentals
![Page 14: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/14.jpg)
Medical Image Processing & Neural Networks Laboratory 14
Chapter 2: Digital Image Fundamentals
![Page 15: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/15.jpg)
Medical Image Processing & Neural Networks Laboratory 15
Chapter 2: Digital Image Fundamentals
![Page 16: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/16.jpg)
Medical Image Processing & Neural Networks Laboratory 16
Chapter 2: Digital Image FundamentalsDigital Image Acquisition Process
![Page 17: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/17.jpg)
Medical Image Processing & Neural Networks Laboratory 17
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
![Page 18: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/18.jpg)
Medical Image Processing & Neural Networks Laboratory 18
Chapter 2: Digital Image FundamentalsImage Sampling and Quantization
![Page 19: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/19.jpg)
Medical Image Processing & Neural Networks Laboratory 19
Chapter 2: Digital Image Fundamentals
![Page 20: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/20.jpg)
Medical Image Processing & Neural Networks Laboratory 20
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
![Page 21: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/21.jpg)
Medical Image Processing & Neural Networks Laboratory 21
Chapter 2: Digital Image Fundamentals
![Page 22: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/22.jpg)
Medical Image Processing & Neural Networks Laboratory 22
Chapter 2: Digital Image Fundamentals Spatial Resolution
The smallest discernible detail in an image. Line pair Size: 1024*1024
![Page 23: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/23.jpg)
Medical Image Processing & Neural Networks Laboratory 23
Chapter 2: Digital Image Fundamentals
![Page 24: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/24.jpg)
Medical Image Processing & Neural Networks Laboratory 24
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.
![Page 25: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/25.jpg)
Medical Image Processing & Neural Networks Laboratory 25
Chapter 2: Digital Image Fundamentals
False contouring
![Page 26: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/26.jpg)
Medical Image Processing & Neural Networks Laboratory 26
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.
![Page 27: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/27.jpg)
Medical Image Processing & Neural Networks Laboratory 27
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.
![Page 28: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/28.jpg)
Medical Image Processing & Neural Networks Laboratory 28
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.
![Page 29: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/29.jpg)
Medical Image Processing & Neural Networks Laboratory 29
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.
![Page 30: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/30.jpg)
Medical Image Processing & Neural Networks Laboratory 30
Zooming (cont.) Example 2.4
Using nearest neighbor gray-level / bilinear interpolation
![Page 31: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/31.jpg)
Medical Image Processing & Neural Networks Laboratory 31
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.
![Page 32: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/32.jpg)
Medical Image Processing & Neural Networks Laboratory 32
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
![Page 33: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/33.jpg)
Medical Image Processing & Neural Networks Laboratory 33
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.
![Page 34: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/34.jpg)
Medical Image Processing & Neural Networks Laboratory 34
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.)
![Page 35: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/35.jpg)
Medical Image Processing & Neural Networks Laboratory 35
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.)
![Page 36: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/36.jpg)
Medical Image Processing & Neural Networks Laboratory 36
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.)
![Page 37: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/37.jpg)
Medical Image Processing & Neural Networks Laboratory 37
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.)
![Page 38: Chapter 2 Digital Image Fundamentals](https://reader035.fdocuments.net/reader035/viewer/2022081416/56814a51550346895db775aa/html5/thumbnails/38.jpg)
Medical Image Processing & Neural Networks Laboratory 38
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.)