1. Chapter 2 Digital 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 212
TEL: ext. 4337
Website: MIPL.yuntech.edu.tw

2. Structure of the Human Eye角膜 虹膜
睫狀體
睫狀肌
水晶體
光受體有兩種：
1.錐狀體(cones)
萬,對色彩很
靈敏，白晝視覺。
2.桿狀體(rods)
萬,對低亮度
很靈敏，夜視視覺。
玻璃體
視網膜 盲點
中央凹 鞏膜
脈絡膜

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

4. Image Formation in the Eye
Graphical representation of the eye looking at a palm tree

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

6. Image Formation in the Eye (cont.)

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

8. Image Formation in the Eye (cont.)

9. Image Formation in the Eye (cont.)

10. Image Formation in the Eye (cont.)
Optical illusion

11. Light and the Electromagnetic Spectrum

12. Light and the Electromagnetic Spectrum (cont.)
=c/v
: wavelength
v: frequency
c: speed of light (2.998*108 m/s)

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16. Chapter 2: Digital Image Fundamentals
Digital Image Acquisition Process

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

18. Chapter 2: Digital Image Fundamentals
Image Sampling and Quantization

19. Chapter 2: Digital Image Fundamentals

20. Representing Digital Images
Chapter 2: Digital Image Fundamentals
Representing Digital Images
The result of sampling and quantization is a matrix of real numbers.

21. Chapter 2: Digital Image Fundamentals

22. Chapter 2: Digital Image Fundamentals
Spatial Resolution
The smallest discernible detail in an image.
Line pair
Size: 1024*1024

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24. Gray-Level Resolution
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.

25. Chapter 2: Digital Image Fundamentals
False contouring

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.

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.

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.

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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.

30. Zooming (cont.) Example 2.4
Using nearest neighbor gray-level / bilinear interpolation

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.

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

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.

34. Some basic relationships between pixels (cont.)
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.

35. Some basic relationships between pixels (cont.)
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.

36. Some basic relationships between pixels (cont.)
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 2 1

37. Some basic relationships between pixels (cont.)
D8 distance (chessboard distance) between p and q is defined as
Example: D8 distance<=2

38. Some basic relationships between pixels (cont.)
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
1 p4 0 p2 p
m-path=3
0 p4 0 p2 p
1 p4 1 p2 p
m-path=2
m-path=4
0 p4 1 p2 p
m-path=3