Tutorial 2. COMP4134 Biometrics Authentication. February 9, Jun Xu, Teaching Asistant

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1 Tutoral 2 COMP434 ometrcs uthentcaton Jun Xu, Teachng sstant csjunxu@comp.polyu.edu.hk February 9, 207

2 Table of Contents Problems Problem : nswer the questons Problem 2: Power law functon Problem 3: Convoluton Problem 4: Nose reducton Problem 5: Flter operatons

3 Outlne Problems Problem : nswer the questons Problem 2: Power law functon Problem 3: Convoluton Problem 4: Nose reducton Problem 5: Flter operatons

4 Problem.a Understand some useful defntons n mage processng: ) pxel, ) mage, ) mage resoluton, d) gray-level mage.

5 Problem.a Dgtal Image Representaton Optcal mage denoted by (x,y) x and y are spatal co-ordnates lens mage CCD sensor (x,y) s the brghtness at poston (x,y) The ponts at whch an mage s sampled are known as pcture elements, or pxels. ometrc uthentcaton Lecture 3-6

6 Problem.a Dgtal Image Representaton pcture element (pxel) ometrc uthentcaton Lecture 3-7

7 Problem.a Dgtal Image Representaton x y (x,y) j,j column Contnuous row Dscrete n mage s a spatal presentaton of an object Matrx representng quantzed ntensty values. ometrc uthentcaton Lecture 3-8

8 Problem.a Image Resoluton Image resoluton: Measure of mage qualty (No. of pxels, M N) 280 x 960 (dgtal camera) 52 x 52 (vdeo camera) 256 x 256 (reasonable processng qualty) Dynamc range: Measure of the range of brghtness values bt (bnary mage) 8 bts (grey mage: 0 for black, 255 for whte) 2 bts (medcal magery) 6 bts (stronomcal magery) 24 bts (colour mage) Hgh Low ometrc uthentcaton Lecture 3-9

9 Problem.a Gray-Level Quantsaton 8 bpp 2 bpp For black and whte mages, a pxel s a sngle value nteger or floatng pont. For dsplay, normally 8 bts per pxel (bpp) s used. The human eye cannot resolve to ths accuracy. 32 gray levels are usually suffcent (5 bpp). t 4 bpp and below, false contourng can become apparent. ometrc uthentcaton Lecture 3-0

10 Problem.b What s mage hstogram? What are peaks and plans n mage hstogram? Compare the dfferences between two types of bmodal hstograms.

11 Problem.b Image Hstograms N j Plot of N j versus j: Shows the dstrbuton of mage pxels n terms of ther gray levels. Gray levels j0,,,255 N j number of pxels n mage wth gray level j ometrc uthentcaton Lecture 3- j

12 Problem.b modal Hstograms Lght object(s) aganst a darker background - whte hot Dark object(s) aganst a lghter background - black hot rght object Dark background ometrc uthentcaton Lecture

13 Problem.c Understand the pont operaton. Contrast enhancement s the man applcaton of pxel operaton. How many methods of contrast enhancement do you learn? Please compare them.

14 Problem.c Pont (Pxel) Operaton Pont operaton: functon s appled to every pxel n an mage, whch operates only on the pxel s current value. Thresholdng - mask may be created by settng a pxel value to or 0 dependng upon f the current value s above or below a certan threshold value. Input pxel value, I, mapped to output pxel value, O, va transfer functon T. OT(I) 255 OUTPUT Transfer functon 0 INPUT 255 ometrc uthentcaton Lecture 3-4

15 Problem.c Contrast Enhancement: Lnear Stretchng 255 OUTPUT 0 INPUT 255 ometrc uthentcaton Lecture 3-5

16 Problem.c rghtness ometrc uthentcaton Lecture 3-6

17 Problem.c Contrast Enhancement: Power Law Functon O I γ γ < to enhance contrast n dark regons γ > to enhance contrast n brght regons. ometrc uthentcaton Lecture 3-7

18 Problem.c Contrast Enhancement: Power Law Functon (γ 0.5) ometrc uthentcaton Lecture 3-8

19 Problem.c Contrast Enhancement: Power Law Functon (γ 3.0) ometrc uthentcaton Lecture 3-9

20 Problem.c Contrast Enhancement: Power Law Functon Look-up Table Transfer functon mplemented as a look-up table (LUT). Implemented n hardware or software. γ2 I O ometrc uthentcaton Lecture 3-20

21 Problem.c Contrast Enhancement: Hstogram Equalsaton Image hstograms consstng of peaks and low plans. Peaks many pxels concentrated n a few grey levels Plans small number of pxels dstrbuted over a wder range of grey levels ometrc uthentcaton Lecture 3-2

22 Problem.c Hstogram Equalsaton Expand pxels n peaks over a wder range of gray-levels. Squeeze low plans pxels nto a narrower range of gray levels. Flat hstogram ometrc uthentcaton Lecture 3-22

23 Problem.c Contrast Enhancement: Comparson Orgnal γ> Hstogram equalsaton ometrc uthentcaton Lecture 3-23

24 Problem.d (d) Why neghbourhood operatons? Gve the applcatons of group operatons.

25 Problem.d Why are Neghbourhoods Important? pxel Provde context for ndvdual pxels. Relatonshps between neghbours determne mage features. ometrc uthentcaton Lecture 3-25

26 Problem.d Neghbourhood Operatons Nose Reducton Edge Enhancement Zoomng ometrc uthentcaton Lecture 3-26

27 Outlne Problems Problem : nswer the questons Problem 2: Power law functon Problem 3: Convoluton Problem 4: Nose reducton Problem 5: Flter operatons

28 Problem 2: Power law functon What s the power law functon? Gve the LUT when γ 0.5 n terms of the table n P3-20. Compare the two LUT and understand the mpact of the parameter γ 0.5.

29 Problem 2: Power law functonterms Contrast Enhancement: Power Law Functon O I γ γ < to enhance contrast n dark regons γ > to enhance contrast n brght regons. ometrc uthentcaton Lecture 3-7

30 Problem 2: Power law functonterms Contrast Enhancement: Power Law Functon (γ 0.5) ometrc uthentcaton Lecture 3-8

31 Problem 2: Power law functonterms Contrast Enhancement: Power Law Functon (γ 3.0) ometrc uthentcaton Lecture 3-9

32 Problem 2: Power law functonterms Contrast Enhancement: Power Law Functon Look-up Table Transfer functon mplemented as a look-up table (LUT). Implemented n hardware or software. γ2 I O ometrc uthentcaton Lecture 3-20

33 Problem 2: Power law functon I [ ] O I γ O [ ] [ ]

34 Outlne Problems Problem : nswer the questons Problem 2: Power law functon Problem 3: Convoluton Problem 4: Nose reducton Problem 5: Flter operatons

35 Problem 3: Convoluton Please check the convoluton result n P3-33 and try to answer the queston n P3-34. Now there s an nput mage and a mask as below. Could you gve the convolved mage?

36 Problem 3: Convolutonterms Convoluton Conssts of flterng an mage usng a flter (mask). Mask s a small mage whose pxel values are called weghts. Weghts modfy relatonshps between pxels. Flter, mask or template Input mage,,2,3,4 C, 2, 2,2 2,3, C,2 C,3,2 2,4 C 2, 3, 3,2 3,3 2, C 2,2 C 2,2 3,4 2,3 C 4, 4,2 4,3 3, C 3,2 C 3,3 4,4 Convolved Image C ometrc uthentcaton Lecture 3-27

37 Problem 3: Convolutonterms Convoluton,,2,3,4 2, 2,2 2,3 2,4,,,2,2 3, 3,2 3,3 3,4 4, 4,2 4,3 4,4 2, 2, 2,2 2,2 C,,, +,2,2 + 2, 2, + 2,2 2,2 ometrc uthentcaton Lecture 3-28

38 Problem 3: Convolutonterms Convoluton,,2,,3,2,4 2, 2,2 2, 2,3,3, 2,2 2,4,4,2 3, 3,2 3,3 3,4 4, 4,2 4,3 4,4 2,3 2, 2,4 2,2 C,3,3, +,4,2 + 2,3 2, + 2,4 2,2 ometrc uthentcaton Lecture 3-29

39 Problem 3: Convolutonterms Convoluton,,2,3,4, 2,,2 2,2 2,3 2,4 2, 3, 2,2 3,2 3,3 3,4 4, 4,2 4,3 4,4 2,, 3, 2, 2,2,2 3,2 2,2 C 2, 2,, + 2,2,2 + 3, 2, + 3,2 2,2 ometrc uthentcaton Lecture 3-30

40 Problem 3: Convolutonterms ometrc uthentcaton Lecture 3-3 Mathematcal Notaton ,,, M k k N l l j l j k j l k C N M,, C, +,2,2 + 2, 2, + 2,2 2,2 ( ) 2 2, 2,,2, 2,2, 2 2, j j

41 Problem 3: Convolutonterms ometrc uthentcaton Lecture ,2 2,2 2, 2,,2,2,, 2,2,2,, 2 2,, 2 2,,,,,, C C j j j j j j M k k N l l j l j k j l k Summatons MN2 kl

42 Problem 3: Convolutonterms Convoluton Flter, mask or template Input mage Convolved Image C ometrc uthentcaton Lecture 3-33

43 Problem 3: Convolutonterms Convoluton Sze Image sze M N Mask sze M 2 N 2 Convoluton sze (M -M 2 +) (N - N 2 +) N N 2 N -N 2 + Typcal Mask szes 3 3, 5 5, 7 7, 9 9, What s the convolved mage sze for a mage and 7 7 mask? ometrc uthentcaton Lecture 3-34

44 Problem 3: Convoluton The convolved mage sze for a mage and a 7 7 mask s

45 Problem 3: Convoluton Mask Input mage

46 Problem 3: Convoluton Output mage

47 Outlne Problems Problem : nswer the questons Problem 2: Power law functon Problem 3: Convoluton Problem 4: Nose reducton Problem 5: Flter operatons

48 Problem 4: Nose reducton There are two methods of nose reducton: low pass flter and medan flter (see P3: 37-46). Please gve the nose reducton results of the nput mage n Q3 by usng the two methods accordng to the condtons: a) the mask of low pass flter s 9, and b) the mask of medan flter s

49 Problem 4: Nose reductonterms Nose Reducton Nose vares above and below uncorrupted mage. ometrc uthentcaton Lecture 3-37

50 Problem 4: Nose reductonterms Nose Reducton-st prncples How do we reduce nose? Consder a unform -d mage and add nose. Focus on a pxel neghbourhood. Central pxel has been ncreased and neghbourng pxels have decreased C ometrc uthentcaton Lecture 3-38

51 Problem 4: Nose reductonterms Nose Reducton-st prncples veragng smoothes the nose fluctuatons. Consder the next pxel + Repeat for remander of pxels C C + ometrc uthentcaton Lecture 3-39

52 Problem 4: Nose reductonterms ometrc uthentcaton Lecture 3-40 Nose Reducton- Neghborhood Operatons ll pxels can be averaged by convolvng -d mage wth mask to gve enhanced mage C. Weghts of must equal one when added together. [ ] [ ] C C C 9 C Extend to two dmensons.

53 Problem 4: Nose reductonterms Nose Reducton Technque reles on hgh frequency nose fluctuatons beng blocked by flter. Hence, low-pass flter. Fne detal n mage may also be smoothed. alance between keepng mage fne detal and reducng nose. Example: Saturn mage coarse detal oat mage contans fne detal Nose reduced but fne detal also smoothed ometrc uthentcaton Lecture 3-4

54 Problem 4: Nose reductonterms Nose Reducton Consder a unform -d mage wth a step functon. Step functon corresponds to fne mage detal such as an edge. Low-pass flter blurs the edge ometrc uthentcaton Lecture 3-42

55 Problem 4: Nose reductonterms Nose Reducton-st prncples How do we reduce nose wthout averagng? Consder a unform -d mage and add nose. Focus on a pxel neghbourhood. Non-lnear operator? Medan flter! C ometrc uthentcaton Lecture 3-43

56 Problem 4: Nose reductonterms ometrc uthentcaton Lecture 3-44 Nose Reducton- Neghborhood Operatons ll pxels can be replaced by neghbourhood medan by convolvng -d mage wth medan flter to gve enhanced mage C. Extend to two dmensons. [ ] { } [ ] { } ,, medan,, medan + + C C C { },j C j l j k j N l l j M k k l k for all medan,,, :, :,

57 Problem 4: Nose reductonterms Nose reducton Orgnal Low-pass Medan ometrc uthentcaton Lecture 3-45

58 Problem 4: Nose reductonterms Low-pass Nose reducton Medan Low-pass: fne detal smoothed by averagng Medan: fne detal passed by flter ometrc uthentcaton Lecture 3-46

59 Problem 4: Nose reducton Input mage Low pass flter mask 9 Result a)

60 Problem 4: Nose reducton Input mage Medan flter mask Result b)

61 Outlne Problems Problem : nswer the questons Problem 2: Power law functon Problem 3: Convoluton Problem 4: Nose reducton Problem 5: Flter operatons

62 Problem 5: Flter operatons In P3: there are some examples of flter operatons. Please pont out the dfference of Low-pass flters, Hgh-pass flters and Edge enhancement flters. Notce that the 0 -Sum mask for Edge enhancement flters and -Sum for others.

63 Problem 5: Flter operatons Flter Operatons Low-Pass Flter Class: Image Enhancement/Restoraton Implementaton: Pxel group process and smooth an mage /9 /0 /6 ometrc uthentcaton Lecture 3-47

64 Problem 5: Flter operatons Flter Operatons 2 Hgh-Pass Flter Implementaton: Pxel group process and sharpen an mage Sobel Edge Enhancement Implementaton: Edge extracton Vertcal mask Horzontal mask ometrc uthentcaton Lecture 3-48

65 Problem 5: Flter operatons Flter Operatons 4 Shft and Dfference Edge Enhancement Implementaton: Vertcal, Horzontal and Dagonal Edge extracton Vertcal Horzontal Dagonal 5 Laplacan Edge Enhancement Implementaton: ll Edge extracton ometrc uthentcaton Lecture 3-49

66 Problem 5: Flter operatons Search: Edge-based lur Kernel Estmaton Usng Patch Prors. ICCP 203

67 Problems ny questons?