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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: 05-5342601 ext. 4337 E-mail: chuanyu@yuntech.edu.tw Website: MIPL.yuntech.edu.tw. 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) 600-700 萬 , 對色彩很
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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 212 TEL: 05-5342601 ext. 4337 E-mail: chuanyu@yuntech.edu.tw Website: MIPL.yuntech.edu.tw
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) 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。 玻璃體 視網膜 盲點 中央凹 鞏膜 脈絡膜
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.) • Typical Weber ratio as a function of intensity
Image Formation in the Eye (cont.) Optical illusion
Light and the Electromagnetic Spectrum (cont.) =c/v : wavelength v: frequency c: speed of light (2.998*108 m/s)
Chapter 2: Digital Image Fundamentals Digital 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 Fundamentals Image Sampling and Quantization
Chapter 2: Digital Image Fundamentals • Representing Digital Images • The result of sampling and quantization is a matrix of real numbers.
Chapter 2: Digital Image Fundamentals • Spatial Resolution • The smallest discernible detail in an image. • Line pair • Size: 1024*1024
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.
Chapter 2: Digital Image Fundamentals 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.
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.
Zooming (cont.) • Example 2.4 • Using nearest neighbor gray-level/ bilinearinterpolation
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.
p p p Some basic relationships between pixels • 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)
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.
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.
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.
2 1 0 1 2 2 1 2 2 1 2 2 2 Some basic relationships between pixels (cont.) • Distance measure • Pixels:p=(x,y), q=(s,t), z=(v, w) • Euclidean distance between p and qis defined as • D4 distance (city-block distance) between p and qis defined as
Some basic relationships between pixels (cont.) • D8 distance (chessboard distance) between p and q is defined as • Example: D8 distance<=2 2 2 2 2 2 2 1 1 1 2 2 1 0 1 22 1 1 1 22 2 2 2 2
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 p4p1 p2p 1p40p2p m-path=3 0p40p2p 1p41p2p m-path=4 m-path=2 0p41p2p m-path=3