Digital Image Processing

1. Digital Image Processing Chapter 2

2. Chapter 2: Digital Image Fundamentals • Digital image processing is based on • Mathematical and probabilistic models • Human intuition and analysis • Resolution • Adaptation

3. 2.2 Light and the EM Spectrum

4. Light is a particular type of EM radiation that can be seen by human eye. • Green object reflect light with wavelengths primarily in 500 to 570 nm range. • Chromatic light spans EM spectrum from 0.43 m(violet) to 0.79 m(red). • Radiance: energy in Watt. • Luminance: in lumens(lm), the amount of energy the observer perceives. • Brightness: subjective description of light perception.

5. Chapter 2: Digital Image Fundamentals

6. A single sensor

7. A sensor strip In flat bed scanners

8. A sensor array In digital cameras

9. 2.4 Image Sampling and Quantization • To acquire digital images from the continuous sensed data f(x, y): • Digitization in coordinate values: Sampling • Digitization in amplitude values: Quantization. • The resulting image has M rows and N columns as

13. The digitization process requires to determine the M, N, and L. • M and N: spatial resolution • L: gray-level resolution L = 2k. L = gray-level • Dynamic range: the range of values spanned by the gray scale, [Lmin, Lmax]. • High dynamic range = high contrast image • The number of bits required to store the image b = M  N k or b = N2k

15. Spatial resolution is the smallest discernible detail in an image. • line pair width = 2W (line width + space) • No. of line pairs per unit distance = 1 / 2W • Resolution is the smallest number of discernible line pairs per unit distance.

16. Gray-level resolution refers to the smallest discernible change in gray level (subjective).

18. Example of false contouring

19. 2.4.4 Aliasing and Moire Patterns • Band-limited function: the highest frequency is finite and the function is of unlimited duration • Undersampling – aliasing. • Aliasing frequencies • Sampling rate: the number of samples taken per unit distance • Reduce high frequency component prior to sampling. • Moire Pattern is caused by a break-up of the periodicity, i.e., images are scanned from a printed page, which consists of periodic ink dots.

20. 2.4.4 Aliasing and Moire Pattern • Aliasing occurs when a signal is sampled at a less than twice the highest frequency present in the signal. • The following figure shows if a signal is sampled at regular time intervals that are slightly less often than once per period of the original signal. • The blue curve is the original signal, and the red dots indicate the sampled values. 資料來源：http://www.wfu.edu/~matthews/misc/DigPhotog/alias/index.html

21. Aliasing • The red dots are what are recorded, since they represent the signal values at the times the signal is sampled. • The pattern of the red dots is a terrible representation of the signal. The red sampled data looks like a sine wave at about one-tenth the frequency of the original! • This is aliasing. 資料來源：http://www.wfu.edu/~matthews/misc/DigPhotog/alias/index.html

22. Moire Pattern

23. 2.4.5 Zooming and Shrinking Digital Images • Zooming: • Create a new pixel location. • Assign a gray-level to those new locations • Nearest neighbor interpolation • Pixel replication: a checkboard effect • Bilinear interpolation using four nearest neighbors • v(x’, y’)=ax’+by’+cx’y’+d • where a, b, c, and d are determined from the gray-level of the four neighbors. • Higher-order non-linear interpolation: using more neighbors for interpolation

24. 2.4.5 Zooming and Shrinking Digital Images • Proof

25. 2.4.5 Zooming and Shrinking Digital Images • Shrinking: • Direct shrinking causes aliasing • Expansion then Shrinking: blurring the image before shrinking it and reduce aliasing.

26. a checkboard effect

27. 2.5 Basic Relations between Pixels • Neighbors of a pixel • Horizontal and vertical neighbors. • (x+1, y), (x-1, y), (x, y+1), (x, y-1) • Four diagonal neighbors: ND(p) • (x+1, y+1), (x+1, y-1), (x-1, y+1), (x-1, y-1) • 4-neighbors of p: N4(p). • 8-neighbors of p: N8(p). • N8(p) = N4(p) ∪ ND(p) • Adjacency • Connectivity • Regions • Boundary

28. p p 4-adjacency: N4(p) 8-adjacency: N4(p) ∪ND(p) Relations between Pixels • Adjacency

29. 4-adjacency: if q is in the set N4(p). • 8-adjacency: if q is in the set N8(p). • m-adjacency: if • if q is in the set N4(p), or • if q is in the set ND(p) and the set N4(p)∩N4(q) has no pixels whose values are from V.

30. m-Adjacency • A mixed adjacency combines 4- and 8-adjacency to avoid the ambigities. m-adjacency Multiple 8-adjacency • Two pixels p and q are m-adjacent if • q is in N4(p) or, • q is in ND(p) and N4(p)∩ N4(q) has no pixel.

31. Connectivity • Path: • (x0, y0), (x1, y1), …, (xn, yn) where (xi, yi) and (xi+1, yi+1) are adjacent. • Closed path: (xn, yn) = (x0, y0) • Connectivity: • Two pixels are said connected if they have the same value and there is a path between them. • If a S is a set of pixels, • For any pixel p in S, the set of pixels that are connected to it is called a connected component of S. • If S has only one connected component, S is called a connected set.

32. Regions • R is a region if R is a connected set. • The pixel in the boundary (contour) has at least one 4-adjacent neighbor whose value is 0.

33. Distance measures • Euclidean distance • City-block distance or D4 distance. D4(p, q)= |x - s | + |y - t | • D8distance or chessboard distance. D8(p, q)= max (|x - s |, | y - t |)