Lecture - 3. by Shahid Farid

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1 Lecture - 3 by Shahid Farid

2 Image Digitization Raster versus vector images Progressive versus interlaced display Popular image file formats Why so many formats? Shahid Farid, PUCIT 2

3 To create a digital image, we need to convert continuous sensed data into digital form. This involves two processes: 1. Sampling 2. Quantization 3

4 Digitizing the coordinate values is called sampling. Digitizing the amplitude values is called quantization. 4

5 Sampling converts a continuous-time signal to a discrete-time signal. 5

6 The duration between each two adjacent samples T s is constant 6

7 The sequence of samples is called digital signal. If the original signal is x(t), then the signal after sampling can be expressed as: x[ n] = x( nt ) s 7

8 Sampling rate is defined as the number of samples obtained in one second. FF ss = 1 TT ss The larger the sampling frequency is, the more samples we have in one second, the more accurate the sampled signal is, compared to the original signal. 8

9 The sampling rate must be at least 2 times the highest frequency contained in the signal Nyquist frequency is defined as half of the sampling rate. F N = F s /2 For any analog signal that we want to sample, to avoid aliasing distortion, the Nyquist frequency cannot be lower than the maximal frequency of this signal. 9

10 Aliasing refers to the distortion effect that results when Nyquist frequency is smaller than the maximum frequency of the original signal (or the sampling frequency is lower than twice the maximum frequency of the signal). 10

11 A high frequency signal sampled at too low a rate looks like a lower frequency signal. 11

12 12

13 Sampling Rate Uses 44.1 khz (44100) CD, DAT 48 khz (48000) DAT, DV, DVD-Video 96 khz (96000) DVD-Audio khz (22050) Old samplers 13

14 To avoid aliasing, the Nyquist has to be greater than the highest frequency component of the signal. Nyquist Frequency > maximum frequency 14

15 Quantization refers to the process to approximate the sampled signal s amplitude values to a set of integer values. The number of the integer values is determined by the required bit resolution (bit depth). Bit resolution refers to the number of bits used to describe each sample in a digital binary format. 15

16 3 bit quantization 16

17 Random fluctuation leads to noise in analog systems SNR: Ratio of the power of the correct signal to the power of the noise, measured in decibel (db). V SNR =10 log10 = 20log10 V 2 signal 2 noise V V signal noise SNR is the measure of quality of signal 17

18 Digital signals stores only quantized values Number of bits/sample dictates the precision Dividing voltage in a fixed range like 0 to 1 into 256 levels leads a round off error. The difference between the value of the analog signal, for a particular sampling time, and the nearest quantization interval value quantization error/noise Quality of quantization is characterized by SQNR 18

19 19

20 N bits/sample can represent the digital signal in the range 2 N-1 to 2 N-1-1 corresponding the the analog signal in the range V max to +V max. Each quantization level represent the voltage of 2V max / 2 N SQNR = N 1 Vsignal 2 20log10 = 20log10 = 20N log 2 = V 1 quan _ noise N(dB) Mapping Vsignal to 2N-1 and Vquan_noise to ½ Since the quantization error is statistically independent & uniformly distributed from 0 to ½, SQNR=6.02N+1.76 (db) 20

21 (0,0) x (x-1,y-1) (x,y-1) (x+1,y-1) y (x-1,y) (x,y) (x+1,y) (x-1,y+1) (x,y+1) (x+1,y+1) Conventional indexing method 21

22 Neighborhood relation is used to tell adjacent pixels. It is useful for analyzing regions. (x,y-1) 4-neighbors of p: (x-1,y) p (x,y+1) (x+1,y) N 4 (p) = (x 1,y) (x+1,y) (x,y 1) (x,y+1) 4-neighborhood relation considers only vertical and horizontal neighbors. Note: q N 4 (p) implies p N 4 (q) 22

23 (x-1,y-1) (x,y-1) (x+1,y-1) 8-neighbors of p: (x-1,y) (x-1,y+1) p (x,y+1) (x+1,y) (x+1,y+1) N 8 (p) = (x 1,y 1) (x,y 1) (x+1,y 1) (x 1,y) (x+1,y) (x 1,y+1) (x,y+1) (x+1,y+1) 8-neighborhood relation considers all neighbor pixels. 23

24 (x-1,y-1) (x+1,y-1) Diagonal neighbors of p: (x-1,y+1) p (x+1,y+1) N D (p) = (x 1,y 1) (x+1,y 1) (x 1,y+1) (x+1,y+1) Diagonal-neighborhood relation considers only diagonal neighbor pixels. 24

25 For pixel p, q, and z with coordinates (x,y), (s,t) and (u,v), D is a distance function or metric D(p,q) 0 (D(p,q) = 0 if and only if p = q) D(p,q) = D(q,p) D(p,z) D(p,q) + D(q,z) 2 D e ( p, q) = ( x s) + ( y t ) 2 25

26 26

27 There are two kinds of computer graphics: Raster and Vector Raster composed of a grid of individual pixels where each pixel can be a different color or shade The number of bits at each pixel determines the maximum number of colors 1 bits = 2 (2 1 ) colors 2 bits = 4 (2 2 ) colors 4 bits = 16 (2 4 ) colors 8 bits = 256 (2 8 ) colors 16 bits = 65,536 (2 16 ) colors 24 bits = 16,777,216 (2 24 ) colors! Raster images are more commonly called bitmap images. Shahid Farid, PUCIT 27

28 Composed of paths Vector graphics use mathematical relationships between points and the paths connecting them to describe an image Resolution-independent: scalable without the problem of pixelating. Not all images are easily described in a mathematical form. Shahid Farid, PUCIT 28

29 The images shown at four times actual size to exaggerate the fact that the edges of a bitmap become jagged as it is scaled up. Shahid Farid, PUCIT 29

30 Shahid Farid, PUCIT 30

31 Resolution-dependent Suitable for photographs Smooth tones and subtle details Larger size Resolution independent Suitable for line drawings, CAD, logos Smooth curves Smaller size Raster Vector Shahid Farid, PUCIT 31

32 Raster: GIF (Graphics Interchange Format), BMP, JPEG, TIFF, PBM (Portable Bit Map - binary), PGM (Portable Gray Map grayscale), PPM(Portable Pixel Map - color), PNM (Portable Any Map any three), PCD(Photo CD), PNG (Portable Network Graphics) Shahid Farid, PUCIT 32

33 Vector: PS(Postscript), EPS (Embedded Postscript), CDW (CorelDraw), WMF (Windows Metafile), SVG (Scalable Vector Graphics) Shahid Farid, PUCIT 33

34 One practical reason for different formats is that each saves a slightly different set of information with the file. For example,.jpg is a compressed format (small files), in which the minimum information is saved. By comparison,.tif is uncompressed and can save more file information. Shahid Farid, PUCIT 34

35 Progressive displays all the horizontal lines of a picture at one time as a single frame Interlaced Displays only half of the horizontal lines at a time First field, containing the odd-numbered lines, is displayed, followed by the second field, containing the even-numbered lines) Shahid Farid, PUCIT 35

36 First standardized in 1987 by CompuServ (called GIF87a) Updated in 1989 to include transparency, interlacing, and animation (called GIF89a) Transparency Transparency is the feature of the GIF89a format which allows for the specification of one of the colors in the palette to be ignored while processing the image for display purpose Use the LZW (Lempel-Ziv Welch) algorithm for compression A maximum of 256 colors, so doesn t work well for photographs Suitable for small images such as icons Shahid Farid, PUCIT 36

37 Images with areas of flat color, such as logos, line art, icons & cartoon-like illustrations Not much suited for photographic images Suited for adding simple animation Whenever transparency in image is required (even though PNG supports this feature, not all web browsers supports it) Shahid Farid, PUCIT 37

38 Portable Network Graphics (PNG) is a bitmapped image format that employs lossless data compression. Supports 48 bit color PNG was created to improve upon and replace GIF (Graphics Interchange Format) As an image-file format not requiring a patent license. It is pronounced /ˈpɪŋ/ or spelled out as P-N-G. The PNG acronym is optionally recursive, unofficially standing for "PNG's Not GIF" Shahid Farid, PUCIT 38

39 Widely used image format Compression standard used is JPEG, Joint Photographic Experts Group Created by the working group, JPEG, of ISO Compression is lossy Like interlaced GIFs, there is progressive JPEGs Shahid Farid, PUCIT 39

40 Originated in 1986 at Aldus Corp. (PageMaker), the latest version 6.0 Developed by Aldus and Microsoft Platform-independent Support compressions of CCITT Fax 3 & 4, LZW, JPEG etc. Support multiple color spaces: Grayscale, RGB, YCbCr, CMYK etc. Shahid Farid, PUCIT 40

41 The TIFF format is widely supported by image-manipulation applications, by publishing and page layout applications, by scanning, faxing, word processing, optical character recognition and other applications. As of 2009, it is under the control of Adobe Systems. Adobe Systems, which acquired Aldus, now holds the copyright to the TIFF specification. Shahid Farid, PUCIT 41

42 A programming language from Adobe for printing graphics and text A page description language that is deviceindependent (introduced in 1985 by Adobe) Different levels: Level 1, 2, 3 Change coordinate system, scaling, translation, rotation, filling, clipping, etc. Main unit: point (1/72 of an inch) Shahid Farid, PUCIT 42

43 Adobe s de facto standard for secure and reliable distribution and exchange of electronic documents Can embed fonts, images, graphics, forms, controls, layouts, media, etc. Searchable, hyperlinks, digital signature, Application and platform independent Shahid Farid, PUCIT 43

44 A high-quality typesetting system Designed to produce technical and scientific documentation Based on Donald E. Knuth's TeX typesetting language First developed in 1985 by Leslie Lamport Cross-platform Useful if you are writing your thesis! Shahid Farid, PUCIT 44

45 No unique answer A small image like icons, a grayscale image GIF A large image, photographs, an image with many colors JPEG Shahid Farid, PUCIT 45

46 Text book and recommended reference books signal_processing% File_Format 46

47 Lecture 3 By: Shahid Farid, PhD Assistant Professor, PUCIT shahid@pucit.edu.pk

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